0.08/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.12 % Command : run_Leo-III %s %d 0.11/0.32 % Computer : n025.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 07:53:41 EDT 2022 0.11/0.32 % CPUTime : 0.87/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 4.86/2.07 % [INFO] Parsing done (1143ms). 4.86/2.09 % [INFO] Running in sequential loop mode. 5.36/2.42 % [INFO] eprover registered as external prover. 5.36/2.42 % [INFO] cvc4 registered as external prover. 5.36/2.43 % [INFO] Scanning for conjecture ... 7.94/3.11 % [INFO] Found a conjecture and 9743 axioms. Running axiom selection ... 9.27/3.54 % [INFO] Axiom selection finished. Selected 518 axioms (removed 9225 axioms). 10.12/3.80 % [INFO] Problem is higher-order (TPTP THF). 10.12/3.83 % [INFO] Type checking passed. 10.12/3.84 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 38.60/11.34 % External prover 'cvc4' found a proof! 38.60/11.34 % [INFO] Killing All external provers ... 38.60/11.34 % Time passed: 10903ms (effective reasoning time: 9251ms) 38.60/11.34 % Solved by strategy 38.60/11.35 % Axioms used in derivation (518): fact_8076_dvd__mult2, fact_9253_top__assn__def, fact_1650_dual__order_Oirrefl, fact_2597_sup__assn__def, fact_1166_order__refl, fact_1674_order_Ostrict__implies__not__eq, fact_1302_dual__order_Oeq__iff, fact_499_Int__commute, fact_1185_Int__mono, fact_1151_boolean__algebra_Oconj__zero__left, fact_1176_Int__subset__iff, fact_791_sup_OcoboundedI2, fact_2349_verit__comp__simplify1_I2_J, fact_415_inf__assoc, fact_1849_Collect__disj__eq, fact_1400_boolean__algebra__cancel_Osup2, fact_1437_boolean__algebra_Odisj__conj__distrib, fact_2864_entails__def, fact_2557_option_Odistinct_I1_J, fact_2286_eq__imp__le, fact_8081_dvd__mult__left, fact_572_inf_OcoboundedI2, fact_724_le__infI1, fact_2869_ent__disjE, fact_388_equals0D, fact_2374_pinf_I5_J, fact_1486_disjoint__mono, fact_2287_le__antisym, fact_1688_order__less__asym, fact_2252_subset__emptyI, fact_2218_memb__imp__not__empty, fact_3604_left__right__inverse__power, fact_2444_pure__assn__eq__conv, fact_100_Int__Un__eq_I3_J, fact_927_sup__least, fact_1312_dual__order_Otrans, fact_2324_complete__interval, fact_17_prod_Oinject, fact_539_Un__assoc, fact_42_prod__induct3, fact_2242_nat__descend__induct, fact_478_inf__sup__aci_I5_J, fact_895_sup__unique, fact_580_inf_OcoboundedI1, fact_1322_Orderings_Oorder__eq__iff, fact_2865_entailsI, fact_2566_split__option__ex, fact_1929_order__less__imp__le, fact_1800_Int__def, fact_2344_verit__la__disequality, fact_555_UnI2, fact_90_assn__times__comm, fact_1911_order__le__less__trans, fact_35_mod__star__conv, fact_935_sup__mono, fact_1027_disjoint__iff, fact_2882_ent__wandI, fact_2871_ent__disjI2, fact_983_le__supI, fact_967_sup__ge2, fact_2872_ent__disjI1_H, fact_1955_dual__order_Ostrict__implies__order, fact_2600_successE, fact_266_mod__or__dist, fact_2281_nat__less__induct, fact_267_star__false__left, fact_660_inf__absorb1, fact_1621_order_Oasym, fact_2470_in__range_Osimps, fact_1194_Int__absorb1, fact_1157_times__assn__raw_Osimps, fact_1633_less__induct, fact_943_sup_Omono, fact_2535_Rep__assn__inverse, fact_53_Pair__inject, fact_453_sup_Oleft__commute, fact_1248_subset__Un__eq, fact_9229_merge__true__star, fact_1781_subset__Collect__conv, fact_2509_hoare__triple__success, fact_604_inf_Ocobounded2, fact_296_le__sup__iff, fact_2023_order_Oorder__iff__strict, fact_513_IntD1, fact_887_sup_Oabsorb1, fact_620_inf_Oorder__iff, fact_1218_Un__least, fact_1268_order__class_Oorder__eq__iff, fact_2398_minf_I5_J, fact_360_sup__bot__right, fact_277_le__inf__iff, fact_463_sup_Ocommute, fact_1153_EX, fact_34_hoare__triple__preI, fact_1072_distrib__imp2, fact_1250_relH__subset, fact_430_inf__sup__aci_I2_J, fact_1395_boolean__algebra__cancel_Osup1, fact_4835_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff, fact_503_Int__assoc, fact_1516_in__mono, fact_1351_linorder__linear, fact_1527_subset__eq, fact_458_sup__commute, fact_2486_wand__raw_Osimps, fact_2859_ent__false__iff, fact_2445_merge__pure__star, fact_2583_Abs__assn__eqI_I1_J, fact_1255_Un__Int__assoc__eq, fact_1504_RH1, fact_2_M2, fact_115_Un__Int__eq_I4_J, fact_1014_disjoint__iff__not__equal, fact_373_star__or__dist1, fact_48_prod__cases3, fact_2761_mult_Oassoc, fact_2295_prop__restrict, fact_2053_nless__le, fact_1317_antisym, fact_195_inf__left__idem, fact_700_inf_OorderI, fact_311_inf__bot__left, fact_2394_minf_I4_J, fact_2244_le__neq__implies__less, fact_2855_ent__pure__post__iff, fact_807_sup_Oabsorb__iff2, fact_23_mod__starD, fact_772_inf__sup__ord_I1_J, fact_951_le__supI2, fact_2386_minf_I2_J, fact_12__092_060open_062relH_Aas2_Ah_Ah_H_092_060close_062, fact_1145_boolean__algebra_Oconj__zero__right, fact_2229_hoare__triple__def, fact_483_inf__sup__aci_I6_J, fact_871_sup__absorb1, fact_8__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_A_K_AR_092_060close_062, fact_823_sup_Ocobounded2, fact_393_emptyE, fact_1905_order__less__le__trans, fact_8096_dvd__mult__right, fact_2461_relH__refl, fact_3106_assn__one__left, fact_2867_ent__fwd, fact_2041_antisym__conv2, fact_628_inf__greatest, fact_588_inf_Oabsorb__iff2, fact_1228_Un__upper2, fact_596_inf_Oabsorb__iff1, fact_1064_inf__sup__distrib1, fact_1660_order_Ostrict__trans, fact_363_mod__h__bot__iff_I7_J, fact_325_sup__bot_Oneutr__eq__iff, fact_2358_pinf_I1_J, fact_166_empty__Collect__eq, fact_2447_pure__assn__eq__false__iff, fact_1973_dual__order_Ostrict__trans2, fact_740_le__infI, fact_2471_Heap__eqI, fact_183_empty__iff, fact_2231_hoare__tripleI, fact_1444_boolean__algebra_Oconj__disj__distrib2, fact_1094_Un__empty__left, fact_518_IntE, fact_269_inf_Obounded__iff, fact_1757_order__less__imp__triv, fact_1985_dual__order_Ostrict__iff__order, fact_1404_bot_Oextremum, fact_563_UnI1, fact_1967_dual__order_Ostrict__iff__not, fact_36_star__assnI, fact_2278_less__not__refl2, fact_29_relH__dist__union, fact_2572_combine__options__cases, fact_2033_less__le__not__le, fact_28_mod__h__bot__indep, fact_1683_linorder__neqE, fact_3471_bounded__Max__nat, fact_676_inf_Oabsorb1, fact_305_inf__bot__right, fact_1347_order__eq__refl, fact_353_bot__eq__sup__iff, fact_1702_order__less__trans, fact_210_inf_Oidem, fact_1697_order__less__asym_H, fact_144_inf__sup__absorb, fact_9230_assn__basic__inequalities_I5_J, fact_2246_le__eq__less__or__eq, fact_1213_Un__mono, fact_879_sup_Oabsorb2, fact_400_inf_Oleft__commute, fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062as1_Aas2_O_A_092_060lbrakk_062as_A_061_Aas1_A_092_060union_062_Aas2_059_Aas1_A_092_060inter_062_Aas2_A_061_A_123_125_059_A_Ih_M_Aas1_J_A_092_060Turnstile_062_AP_059_A_Ih_M_Aas2_J_A_092_060Turnstile_062_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_1087_Un__empty__right, fact_2450_in__range__empty, fact_1382_boolean__algebra__cancel_Oinf1, fact_959_le__supI1, fact_2005_order_Ostrict__trans2, fact_2532_not__Some__eq, fact_2063_leD, fact_105_Int__Un__eq_I2_J, fact_2288_nat__le__linear, fact_332_sup__bot_Oleft__neutral, fact_855_sup_OboundedE, fact_383_equals0I, fact_1048_sup__inf__distrib1, fact_1917_order__neq__le__trans, fact_2922_mult_Oright__neutral, fact_435_inf__sup__aci_I3_J, fact_497_Int__left__absorb, fact_223_sup__left__idem, fact_1949_order__le__less, fact_1807_Int__Collect, fact_2875_ent__disjI2__direct, fact_1534_subset__iff, fact_410_inf_Ocommute, fact_1979_dual__order_Ostrict__trans1, fact_1727_order__less__irrefl, fact_975_sup__ge1, fact_2310_minf_I6_J, fact_1610_gt__ex, fact_218_sup_Oright__idem, fact_4833_boolean__algebra__class_Oboolean__algebra_Odouble__compl, fact_110_Int__Un__eq_I1_J, fact_2951_assn__basic__inequalities_I3_J, fact_27__092_060open_062as_A_061_Aas1_A_092_060union_062_Aas2_092_060close_062, fact_1380_order__antisym__conv, fact_9252_mod__star__trueE, fact_1233_Un__absorb1, fact_531_Un__commute, fact_1293_order__trans, fact_2282_infinite__descent, fact_1115_Int__Un__distrib, fact_1414_bot_Oextremum__uniqueI, fact_2618_success__def, fact_1056_inf__sup__distrib2, fact_1664_not__less__iff__gr__or__eq, fact_2458_models__in__range, fact_1259_nle__le, fact_1467__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062r_Ah_H_At_O_A_092_060lbrakk_062execute_Ac_Ah_A_061_ASome_A_Ir_M_Ah_H_M_At_J_059_A_Ih_H_M_Anew__addrs_Ah_Aas1_Ah_H_J_A_092_060Turnstile_062_AQ_Ar_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_Ah_Ah_H_059_Alim_Ah_A_092_060le_062_Alim_Ah_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_1278_ord__le__eq__trans, fact_2289_Nat_Oex__has__greatest__nat, fact_173_Collect__empty__eq, fact_692_inf__unique, fact_2225_inter__eq__subsetI, fact_527_Un__left__absorb, fact_228_sup_Oleft__idem, fact_125_Un__Int__eq_I2_J, fact_1154_times__assn__raw_Oelims_I3_J, fact_2047_antisym__conv1, fact_3057_comm__monoid__mult__class_Omult__1, fact_178_all__not__in__conv, fact_1859_linorder__le__less__linear, fact_2527_conj__subset__def, fact_1626_ord__eq__less__trans, fact_2862_ent__iffI, fact_1451_boolean__algebra_Odisj__conj__distrib2, fact_1655_linorder__less__wlog, fact_468_sup__assoc, fact_847_sup_OboundedI, fact_9235_mod__true, fact_2432_mod__h__bot__iff_I1_J, fact_130_Un__Int__eq_I1_J, fact_88_one__assn__raw_Ocases, fact_243_Int__iff, fact_9387_mod__star__trueE_H, fact_732_inf__mono, fact_2766_ab__semigroup__mult__class_Omult_Ocommute, fact_1761_linorder__less__linear, fact_5339_uminus__assn__def, fact_2584_Abs__assn__eqI_I2_J, fact_2362_pinf_I2_J, fact_1679_dual__order_Ostrict__implies__not__eq, fact_543_ball__Un, fact_8066_dvd__def, fact_2883_ent__mp, fact_1468_option_Oinject, fact_2314_pinf_I8_J, fact_95_Int__Un__eq_I4_J, fact_2870_ent__disjI1, fact_58_prod__cases, fact_1430_boolean__algebra_Oconj__disj__distrib, fact_2284_le__refl, fact_2515_subset__Collect__iff, fact_1174_empty__subsetI, fact_999_inf__sup__ord_I3_J, fact_1223_Un__upper1, fact_1307_dual__order_Oantisym, fact_2378_pinf_I7_J, fact_547_bex__Un, fact_3012_ent__pure__pre__iff__sng, fact_2201_ord__eq__le__eq__trans, fact_2874_ent__disjI1__direct, fact_2613_not__Some__eq2, fact_2370_pinf_I4_J, fact_26__092_060open_062lim_Ah_A_092_060le_062_Alim_Ah_H_092_060close_062, fact_644_inf_OboundedE, fact_1022_Int__empty__left, fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062, fact_1105_Int__Un__distrib2, fact_159_sup__bot__left, fact_919_le__iff__sup, fact_799_sup_OcoboundedI1, fact_87_old_Oprod_Oexhaust, fact_1645_dual__order_Oasym, fact_2504_times__assn__def, fact_205_inf__idem, fact_2276_nat__neq__iff, fact_1007_inf__sup__ord_I4_J, fact_2277_less__not__refl, fact_288_sup_Obounded__iff, fact_8056_dvdE, fact_748_le__infE, fact_2484_wand__raw_Oelims_I2_J, fact_32_relH__trans, fact_1100_Un__Int__distrib2, fact_1297_linorder__wlog, fact_31_relH__sym, fact_2280_less__irrefl__nat, fact_2771_ab__semigroup__mult__class_Omult_Oleft__commute, fact_8086_dvd__triv__left, fact_2569_split__option__all, fact_346_sup__eq__bot__iff, fact_2452_in__range__dist__union, fact_3062_mult_Ocomm__neutral, fact_24_mod__starE, fact_3422_mod__emp__simp, fact_9231_assn__basic__inequalities_I1_J, fact_420_inf_Oassoc, fact_2443_wand__assnI, fact_1669_dual__order_Ostrict__trans, fact_1991_dual__order_Oorder__iff__strict, fact_265_UnCI, fact_523_Un__left__commute, fact_2529_not__None__eq, fact_1511__092_060open_062as2_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062, fact_405_inf__commute, fact_612_inf_Ocobounded1, fact_1831_Un__def, fact_10_Rep__assn__inject, fact_2027_not__le__imp__less, fact_2451_mod__pure__star__dist, fact_9257_mod__h__bot__iff_I2_J, fact_2285_le__trans, fact_2560_option_OdiscI, fact_69_mem__Collect__eq, fact_1197_Int__absorb2, fact_2858_ent__pure__pre__iff, fact_2563_option_Oexhaust, fact_2522_subset__CollectI, fact_372_mod__false, fact_1238_Un__absorb2, fact_1200_Int__greatest, fact_839_sup_Oorder__iff, fact_8101_dvd__triv__right, fact_1161_dual__order_Orefl, fact_378_ex__in__conv, fact_668_inf_Oabsorb2, fact_8091_mult__dvd__mono, fact_903_sup_OorderI, fact_2873_ent__disjI2_H, fact_1263_le__cases3, fact_22_old_Oprod_Oinject, fact_1207_Int__Collect__mono, fact_911_sup_OorderE, fact_9386_mod__emp, fact_2248_nat__less__le, fact_25_assms, fact_425_inf__sup__aci_I1_J, fact_374_star__or__dist2, fact_11_mod__h__bot__iff_I5_J, fact_1375_linorder__le__cases, fact_652_inf__absorb2, fact_1587_Collect__mono__iff, fact_1820_Collect__conj__eq, fact_2017_order_Ostrict__iff__order, fact_2402_minf_I7_J, fact_63_surj__pair, fact_2247_less__imp__le__nat, fact_863_sup__absorb2, fact_33_mod__relH, fact_1170_subset__empty, fact_1557_Collect__subset, fact_395_inf__left__commute, fact_2485_wand__raw_Oelims_I1_J, fact_2878_ent__false, fact_1855_order__le__imp__less__or__eq, fact_0_DJ, fact_3553_power__commuting__commutes, fact_2243_less__mono__imp__le__mono, fact_493_inf__sup__aci_I8_J, fact_1631_ord__less__eq__trans, fact_1182_Un__subset__iff, fact_152_sup__inf__absorb, fact_1540_Collect__mono, fact_2459_relH__in__rangeI_I2_J, fact_8071_dvd__mult, fact_318_sup__bot_Oright__neutral, fact_1636_antisym__conv3, fact_2302_Collect__restrict, fact_185_inf__right__idem, fact_2223_set__notEmptyE, fact_257_Un__iff, fact_1776_order__less__imp__not__less, fact_1943_order__less__le, fact_2466_effect__def, fact_1409_bot_Oextremum__unique, fact_2390_minf_I3_J, fact_501_Int__absorb, fact_1766_order__less__imp__not__eq, fact_2283_linorder__neqE__nat, fact_3135_lambda__one, fact_1136_distrib__inf__le, fact_2322_verit__comp__simplify1_I3_J, fact_2927_mult__1, fact_2354_verit__comp__simplify1_I1_J, fact_2245_less__or__eq__imp__le, fact_9242_ent__true, fact_2233_hoare__tripleE, fact_2464_effectI, fact_2462_in__range__subset, fact_2446_merge__pure__or, fact_7_MDL, fact_1018_Int__empty__right, fact_81_Collect__cong, fact_9251_mod__star__trueI, fact_1156_times__assn__raw_Oelims_I1_J, fact_1616_less__imp__neq, fact_1126_distrib__sup__le, fact_1961_order_Ostrict__implies__order, fact_1110_Un__Int__distrib, fact_495_Int__left__commute, fact_1491_disjointI, fact_2494_wand__assn__def, fact_89_assn__times__assoc, fact_6_M1, fact_2306_minf_I8_J, fact_4882_mod__not__dist, fact_780_inf__sup__ord_I2_J, fact_9385_mod__pure, fact_2366_pinf_I3_J, fact_1040_sup__inf__distrib2, fact_2468_in__range_Oelims_I2_J, fact_190_inf_Oright__idem, fact_1923_order__le__neq__trans, fact_3563_power__commutes, fact_571_UnE, fact_2382_minf_I1_J, fact_815_sup_Oabsorb__iff1, fact_2889_ent__pure__post__iff__sng, fact_268_star__false__right, fact_120_Un__Int__eq_I3_J, fact_2318_pinf_I6_J, fact_2950_pure__assn__eq__emp__iff, fact_1933_linorder__not__less, fact_1155_times__assn__raw_Oelims_I2_J, fact_488_inf__sup__aci_I7_J, fact_2469_in__range_Oelims_I1_J, fact_535_Un__absorb, fact_1521_subsetD, fact_508_IntD2, fact_1273_ord__eq__le__trans, fact_3_DJN, fact_1510__092_060open_062relH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_Ah_Ah_H_092_060close_062, fact_76_Collect__mem__eq, fact_708_inf_OorderE, fact_233_sup__idem, fact_1501_subsetI, fact_8061_dvdI, fact_684_le__iff__inf, fact_1288_order_Otrans, fact_1512__092_060open_062_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062, fact_2197_new__addrs__def, fact_1283_order__antisym, fact_2868_ent__star__mono, fact_1652_exists__least__iff, fact_1771_order__less__imp__not__eq2, fact_448_sup__left__commute, fact_1080_distrib__imp1, fact_3558_power__mult__distrib, fact_1032_Int__emptyI, fact_5_new__addr__refl, fact_2279_less__not__refl3, fact_136_Un__empty, fact_1243_subset__UnE, fact_2483_wand__raw_Oelims_I3_J, fact_2861_ent__refl, fact_2011_order_Ostrict__trans1, fact_440_inf__sup__aci_I4_J, fact_1692_linorder__neq__iff, fact_2460_relH__in__rangeI_I1_J, fact_2619_successI, fact_248_IntI, fact_756_inf__le2, fact_1999_order_Ostrict__iff__not, fact_2433_hoare__triple__effect, fact_1422_boolean__algebra_Odisj__zero__right, fact_764_inf__le1, fact_200_inf_Oleft__idem, fact_473_sup_Oassoc, fact_2866_entailsD, fact_1752_order__less__not__sym, fact_2057_leI, fact_339_sup__bot_Oeq__neutr__iff, fact_1937_linorder__not__le, fact_1191_Int__lower2, fact_991_le__supE, fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062, fact_716_le__infI2, fact_2860_ent__trans, fact_1850_exists__leI, fact_636_inf_OboundedI, fact_1120_Un__Int__crazy, fact_831_sup_Ocobounded1, fact_1188_Int__lower1, fact_1640_linorder__cases, fact_2636_Heap__cases, fact_238_sup_Oidem, fact_1387_boolean__algebra__cancel_Oinf2, fact_2467_in__range_Oelims_I3_J 38.60/11.35 % No. of inferences in proof: 1040 38.60/11.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10903 ms resp. 9251 ms w/o parsing 39.62/11.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.62/11.62 thf(option2860828798490689354et_nat_type, type, option2860828798490689354et_nat: $tType). 39.62/11.62 thf(set_Pr8536935166611901872et_nat_type, type, set_Pr8536935166611901872et_nat: $tType). 39.62/11.62 thf(produc4193628355235574503at_nat_type, type, produc4193628355235574503at_nat: $tType). 39.62/11.62 thf(produc2732055786443039994et_nat_type, type, produc2732055786443039994et_nat: $tType). 39.62/11.62 thf(produc1319942482725812455at_nat_type, type, produc1319942482725812455at_nat: $tType). 39.62/11.62 thf(produc989692990947075319atural_type, type, produc989692990947075319atural: $tType). 39.62/11.62 thf(produc1908205239877642774nteger_type, type, produc1908205239877642774nteger: $tType). 39.62/11.62 thf(option7541221861074943443nt_int_type, type, option7541221861074943443nt_int: $tType). 39.62/11.62 thf(set_Pr9222295170931077689nt_int_type, type, set_Pr9222295170931077689nt_int: $tType). 39.62/11.62 thf(produc2285326912895808259nt_int_type, type, produc2285326912895808259nt_int: $tType). 39.62/11.62 thf(option5190343406534369742et_nat_type, type, option5190343406534369742et_nat: $tType). 39.62/11.62 thf(set_Pr3286484037609594932et_nat_type, type, set_Pr3286484037609594932et_nat: $tType). 39.62/11.62 thf(produc3925858234332021118et_nat_type, type, produc3925858234332021118et_nat: $tType). 39.62/11.62 thf(produc8731074985263844745atural_type, type, produc8731074985263844745atural: $tType). 39.62/11.62 thf(produc8763457246119570046nteger_type, type, produc8763457246119570046nteger: $tType). 39.62/11.62 thf(produc6576344331059438605e_term_type, type, produc6576344331059438605e_term: $tType). 39.62/11.62 thf(option4256020574406277085nt_int_type, type, option4256020574406277085nt_int: $tType). 39.62/11.62 thf(option2498585697089621389at_nat_type, type, option2498585697089621389at_nat: $tType). 39.62/11.62 thf(set_Pr1872883991513573699nt_int_type, type, set_Pr1872883991513573699nt_int: $tType). 39.62/11.62 thf(produc3911288613690379145it_nat_type, type, produc3911288613690379145it_nat: $tType). 39.62/11.62 thf(option1583680563626158861at_nat_type, type, option1583680563626158861at_nat: $tType). 39.62/11.62 thf(produc7773217078559923341nt_int_type, type, produc7773217078559923341nt_int: $tType). 39.62/11.62 thf(set_Pr8551490117392284871at_nat_type, type, set_Pr8551490117392284871at_nat: $tType). 39.62/11.62 thf(produc6756470014200349799atural_type, type, produc6756470014200349799atural: $tType). 39.62/11.62 thf(produc4453839368661128058it_nat_type, type, produc4453839368661128058it_nat: $tType). 39.62/11.62 thf(set_op239864471688321678it_nat_type, type, set_op239864471688321678it_nat: $tType). 39.62/11.62 thf(produc4166570645942440679at_nat_type, type, produc4166570645942440679at_nat: $tType). 39.62/11.62 thf(set_Pr4329608150637261639at_nat_type, type, set_Pr4329608150637261639at_nat: $tType). 39.62/11.62 thf(produc4471711990508489141at_nat_type, type, produc4471711990508489141at_nat: $tType). 39.62/11.62 thf(option2158460348403737357at_nat_type, type, option2158460348403737357at_nat: $tType). 39.62/11.62 thf(option8956607266484857688it_nat_type, type, option8956607266484857688it_nat: $tType). 39.62/11.62 thf(set_op4617111635268443007it_nat_type, type, set_op4617111635268443007it_nat: $tType). 39.62/11.62 thf(produc3843707927480180839at_nat_type, type, produc3843707927480180839at_nat: $tType). 39.62/11.62 thf(set_Pr1354866905816374718it_nat_type, type, set_Pr1354866905816374718it_nat: $tType). 39.62/11.62 thf(set_Pr457366540195662369at_nat_type, type, set_Pr457366540195662369at_nat: $tType). 39.62/11.62 thf(option3562590408128118217it_nat_type, type, option3562590408128118217it_nat: $tType). 39.62/11.62 thf(set_Pr8693737435421807431at_nat_type, type, set_Pr8693737435421807431at_nat: $tType). 39.62/11.62 thf(produc8664842809031399944it_nat_type, type, produc8664842809031399944it_nat: $tType). 39.62/11.62 thf(produc732395585841259969at_nat_type, type, produc732395585841259969at_nat: $tType). 39.62/11.62 thf(list_P6935614879863011209it_nat_type, type, list_P6935614879863011209it_nat: $tType). 39.62/11.62 thf(set_Pr1932065953672099015od_o_o_type, type, set_Pr1932065953672099015od_o_o: $tType). 39.62/11.62 thf(set_Pr7098220151150636591it_nat_type, type, set_Pr7098220151150636591it_nat: $tType). 39.62/11.62 thf(produc6197004810343482825et_nat_type, type, produc6197004810343482825et_nat: $tType). 39.62/11.62 thf(produc5835291356934675326atural_type, type, produc5835291356934675326atural: $tType). 39.62/11.62 thf(produc859450856879609959at_nat_type, type, produc859450856879609959at_nat: $tType). 39.62/11.62 thf(option936205604648967762et_nat_type, type, option936205604648967762et_nat: $tType). 39.62/11.62 thf(produc2934264451710624999od_o_o_type, type, produc2934264451710624999od_o_o: $tType). 39.62/11.62 thf(produc3260487557148687353it_nat_type, type, produc3260487557148687353it_nat: $tType). 39.62/11.62 thf(set_Pr7577011563204128103nteger_type, type, set_Pr7577011563204128103nteger: $tType). 39.62/11.62 thf(produc4972180933644002618e_term_type, type, produc4972180933644002618e_term: $tType). 39.62/11.62 thf(produc6241069584506657477e_term_type, type, produc6241069584506657477e_term: $tType). 39.62/11.62 thf(option233860712434008220it_nat_type, type, option233860712434008220it_nat: $tType). 39.62/11.62 thf(produc6491284506569428743nteger_type, type, produc6491284506569428743nteger: $tType). 39.62/11.62 thf(list_P131111800688179804it_nat_type, type, list_P131111800688179804it_nat: $tType). 39.62/11.62 thf(produc3658429121746597890et_nat_type, type, produc3658429121746597890et_nat: $tType). 39.62/11.62 thf(produc8551481072490612790e_term_type, type, produc8551481072490612790e_term: $tType). 39.62/11.62 thf(set_Pr5488025237498180813et_nat_type, type, set_Pr5488025237498180813et_nat: $tType). 39.62/11.62 thf(set_Pr2522554150109002629et_int_type, type, set_Pr2522554150109002629et_int: $tType). 39.62/11.62 thf(option6357759511663192854e_term_type, type, option6357759511663192854e_term: $tType). 39.62/11.62 thf(produc6653097349344004940it_nat_type, type, produc6653097349344004940it_nat: $tType). 39.62/11.62 thf(produc7248412053542808358at_nat_type, type, produc7248412053542808358at_nat: $tType). 39.62/11.62 thf(set_Pr5094982260447487303t_unit_type, type, set_Pr5094982260447487303t_unit: $tType). 39.62/11.62 thf(set_mu2057375006010111271at_nat_type, type, set_mu2057375006010111271at_nat: $tType). 39.62/11.62 thf(option8963830502488799655at_nat_type, type, option8963830502488799655at_nat: $tType). 39.62/11.62 thf(set_se7855581050983116737at_nat_type, type, set_se7855581050983116737at_nat: $tType). 39.62/11.62 thf(produc7819656566062154093et_nat_type, type, produc7819656566062154093et_nat: $tType). 39.62/11.62 thf(produc2115011035271226405et_int_type, type, produc2115011035271226405et_int: $tType). 39.62/11.62 thf(produc7822875418678951345atural_type, type, produc7822875418678951345atural: $tType). 39.62/11.62 thf(produc8923325533196201883nteger_type, type, produc8923325533196201883nteger: $tType). 39.62/11.62 thf(multis2468970476368604999at_nat_type, type, multis2468970476368604999at_nat: $tType). 39.62/11.62 thf(option4624381673175914239nt_int_type, type, option4624381673175914239nt_int: $tType). 39.62/11.62 thf(set_He475150555083384525t_unit_type, type, set_He475150555083384525t_unit: $tType). 39.62/11.62 thf(list_P6011104703257516679at_nat_type, type, list_P6011104703257516679at_nat: $tType). 39.62/11.62 thf(list_P3521021558325789923at_int_type, type, list_P3521021558325789923at_int: $tType). 39.62/11.62 thf(list_P8198026277950538467nt_nat_type, type, list_P8198026277950538467nt_nat: $tType). 39.62/11.62 thf(list_P5707943133018811711nt_int_type, type, list_P5707943133018811711nt_int: $tType). 39.62/11.62 thf(set_Pr1261947904930325089at_nat_type, type, set_Pr1261947904930325089at_nat: $tType). 39.62/11.62 thf(set_Pr958786334691620121nt_int_type, type, set_Pr958786334691620121nt_int: $tType). 39.62/11.62 thf(list_P7333126701944960589_nat_o_type, type, list_P7333126701944960589_nat_o: $tType). 39.62/11.62 thf(list_P5087981734274514673_int_o_type, type, list_P5087981734274514673_int_o: $tType). 39.62/11.62 thf(list_P6285523579766656935_o_nat_type, type, list_P6285523579766656935_o_nat: $tType). 39.62/11.62 thf(list_P3795440434834930179_o_int_type, type, list_P3795440434834930179_o_int: $tType). 39.62/11.62 thf(set_set_list_nat_type, type, set_set_list_nat: $tType). 39.62/11.62 thf(produc6271795597528267376eger_o_type, type, produc6271795597528267376eger_o: $tType). 39.62/11.62 thf(set_set_set_nat_type, type, set_set_set_nat: $tType). 39.62/11.62 thf(set_set_Code_integer_type, type, set_set_Code_integer: $tType). 39.62/11.62 thf(heap_T5738788834812785303t_unit_type, type, heap_T5738788834812785303t_unit: $tType). 39.62/11.62 thf(heap_e7401611519738050253t_unit_type, type, heap_e7401611519738050253t_unit: $tType). 39.62/11.62 thf(product_prod_num_num_type, type, product_prod_num_num: $tType). 39.62/11.62 thf(product_prod_nat_num_type, type, product_prod_nat_num: $tType). 39.62/11.62 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 39.62/11.62 thf(product_prod_nat_int_type, type, product_prod_nat_int: $tType). 39.62/11.62 thf(product_prod_int_nat_type, type, product_prod_int_nat: $tType). 39.62/11.62 thf(product_prod_int_int_type, type, product_prod_int_int: $tType). 39.62/11.62 thf(list_P4002435161011370285od_o_o_type, type, list_P4002435161011370285od_o_o: $tType). 39.62/11.62 thf(set_Product_prod_o_o_type, type, set_Product_prod_o_o: $tType). 39.62/11.62 thf(set_option_num_type, type, set_option_num: $tType). 39.62/11.62 thf(option_set_nat_type, type, option_set_nat: $tType). 39.62/11.62 thf(option_set_int_type, type, option_set_int: $tType). 39.62/11.62 thf(filter_set_nat_type, type, filter_set_nat: $tType). 39.62/11.62 thf(option_Product_unit_type, type, option_Product_unit: $tType). 39.62/11.62 thf(set_list_nat_type, type, set_list_nat: $tType). 39.62/11.62 thf(product_prod_nat_o_type, type, product_prod_nat_o: $tType). 39.62/11.62 thf(product_prod_int_o_type, type, product_prod_int_o: $tType). 39.62/11.62 thf(product_prod_o_nat_type, type, product_prod_o_nat: $tType). 39.62/11.62 thf(product_prod_o_int_type, type, product_prod_o_int: $tType). 39.62/11.62 thf(set_set_nat_type, type, set_set_nat: $tType). 39.62/11.62 thf(set_set_int_type, type, set_set_int: $tType). 39.62/11.62 thf(set_Code_integer_type, type, set_Code_integer: $tType). 39.62/11.62 thf(option_assn_type, type, option_assn: $tType). 39.62/11.62 thf(set_Product_unit_type, type, set_Product_unit: $tType). 39.62/11.62 thf(option_set_o_type, type, option_set_o: $tType). 39.62/11.62 thf(heap_Time_Heap_a_type, type, heap_Time_Heap_a: $tType). 39.62/11.62 thf(set_list_o_type, type, set_list_o: $tType). 39.62/11.62 thf(product_prod_o_o_type, type, product_prod_o_o: $tType). 39.62/11.62 thf(set_assn_type, type, set_assn: $tType). 39.62/11.62 thf(option_rat_type, type, option_rat: $tType). 39.62/11.62 thf(option_num_type, type, option_num: $tType). 39.62/11.62 thf(option_nat_type, type, option_nat: $tType). 39.62/11.62 thf(option_int_type, type, option_int: $tType). 39.62/11.62 thf(list_char_type, type, list_char: $tType). 39.62/11.62 thf(filter_nat_type, type, filter_nat: $tType). 39.62/11.62 thf(list_rat_type, type, list_rat: $tType). 39.62/11.62 thf(list_num_type, type, list_num: $tType). 39.62/11.62 thf(list_nat_type, type, list_nat: $tType). 39.62/11.62 thf(list_int_type, type, list_int: $tType). 39.62/11.62 thf(set_rat_type, type, set_rat: $tType). 39.62/11.62 thf(set_num_type, type, set_num: $tType). 39.62/11.62 thf(set_nat_type, type, set_nat: $tType). 39.62/11.62 thf(set_int_type, type, set_int: $tType). 39.62/11.62 thf(code_natural_type, type, code_natural: $tType). 39.62/11.62 thf(code_integer_type, type, code_integer: $tType). 39.62/11.62 thf(product_unit_type, type, product_unit: $tType). 39.62/11.62 thf(list_a_type, type, list_a: $tType). 39.62/11.62 thf(list_o_type, type, list_o: $tType). 39.62/11.62 thf(assn_type, type, assn: $tType). 39.62/11.62 thf(set_o_type, type, set_o: $tType). 39.62/11.62 thf(rat_type, type, rat: $tType). 39.62/11.62 thf(num_type, type, num: $tType). 39.62/11.62 thf(nat_type, type, nat: $tType). 39.62/11.62 thf(int_type, type, int: $tType). 39.62/11.62 thf(a_type, type, a: $tType). 39.62/11.62 thf(abs_assn_type, type, abs_assn: ((produc3658429121746597890et_nat > $o) > assn)). 39.62/11.62 thf(rep_assn_type, type, rep_assn: (assn > (produc3658429121746597890et_nat > $o))). 39.62/11.62 thf(entails_type, type, entails: (assn > (assn > $o))). 39.62/11.62 thf(in_range_type, type, in_range: (produc3658429121746597890et_nat > $o)). 39.62/11.62 thf(pure_assn_type, type, pure_assn: ($o > assn)). 39.62/11.62 thf(relH_type, type, relH: (set_nat > (heap_e7401611519738050253t_unit > (heap_e7401611519738050253t_unit > $o)))). 39.62/11.62 thf(times_assn_raw_type, type, times_assn_raw: ((produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o)))). 39.62/11.62 thf(wand_assn_type, type, wand_assn: (assn > (assn > assn))). 39.62/11.62 thf(wand_raw_type, type, wand_raw: ((produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o)))). 39.62/11.62 thf(one_one_assn_type, type, one_one_assn: assn). 39.62/11.62 thf(times_times_assn_type, type, times_times_assn: (assn > (assn > assn))). 39.62/11.62 thf(uminus_uminus_assn_type, type, uminus_uminus_assn: (assn > assn)). 39.62/11.62 thf(lim_Product_unit_type, type, lim_Product_unit: (heap_e7401611519738050253t_unit > nat)). 39.62/11.62 thf(heap_Time_effect_a_type, type, heap_Time_effect_a: (heap_Time_Heap_a > (heap_e7401611519738050253t_unit > (heap_e7401611519738050253t_unit > (a > (nat > $o)))))). 39.62/11.62 thf(heap_Time_execute_a_type, type, heap_Time_execute_a: (heap_Time_Heap_a > (heap_e7401611519738050253t_unit > option3562590408128118217it_nat))). 39.62/11.62 thf(heap_Time_success_a_type, type, heap_Time_success_a: (heap_Time_Heap_a > (heap_e7401611519738050253t_unit > $o))). 39.62/11.62 thf(hoare_hoare_triple_a_type, type, hoare_hoare_triple_a: (assn > (heap_Time_Heap_a > ((a > assn) > $o)))). 39.62/11.62 thf(hoare_new_addrs_type, type, hoare_new_addrs: (heap_e7401611519738050253t_unit > (set_nat > (heap_e7401611519738050253t_unit > set_nat)))). 39.62/11.62 thf(inf_inf_set_nat_type, type, inf_inf_set_nat: (set_nat > (set_nat > set_nat))). 39.62/11.62 thf(sup_sup_assn_type, type, sup_sup_assn: (assn > (assn > assn))). 39.62/11.62 thf(sup_sup_set_nat_type, type, sup_sup_set_nat: (set_nat > (set_nat > set_nat))). 39.62/11.62 thf(none_P2651198173097904984it_nat_type, type, none_P2651198173097904984it_nat: option3562590408128118217it_nat). 39.62/11.62 thf(some_P7913643980934408916it_nat_type, type, some_P7913643980934408916it_nat: (produc3260487557148687353it_nat > option3562590408128118217it_nat)). 39.62/11.62 thf(bot_bot_assn_type, type, bot_bot_assn: assn). 39.62/11.62 thf(bot_bot_set_nat_type, type, bot_bot_set_nat: set_nat). 39.62/11.62 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 39.62/11.62 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 39.62/11.62 thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))). 39.62/11.62 thf(top_top_assn_type, type, top_top_assn: assn). 39.62/11.62 thf(power_power_assn_type, type, power_power_assn: (assn > (nat > assn))). 39.62/11.62 thf(produc584006145561248582it_nat_type, type, produc584006145561248582it_nat: (heap_e7401611519738050253t_unit > (nat > produc6653097349344004940it_nat))). 39.62/11.62 thf(produc7507926704131184380et_nat_type, type, produc7507926704131184380et_nat: (heap_e7401611519738050253t_unit > (set_nat > produc3658429121746597890et_nat))). 39.62/11.62 thf(produc9178034014595674355it_nat_type, type, produc9178034014595674355it_nat: (a > (produc6653097349344004940it_nat > produc3260487557148687353it_nat))). 39.62/11.62 thf(produc1824681642469235216et_nat_type, type, produc1824681642469235216et_nat: (produc3658429121746597890et_nat > heap_e7401611519738050253t_unit)). 39.62/11.62 thf(produc8586169260539613262et_nat_type, type, produc8586169260539613262et_nat: (produc3658429121746597890et_nat > set_nat)). 39.62/11.62 thf(dvd_dvd_assn_type, type, dvd_dvd_assn: (assn > (assn > $o))). 39.62/11.62 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 39.62/11.62 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 39.62/11.62 thf(p_type, type, p: assn). 39.62/11.62 thf(q_type, type, q: (a > assn)). 39.62/11.62 thf(r_type, type, r: assn). 39.62/11.62 thf(as1_type, type, as1: set_nat). 39.62/11.62 thf(as2_type, type, as2: set_nat). 39.62/11.62 thf(as_type, type, as: set_nat). 39.62/11.62 thf(c_type, type, c: heap_Time_Heap_a). 39.62/11.62 thf(h_type, type, h: heap_e7401611519738050253t_unit). 39.62/11.62 thf(h2_type, type, h2: heap_e7401611519738050253t_unit). 39.62/11.62 thf(r2_type, type, r2: a). 39.62/11.62 thf(t_type, type, t: nat). 39.62/11.62 thf(344,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:heap_e7401611519738050253t_unit,D:set_nat]: ((wand_raw @ A @ B @ (produc7507926704131184380et_nat @ C @ D)) = ((in_range @ (produc7507926704131184380et_nat @ C @ D)) & ! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((B @ (produc7507926704131184380et_nat @ E @ (sup_sup_set_nat @ D @ F))) <= ((in_range @ (produc7507926704131184380et_nat @ E @ D)) & (A @ (produc7507926704131184380et_nat @ E @ F)) & (relH @ D @ C @ E) & ((inf_inf_set_nat @ D @ F) = bot_bot_set_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2486_wand__raw_Osimps)). 39.62/11.62 thf(1665,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:heap_e7401611519738050253t_unit,D:set_nat]: ((wand_raw @ (A) @ (B) @ (produc7507926704131184380et_nat @ C @ D)) = ((in_range @ (produc7507926704131184380et_nat @ C @ D)) & ! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((B @ (produc7507926704131184380et_nat @ E @ (sup_sup_set_nat @ D @ F))) | ~ ((in_range @ (produc7507926704131184380et_nat @ E @ D)) & (A @ (produc7507926704131184380et_nat @ E @ F)) & (relH @ D @ C @ E) & ((inf_inf_set_nat @ D @ F) = bot_bot_set_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 39.62/11.62 thf(293,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1409_bot_Oextremum__unique)). 39.62/11.62 thf(1501,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 39.62/11.62 thf(239,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: (B = (sup_sup_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_sup_Oorder__iff)). 39.62/11.62 thf(1337,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: (B = (sup_sup_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 39.62/11.62 thf(281,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_inf__idem)). 39.62/11.62 thf(1469,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 39.62/11.62 thf(336,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_order__refl)). 39.62/11.62 thf(1633,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 39.62/11.62 thf(469,axiom,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (sup_sup_assn @ A @ B) @ C) = ((rep_assn @ B @ C) | (rep_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_mod__or__dist)). 39.62/11.62 thf(2072,plain,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (sup_sup_assn @ A @ B) @ C) = ((rep_assn @ B @ C) | (rep_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 39.62/11.62 thf(420,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_1297_linorder__wlog)). 39.62/11.62 thf(1899,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)],[420])). 39.62/11.62 thf(231,axiom,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = B) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1233_Un__absorb1)). 39.62/11.62 thf(1315,plain,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 39.62/11.62 thf(163,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_1967_dual__order_Ostrict__iff__not)). 39.62/11.62 thf(1083,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)],[163])). 39.62/11.62 thf(194,axiom,((! [A:assn]: (entails @ A @ top_top_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9242_ent__true)). 39.62/11.62 thf(1179,plain,((! [A:assn]: (entails @ A @ top_top_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 39.62/11.62 thf(496,axiom,(((hoare_new_addrs @ h2 @ as @ h) = (sup_sup_set_nat @ (hoare_new_addrs @ h2 @ as1 @ h) @ as2))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062)). 39.62/11.62 thf(2163,plain,(((hoare_new_addrs @ h2 @ as @ h) = (sup_sup_set_nat @ (hoare_new_addrs @ h2 @ as1 @ h) @ as2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 39.62/11.62 thf(107,axiom,((! [A:assn]: ((uminus_uminus_assn @ (uminus_uminus_assn @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4833_boolean__algebra__class_Oboolean__algebra_Odouble__compl)). 39.62/11.62 thf(892,plain,((! [A:assn]: ((uminus_uminus_assn @ (uminus_uminus_assn @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 39.62/11.62 thf(473,axiom,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ A @ B) => (in_range @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2458_models__in__range)). 39.62/11.62 thf(2094,plain,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ A @ B) => (in_range @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 39.62/11.62 thf(263,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_Int__empty__left)). 39.62/11.62 thf(1411,plain,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 39.62/11.62 thf(113,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_2244_le__neq__implies__less)). 39.62/11.62 thf(909,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)],[113])). 39.62/11.62 thf(147,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ B @ C)) = ((member_nat @ A @ B) | (member_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Un__iff)). 39.62/11.62 thf(1031,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ B @ C)) = ((member_nat @ A @ B) | (member_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 39.62/11.62 thf(431,axiom,((! [A:set_nat,B:set_nat]: ((A = (inf_inf_set_nat @ A @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_inf_OorderE)). 39.62/11.62 thf(1950,plain,((! [A:set_nat,B:set_nat]: ((A = (inf_inf_set_nat @ A @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 39.62/11.62 thf(310,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_1380_order__antisym__conv)). 39.62/11.62 thf(1549,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)],[310])). 39.62/11.62 thf(129,axiom,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) => (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_equals0I)). 39.62/11.62 thf(977,plain,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) => (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 39.62/11.62 thf(71,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2053_nless__le)). 39.62/11.62 thf(762,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 39.62/11.62 thf(477,axiom,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ (power_power_assn @ A @ C) @ B) = (times_times_assn @ B @ (power_power_assn @ A @ C))) <= ((times_times_assn @ A @ B) = (times_times_assn @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3553_power__commuting__commutes)). 39.62/11.62 thf(2104,plain,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ (power_power_assn @ A @ C) @ B) = (times_times_assn @ B @ (power_power_assn @ A @ C))) | ~ ((times_times_assn @ A @ B) = (times_times_assn @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 39.62/11.62 thf(52,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ F @ E))) => ((? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((D @ F) | (B @ F))) <= (ord_less_nat @ F @ E))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2386_minf_I2_J)). 39.62/11.62 thf(683,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ F @ E))) => (? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((D @ F) | (B @ F))) | ~ (ord_less_nat @ F @ E)) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 39.62/11.62 thf(414,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_inf_Oidem)). 39.62/11.62 thf(1882,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 39.62/11.62 thf(160,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2027_not__le__imp__less)). 39.62/11.62 thf(1068,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 39.62/11.62 thf(300,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_inf__bot__right)). 39.62/11.62 thf(1522,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 39.62/11.62 thf(316,axiom,((! [A:heap_e7401611519738050253t_unit,B:set_nat,C:assn,D:assn]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) => ((rep_assn @ (wand_assn @ C @ D) @ (produc7507926704131184380et_nat @ A @ B)) <= (! [E:heap_e7401611519738050253t_unit,F:set_nat]: (((((rep_assn @ C @ (produc7507926704131184380et_nat @ E @ F)) => (rep_assn @ D @ (produc7507926704131184380et_nat @ E @ (sup_sup_set_nat @ B @ F)))) <= (in_range @ (produc7507926704131184380et_nat @ E @ B))) <= (relH @ B @ A @ E)) <= ((inf_inf_set_nat @ B @ F) = bot_bot_set_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2443_wand__assnI)). 39.62/11.62 thf(1569,plain,((! [A:heap_e7401611519738050253t_unit,B:set_nat,C:assn,D:assn]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) => ((rep_assn @ (wand_assn @ C @ D) @ (produc7507926704131184380et_nat @ A @ B)) | ~ (! [E:heap_e7401611519738050253t_unit,F:set_nat]: (((rep_assn @ C @ (produc7507926704131184380et_nat @ E @ F)) => (rep_assn @ D @ (produc7507926704131184380et_nat @ E @ (sup_sup_set_nat @ B @ F)))) | ~ (in_range @ (produc7507926704131184380et_nat @ E @ B)) | ~ (relH @ B @ A @ E) | ~ ((inf_inf_set_nat @ B @ F) = bot_bot_set_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 39.62/11.62 thf(364,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_sup__absorb1)). 39.62/11.62 thf(1728,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 39.62/11.62 thf(100,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2247_less__imp__le__nat)). 39.62/11.62 thf(873,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 39.62/11.62 thf(304,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (in_range @ (produc7507926704131184380et_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2459_relH__in__rangeI_I2_J)). 39.62/11.62 thf(1533,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (in_range @ (produc7507926704131184380et_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 39.62/11.62 thf(26,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_eq_nat @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2047_antisym__conv1)). 39.62/11.62 thf(597,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_eq_nat @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 39.62/11.62 thf(270,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_1278_ord__le__eq__trans)). 39.62/11.62 thf(1437,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)],[270])). 39.62/11.62 thf(406,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_boolean__algebra_Oconj__zero__left)). 39.62/11.62 thf(1855,plain,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 39.62/11.62 thf(198,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ B) = (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_sup_Oright__idem)). 39.62/11.62 thf(1200,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ B) = (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 39.62/11.62 thf(480,axiom,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ top_top_assn) @ B) <= (rep_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9251_mod__star__trueI)). 39.62/11.62 thf(2114,plain,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ top_top_assn) @ B) | ~ (rep_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 39.62/11.62 thf(220,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E))))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2289_Nat_Oex__has__greatest__nat)). 39.62/11.62 thf(1269,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E))))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 39.62/11.62 thf(32,axiom,((! [A:option3562590408128118217it_nat]: ((A != none_P2651198173097904984it_nat) = (? [B:produc3260487557148687353it_nat]: (A = (some_P7913643980934408916it_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2529_not__None__eq)). 39.62/11.62 thf(614,plain,((! [A:option3562590408128118217it_nat]: ((~ (A = none_P2651198173097904984it_nat)) = (? [B:produc3260487557148687353it_nat]: (A = (some_P7913643980934408916it_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 39.62/11.62 thf(353,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_boolean__algebra_Oconj__zero__right)). 39.62/11.62 thf(1692,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 39.62/11.62 thf(50,axiom,((! [A:set_nat,B:(nat > $o),C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((B @ D) & (C @ D))))) = ((ord_less_eq_set_nat @ A @ (collect_nat @ C)) & (ord_less_eq_set_nat @ A @ (collect_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2527_conj__subset__def)). 39.62/11.62 thf(677,plain,((! [A:set_nat,B:(nat > $o),C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((B @ D) & (C @ D))))) = ((ord_less_eq_set_nat @ A @ (collect_nat @ (C))) & (ord_less_eq_set_nat @ A @ (collect_nat @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 39.62/11.62 thf(6,axiom,((! [A:set_nat,B:nat]: ((A = bot_bot_set_nat) => (~ (member_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_equals0D)). 39.62/11.62 thf(533,plain,((! [A:set_nat,B:nat]: ((A = bot_bot_set_nat) => (~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 39.62/11.62 thf(504,axiom,((! [A:assn,B:assn]: (dvd_dvd_assn @ A @ (times_times_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8086_dvd__triv__left)). 39.62/11.62 thf(2184,plain,((! [A:assn,B:assn]: (dvd_dvd_assn @ A @ (times_times_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 39.62/11.62 thf(121,axiom,((! [A:$o,B:assn]: ((entails @ (pure_assn @ A) @ B) = ((A) => (entails @ one_one_assn @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3012_ent__pure__pre__iff__sng)). 39.62/11.62 thf(945,plain,((! [A:$o,B:assn]: ((entails @ (pure_assn @ A) @ B) = ((A) => (entails @ one_one_assn @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 39.62/11.62 thf(159,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1626_ord__eq__less__trans)). 39.62/11.62 thf(1063,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 39.62/11.62 thf(460,axiom,(((times_times_assn @ top_top_assn @ top_top_assn) = top_top_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9229_merge__true__star)). 39.62/11.62 thf(2042,plain,(((times_times_assn @ top_top_assn @ top_top_assn) = top_top_assn)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 39.62/11.62 thf(448,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((~ (! [D:set_nat]: ((ord_less_eq_set_nat @ D @ B) => (! [E:set_nat]: ((ord_less_eq_set_nat @ E @ C) => (A != (sup_sup_set_nat @ D @ E))))))) <= (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1243_subset__UnE)). 39.62/11.62 thf(1999,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (~ (! [D:set_nat]: ((ord_less_eq_set_nat @ D @ B) => (! [E:set_nat]: ((ord_less_eq_set_nat @ E @ C) => (~ (A = (sup_sup_set_nat @ D @ E))))))) | ~ (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 39.62/11.62 thf(83,axiom,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ A @ B) = one_one_assn) => ((times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C)) = one_one_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3604_left__right__inverse__power)). 39.62/11.62 thf(797,plain,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ A @ B) = one_one_assn) => ((times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C)) = one_one_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 39.62/11.62 thf(7,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1776_order__less__imp__not__less)). 39.62/11.62 thf(538,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 39.62/11.62 thf(489,axiom,((ord_less_eq_nat @ (lim_Product_unit @ h2) @ (lim_Product_unit @ h))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__092_060open_062lim_Ah_A_092_060le_062_Alim_Ah_H_092_060close_062)). 39.62/11.62 thf(2146,plain,((ord_less_eq_nat @ (lim_Product_unit @ h2) @ (lim_Product_unit @ h))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 39.62/11.62 thf(295,axiom,((! [A:produc3658429121746597890et_nat]: ((rep_assn @ one_one_assn @ A) = ((produc8586169260539613262et_nat @ A) = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9386_mod__emp)). 39.62/11.62 thf(1507,plain,((! [A:produc3658429121746597890et_nat]: ((rep_assn @ one_one_assn @ A) = ((produc8586169260539613262et_nat @ A) = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 39.62/11.62 thf(115,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2017_order_Ostrict__iff__order)). 39.62/11.62 thf(930,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 39.62/11.62 thf(167,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2023_order_Oorder__iff__strict)). 39.62/11.62 thf(1095,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 39.62/11.62 thf(137,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mem__Collect__eq)). 39.62/11.62 thf(1001,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 39.62/11.62 thf(176,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((member_nat @ A @ B) & (member_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Int__iff)). 39.62/11.62 thf(1127,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((member_nat @ A @ B) & (member_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 39.62/11.62 thf(257,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_le__sup__iff)). 39.62/11.62 thf(1391,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 39.62/11.62 thf(77,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1534_subset__iff)). 39.62/11.62 thf(782,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 39.62/11.62 thf(454,axiom,((! [A:heap_Time_Heap_a,B:heap_Time_Heap_a]: ((! [C:heap_e7401611519738050253t_unit]: ((heap_Time_execute_a @ A @ C) = (heap_Time_execute_a @ B @ C))) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2471_Heap__eqI)). 39.62/11.62 thf(2020,plain,((! [A:heap_Time_Heap_a,B:heap_Time_Heap_a]: ((! [C:heap_e7401611519738050253t_unit]: ((heap_Time_execute_a @ A @ C) = (heap_Time_execute_a @ B @ C))) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 39.62/11.62 thf(128,axiom,((! [A:produc3260487557148687353it_nat]: (none_P2651198173097904984it_nat != (some_P7913643980934408916it_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2557_option_Odistinct_I1_J)). 39.62/11.62 thf(973,plain,((! [A:produc3260487557148687353it_nat]: ~ (none_P2651198173097904984it_nat = (some_P7913643980934408916it_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 39.62/11.62 thf(425,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_inf__sup__aci_I3_J)). 39.62/11.62 thf(1935,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 39.62/11.62 thf(248,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1223_Un__upper1)). 39.62/11.62 thf(1359,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 39.62/11.62 thf(325,axiom,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2344_verit__la__disequality)). 39.62/11.62 thf(1601,plain,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 39.62/11.62 thf(283,axiom,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_sup__bot_Oeq__neutr__iff)). 39.62/11.62 thf(1475,plain,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 39.62/11.62 thf(416,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_le__supI1)). 39.62/11.62 thf(1887,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 39.62/11.62 thf(370,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B) <= (ord_less_eq_set_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_sup__least)). 39.62/11.62 thf(1746,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B) | ~ (ord_less_eq_set_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 39.62/11.62 thf(109,axiom,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1855_order__le__imp__less__or__eq)). 39.62/11.62 thf(898,plain,((! [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 39.62/11.62 thf(17,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ (collect_nat @ C)) @ (inf_inf_set_nat @ B @ (collect_nat @ D))) <= (! [E:nat]: (((C @ E) => (D @ E)) <= (member_nat @ E @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1207_Int__Collect__mono)). 39.62/11.62 thf(565,plain,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ (collect_nat @ (C))) @ (inf_inf_set_nat @ B @ (collect_nat @ (D)))) | ~ (! [E:nat]: (((C @ E) => (D @ E)) | ~ (member_nat @ E @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 39.62/11.62 thf(251,axiom,((sup_sup_set_nat = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_Un__commute)). 39.62/11.62 thf(1366,plain,(((sup_sup_set_nat) = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 39.62/11.62 thf(486,axiom,((! [A:assn,B:assn]: ((~ (! [C:assn]: (B != (times_times_assn @ A @ C)))) <= (dvd_dvd_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8056_dvdE)). 39.62/11.62 thf(2136,plain,((! [A:assn,B:assn]: (~ (! [C:assn]: ~ (B = (times_times_assn @ A @ C))) | ~ (dvd_dvd_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 39.62/11.62 thf(356,axiom,((! [A:assn,B:heap_e7401611519738050253t_unit,C:set_nat,D:assn,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ B @ C)) => ((rep_assn @ D @ (produc7507926704131184380et_nat @ B @ E)) => (((inf_inf_set_nat @ C @ E) = bot_bot_set_nat) => (rep_assn @ (times_times_assn @ A @ D) @ (produc7507926704131184380et_nat @ B @ (sup_sup_set_nat @ C @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_star__assnI)). 39.62/11.62 thf(1703,plain,((! [A:assn,B:heap_e7401611519738050253t_unit,C:set_nat,D:assn,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ B @ C)) => ((rep_assn @ D @ (produc7507926704131184380et_nat @ B @ E)) => (((inf_inf_set_nat @ C @ E) = bot_bot_set_nat) => (rep_assn @ (times_times_assn @ A @ D) @ (produc7507926704131184380et_nat @ B @ (sup_sup_set_nat @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 39.62/11.62 thf(334,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_Int__subset__iff)). 39.62/11.62 thf(1628,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 39.62/11.62 thf(225,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat,D:$o]: (((wand_raw @ A @ B @ C) = D) => (~ (! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((C = (produc7507926704131184380et_nat @ E @ F)) => (D = (~ ((in_range @ (produc7507926704131184380et_nat @ E @ F)) & ! [G:heap_e7401611519738050253t_unit,H:set_nat]: ((B @ (produc7507926704131184380et_nat @ G @ (sup_sup_set_nat @ F @ H))) <= (((inf_inf_set_nat @ F @ H) = bot_bot_set_nat) & (relH @ F @ E @ G) & (A @ (produc7507926704131184380et_nat @ G @ H)) & (in_range @ (produc7507926704131184380et_nat @ G @ F))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2485_wand__raw_Oelims_I1_J)). 39.62/11.62 thf(1287,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat,D:$o]: (((wand_raw @ (A) @ (B) @ C) = D) => (~ (! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((C = (produc7507926704131184380et_nat @ E @ F)) => (D = (~ ((in_range @ (produc7507926704131184380et_nat @ E @ F)) & ! [G:heap_e7401611519738050253t_unit,H:set_nat]: ((B @ (produc7507926704131184380et_nat @ G @ (sup_sup_set_nat @ F @ H))) | ~ (((inf_inf_set_nat @ F @ H) = bot_bot_set_nat) & (relH @ F @ E @ G) & (A @ (produc7507926704131184380et_nat @ G @ H)) & (in_range @ (produc7507926704131184380et_nat @ G @ F))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 39.62/11.62 thf(18,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1501_subsetI)). 39.62/11.62 thf(570,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 39.62/11.62 thf(269,axiom,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: (((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (~ (! [F:a,G:heap_e7401611519738050253t_unit]: ((? [H:nat]: ((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H))))) => (((relH @ (collect_nat @ (^ [H:nat]: (~ (member_nat @ H @ E) & (ord_less_nat @ H @ (lim_Product_unit @ D))))) @ D @ G) => (~ (ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)))) <= (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G)))))))) <= (hoare_hoare_triple_a @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2233_hoare__tripleE)). 39.62/11.62 thf(1430,plain,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: (((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (~ (! [F:a,G:heap_e7401611519738050253t_unit]: ((? [H:nat]: ((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H))))) => (((relH @ (collect_nat @ (^ [H:nat]: (~ (member_nat @ H @ E) & (ord_less_nat @ H @ (lim_Product_unit @ D))))) @ D @ G) => (~ (ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)))) | ~ (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G)))))))) | ~ (hoare_hoare_triple_a @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 39.62/11.62 thf(459,axiom,((! [A:assn,B:assn,C:assn,D:assn]: (((dvd_dvd_assn @ C @ D) => (dvd_dvd_assn @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D))) <= (dvd_dvd_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8091_mult__dvd__mono)). 39.62/11.62 thf(2039,plain,((! [A:assn,B:assn,C:assn,D:assn]: (((dvd_dvd_assn @ C @ D) => (dvd_dvd_assn @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D))) | ~ (dvd_dvd_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 39.62/11.62 thf(342,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_subset__empty)). 39.62/11.62 thf(1660,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 39.62/11.62 thf(411,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => (((inf_inf_set_nat @ A @ C) = bot_bot_set_nat) <= ((inf_inf_set_nat @ B @ D) = bot_bot_set_nat))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1486_disjoint__mono)). 39.62/11.62 thf(1871,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => (((inf_inf_set_nat @ A @ C) = bot_bot_set_nat) | ~ ((inf_inf_set_nat @ B @ D) = bot_bot_set_nat))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 39.62/11.62 thf(68,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) <= (! [C:nat]: ((~ (member_nat @ C @ B)) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_Int__emptyI)). 39.62/11.62 thf(751,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) | ~ (! [C:nat]: (~ (member_nat @ C @ B) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 39.62/11.62 thf(395,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_Un__subset__iff)). 39.62/11.62 thf(1826,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 39.62/11.62 thf(445,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: (A = (inf_inf_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_inf_Oorder__iff)). 39.62/11.62 thf(1992,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: (A = (inf_inf_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 39.62/11.62 thf(178,axiom,((ord_less_eq_set_nat @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))) @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as1) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1512__092_060open_062_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062)). 39.62/11.62 thf(1132,plain,((ord_less_eq_set_nat @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))) @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as1) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 39.62/11.62 thf(9,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1636_antisym__conv3)). 39.62/11.62 thf(542,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 39.62/11.62 thf(156,axiom,((! [A:(nat > $o)]: ((bot_bot_set_nat = (collect_nat @ A)) = (! [B:nat]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_empty__Collect__eq)). 39.62/11.62 thf(1055,plain,((! [A:(nat > $o)]: ((bot_bot_set_nat = (collect_nat @ (A))) = (! [B:nat]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 39.62/11.62 thf(61,axiom,((! [A:option3562590408128118217it_nat]: ((! [B:produc3260487557148687353it_nat]: (A != (some_P7913643980934408916it_nat @ B))) = (A = none_P2651198173097904984it_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2532_not__Some__eq)). 39.62/11.62 thf(724,plain,((! [A:option3562590408128118217it_nat]: ((! [B:produc3260487557148687353it_nat]: ~ (A = (some_P7913643980934408916it_nat @ B))) = (A = none_P2651198173097904984it_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 39.62/11.62 thf(408,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((wand_raw @ A @ B @ C) => (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (~ ((in_range @ (produc7507926704131184380et_nat @ D @ E)) & ! [F:heap_e7401611519738050253t_unit,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ F @ (sup_sup_set_nat @ E @ G))) <= ((in_range @ (produc7507926704131184380et_nat @ F @ E)) & (A @ (produc7507926704131184380et_nat @ F @ G)) & (relH @ E @ D @ F) & ((inf_inf_set_nat @ E @ G) = bot_bot_set_nat))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2484_wand__raw_Oelims_I2_J)). 39.62/11.62 thf(1860,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((wand_raw @ (A) @ (B) @ C) => (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (~ ((in_range @ (produc7507926704131184380et_nat @ D @ E)) & ! [F:heap_e7401611519738050253t_unit,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ F @ (sup_sup_set_nat @ E @ G))) | ~ ((in_range @ (produc7507926704131184380et_nat @ F @ E)) & (A @ (produc7507926704131184380et_nat @ F @ G)) & (relH @ E @ D @ F) & ((inf_inf_set_nat @ E @ G) = bot_bot_set_nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 39.62/11.62 thf(218,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((~ ((~ (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B))) <= (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_inf_OboundedE)). 39.62/11.62 thf(1264,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (~ (~ (ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ A @ B)) | ~ (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 39.62/11.62 thf(24,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1757_order__less__imp__triv)). 39.62/11.62 thf(587,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 39.62/11.62 thf(234,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1317_antisym)). 39.62/11.62 thf(1323,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 39.62/11.62 thf(317,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_sup__bot_Oright__neutral)). 39.62/11.62 thf(1577,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 39.62/11.62 thf(277,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (inf_inf_set_nat @ B @ C)) => ((inf_inf_set_nat @ A @ D) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1382_boolean__algebra__cancel_Oinf1)). 39.62/11.62 thf(1455,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (inf_inf_set_nat @ B @ C)) => ((inf_inf_set_nat @ A @ D) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 39.62/11.62 thf(397,axiom,((! [A:assn]: (entails @ bot_bot_assn @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2878_ent__false)). 39.62/11.62 thf(1832,plain,((! [A:assn]: (entails @ bot_bot_assn @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 39.62/11.62 thf(117,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_comm__monoid__mult__class_Omult__1)). 39.62/11.62 thf(934,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 39.62/11.62 thf(197,axiom,((! [A:$o,B:produc3658429121746597890et_nat]: ((rep_assn @ (pure_assn @ A) @ B) = ((A) & ((produc8586169260539613262et_nat @ B) = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9385_mod__pure)). 39.62/11.62 thf(1191,plain,((! [A:$o,B:produc3658429121746597890et_nat]: ((rep_assn @ (pure_assn @ A) @ B) = ((A) & ((produc8586169260539613262et_nat @ B) = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 39.62/11.62 thf(423,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E))))))) <= (! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3471_bounded__Max__nat)). 39.62/11.62 thf(1922,plain,((! [A:(nat > $o),B:nat,C:nat]: (~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)))))) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 39.62/11.62 thf(93,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1933_linorder__not__less)). 39.62/11.62 thf(853,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 39.62/11.62 thf(499,axiom,((! [A:assn]: ((times_times_assn @ bot_bot_assn @ A) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_star__false__left)). 39.62/11.62 thf(2169,plain,((! [A:assn]: ((times_times_assn @ bot_bot_assn @ A) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 39.62/11.62 thf(328,axiom,((! [A:(produc3260487557148687353it_nat > $o),B:produc3260487557148687353it_nat]: ((A @ B) <= (! [C:a,D:produc6653097349344004940it_nat]: (A @ (produc9178034014595674355it_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_prod__cases)). 39.62/11.62 thf(1609,plain,((! [A:(produc3260487557148687353it_nat > $o),B:produc3260487557148687353it_nat]: ((A @ B) | ~ (! [C:a,D:produc6653097349344004940it_nat]: (A @ (produc9178034014595674355it_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 39.62/11.62 thf(339,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ D))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_inf__mono)). 39.62/11.62 thf(1641,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ D))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 39.62/11.62 thf(435,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_sup_Oidem)). 39.62/11.62 thf(1963,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 39.62/11.62 thf(207,axiom,((! [A:produc3260487557148687353it_nat]: ~ (! [B:a,C:heap_e7401611519738050253t_unit,D:nat]: (A != (produc9178034014595674355it_nat @ B @ (produc584006145561248582it_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_prod__cases3)). 39.62/11.62 thf(1232,plain,((! [A:produc3260487557148687353it_nat]: ~ (! [B:a,C:heap_e7401611519738050253t_unit,D:nat]: ~ (A = (produc9178034014595674355it_nat @ B @ (produc584006145561248582it_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 39.62/11.62 thf(99,axiom,((! [A:nat,B:set_nat,C:(nat > $o)]: ((member_nat @ A @ (inf_inf_set_nat @ B @ (collect_nat @ C))) = ((member_nat @ A @ B) & (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1807_Int__Collect)). 39.62/11.62 thf(870,plain,((! [A:nat,B:set_nat,C:(nat > $o)]: ((member_nat @ A @ (inf_inf_set_nat @ B @ (collect_nat @ (C)))) = ((member_nat @ A @ B) & (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 39.62/11.62 thf(417,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_inf_Oabsorb2)). 39.62/11.62 thf(1890,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 39.62/11.62 thf(412,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (sup_sup_set_nat @ B @ C)) => ((sup_sup_set_nat @ A @ D) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1395_boolean__algebra__cancel_Osup1)). 39.62/11.62 thf(1875,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (sup_sup_set_nat @ B @ C)) => ((sup_sup_set_nat @ A @ D) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 39.62/11.62 thf(379,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_sup_Oleft__commute)). 39.62/11.62 thf(1778,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 39.62/11.62 thf(289,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1451_boolean__algebra_Odisj__conj__distrib2)). 39.62/11.62 thf(1489,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 39.62/11.62 thf(69,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1727_order__less__irrefl)). 39.62/11.62 thf(756,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 39.62/11.62 thf(80,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1955_dual__order_Ostrict__implies__order)). 39.62/11.62 thf(789,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 39.62/11.62 thf(390,axiom,(((inf_inf_set_nat @ as1 @ as2) = bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_DJ)). 39.62/11.62 thf(1811,plain,(((inf_inf_set_nat @ as1 @ as2) = bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 39.62/11.62 thf(238,axiom,((! [A:produc3260487557148687353it_nat]: ? [B:a,C:produc6653097349344004940it_nat]: (A = (produc9178034014595674355it_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_surj__pair)). 39.62/11.62 thf(1334,plain,((! [A:produc3260487557148687353it_nat]: ? [B:a,C:produc6653097349344004940it_nat]: (A = (produc9178034014595674355it_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 39.62/11.62 thf(180,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1752_order__less__not__sym)). 39.62/11.62 thf(1136,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 39.62/11.62 thf(407,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) @ (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_distrib__sup__le)). 39.62/11.62 thf(1858,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) @ (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 39.62/11.62 thf(118,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2927_mult__1)). 39.62/11.62 thf(937,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 39.62/11.62 thf(434,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_inf__sup__aci_I2_J)). 39.62/11.62 thf(1960,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 39.62/11.62 thf(154,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_2306_minf_I8_J)). 39.62/11.62 thf(1051,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)],[154])). 39.62/11.62 thf(453,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_sup_OcoboundedI1)). 39.62/11.62 thf(2017,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 39.62/11.62 thf(196,axiom,((! [A:(set_nat > (set_nat > set_nat)),B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ (A @ D @ E) @ D)) => (((! [D:set_nat,E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ D @ E) => ((ord_less_eq_set_nat @ D @ F) => (ord_less_eq_set_nat @ D @ (A @ E @ F))))) => ((inf_inf_set_nat @ B @ C) = (A @ B @ C))) <= (! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ (A @ D @ E) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_inf__unique)). 39.62/11.62 thf(1183,plain,((! [A:(set_nat > (set_nat > set_nat)),B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ (A @ D @ E) @ D)) => (((! [D:set_nat,E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ D @ E) => ((ord_less_eq_set_nat @ D @ F) => (ord_less_eq_set_nat @ D @ (A @ E @ F))))) => ((inf_inf_set_nat @ B @ C) = (A @ B @ C))) | ~ (! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ (A @ D @ E) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 39.62/11.62 thf(223,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_le__iff__sup)). 39.62/11.62 thf(1283,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 39.62/11.62 thf(255,axiom,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit,C:a,D:heap_e7401611519738050253t_unit,E:nat]: ((heap_Time_effect_a @ A @ B @ D @ C @ E) <= ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ (produc584006145561248582it_nat @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2464_effectI)). 39.62/11.62 thf(1377,plain,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit,C:a,D:heap_e7401611519738050253t_unit,E:nat]: ((heap_Time_effect_a @ A @ B @ D @ C @ E) | ~ ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ (produc584006145561248582it_nat @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 39.62/11.62 thf(97,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_2314_pinf_I8_J)). 39.62/11.62 thf(866,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)],[97])). 39.62/11.62 thf(384,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ C @ D) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_sup_Omono)). 39.62/11.62 thf(1796,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ C @ D) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 39.62/11.62 thf(258,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:heap_e7401611519738050253t_unit,D:set_nat]: ((times_assn_raw @ A @ B @ (produc7507926704131184380et_nat @ C @ D)) = (? [E:set_nat,F:set_nat]: ((D = (sup_sup_set_nat @ E @ F)) & (A @ (produc7507926704131184380et_nat @ C @ E)) & (B @ (produc7507926704131184380et_nat @ C @ F)) & ((inf_inf_set_nat @ E @ F) = bot_bot_set_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_times__assn__raw_Osimps)). 39.62/11.62 thf(1394,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:heap_e7401611519738050253t_unit,D:set_nat]: ((times_assn_raw @ (A) @ (B) @ (produc7507926704131184380et_nat @ C @ D)) = (? [E:set_nat,F:set_nat]: ((D = (sup_sup_set_nat @ E @ F)) & (A @ (produc7507926704131184380et_nat @ C @ E)) & (B @ (produc7507926704131184380et_nat @ C @ F)) & ((inf_inf_set_nat @ E @ F) = bot_bot_set_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 39.62/11.62 thf(245,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_2871_ent__disjI2)). 39.62/11.62 thf(1351,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)],[245])). 39.62/11.62 thf(44,axiom,((! [A:option3562590408128118217it_nat,B:produc3260487557148687353it_nat]: ((A != none_P2651198173097904984it_nat) <= (A = (some_P7913643980934408916it_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2560_option_OdiscI)). 39.62/11.62 thf(660,plain,((! [A:option3562590408128118217it_nat,B:produc3260487557148687353it_nat]: (~ (A = none_P2651198173097904984it_nat) | ~ (A = (some_P7913643980934408916it_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 39.62/11.62 thf(136,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1937_linorder__not__le)). 39.62/11.62 thf(998,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 39.62/11.62 thf(132,axiom,((! [A:heap_e7401611519738050253t_unit]: (rep_assn @ one_one_assn @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3422_mod__emp__simp)). 39.62/11.62 thf(988,plain,((! [A:heap_e7401611519738050253t_unit]: (rep_assn @ one_one_assn @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 39.62/11.62 thf(261,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_sup__idem)). 39.62/11.62 thf(1405,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 39.62/11.62 thf(4,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2398_minf_I5_J)). 39.62/11.62 thf(527,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 39.62/11.62 thf(314,axiom,((sup_sup_set_nat = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_sup_Ocommute)). 39.62/11.62 thf(1564,plain,(((sup_sup_set_nat) = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 39.62/11.62 thf(28,axiom,((! [A:option3562590408128118217it_nat]: ((! [B:a,C:produc6653097349344004940it_nat]: (A != (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ B @ C)))) = (A = none_P2651198173097904984it_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2613_not__Some__eq2)). 39.62/11.62 thf(602,plain,((! [A:option3562590408128118217it_nat]: ((! [B:a,C:produc6653097349344004940it_nat]: ~ (A = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ B @ C)))) = (A = none_P2651198173097904984it_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 39.62/11.62 thf(130,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2278_less__not__refl2)). 39.62/11.62 thf(981,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 39.62/11.62 thf(419,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_Un__left__commute)). 39.62/11.62 thf(1896,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 39.62/11.62 thf(102,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_1911_order__le__less__trans)). 39.62/11.62 thf(877,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)],[102])). 39.62/11.62 thf(507,axiom,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: ((hoare_hoare_triple_a @ A @ B @ C) => ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (heap_Time_success_a @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2509_hoare__triple__success)). 39.62/11.62 thf(2190,plain,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: ((hoare_hoare_triple_a @ A @ B @ (C)) => ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (heap_Time_success_a @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 39.62/11.62 thf(273,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_inf__sup__ord_I1_J)). 39.62/11.62 thf(1447,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 39.62/11.62 thf(123,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3106_assn__one__left)). 39.62/11.62 thf(956,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 39.62/11.62 thf(332,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => ((relH @ A @ B @ D) <= (relH @ A @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_relH__trans)). 39.62/11.62 thf(1622,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => ((relH @ A @ B @ D) | ~ (relH @ A @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 39.62/11.62 thf(75,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (collect_nat @ (^ [E:nat]: ((member_nat @ E @ A) & (C @ E)))) @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ B))))) <= (! [E:nat]: (((C @ E) => (D @ E)) <= (member_nat @ E @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2522_subset__CollectI)). 39.62/11.62 thf(774,plain,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (collect_nat @ (^ [E:nat]: ((member_nat @ E @ A) & (C @ E)))) @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ B))))) | ~ (! [E:nat]: (((C @ E) => (D @ E)) | ~ (member_nat @ E @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 39.62/11.62 thf(171,axiom,((! [A:option3562590408128118217it_nat,B:(option3562590408128118217it_nat > (option3562590408128118217it_nat > $o)),C:option3562590408128118217it_nat]: ((((! [D:produc3260487557148687353it_nat,E:produc3260487557148687353it_nat]: (((B @ A @ C) <= (C = (some_P7913643980934408916it_nat @ E))) <= (A = (some_P7913643980934408916it_nat @ D)))) => (B @ A @ C)) <= ((B @ A @ C) <= (C = none_P2651198173097904984it_nat))) <= ((A = none_P2651198173097904984it_nat) => (B @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2572_combine__options__cases)). 39.62/11.62 thf(1104,plain,((! [A:option3562590408128118217it_nat,B:(option3562590408128118217it_nat > (option3562590408128118217it_nat > $o)),C:option3562590408128118217it_nat]: (((! [D:produc3260487557148687353it_nat,E:produc3260487557148687353it_nat]: ((B @ A @ C) | ~ (C = (some_P7913643980934408916it_nat @ E)) | ~ (A = (some_P7913643980934408916it_nat @ D)))) => (B @ A @ C)) | ~ ((B @ A @ C) | ~ (C = none_P2651198173097904984it_nat)) | ~ ((A = none_P2651198173097904984it_nat) => (B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 39.62/11.62 thf(210,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_inf__left__idem)). 39.62/11.62 thf(1242,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 39.62/11.62 thf(326,axiom,((! [A:assn]: ((entails @ A @ bot_bot_assn) = (! [B:produc3658429121746597890et_nat]: ~ (rep_assn @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2859_ent__false__iff)). 39.62/11.62 thf(1604,plain,((! [A:assn]: ((entails @ A @ bot_bot_assn) = (! [B:produc3658429121746597890et_nat]: ~ (rep_assn @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 39.62/11.62 thf(200,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat,F:set_nat]: ((sup_sup_set_nat @ D @ (inf_inf_set_nat @ E @ F)) = (inf_inf_set_nat @ (sup_sup_set_nat @ D @ E) @ (sup_sup_set_nat @ D @ F)))) => ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_distrib__imp2)). 39.62/11.62 thf(1206,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat,F:set_nat]: ((sup_sup_set_nat @ D @ (inf_inf_set_nat @ E @ F)) = (inf_inf_set_nat @ (sup_sup_set_nat @ D @ E) @ (sup_sup_set_nat @ D @ F)))) => ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 39.62/11.62 thf(120,axiom,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) => (ord_less_eq_set_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2252_subset__emptyI)). 39.62/11.62 thf(942,plain,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) => (ord_less_eq_set_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 39.62/11.62 thf(512,axiom,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ (times_times_assn @ A @ B) @ C) => (dvd_dvd_assn @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8096_dvd__mult__right)). 39.62/11.62 thf(2204,plain,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ (times_times_assn @ A @ B) @ C) => (dvd_dvd_assn @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 39.62/11.62 thf(5,axiom,((! [A:produc3658429121746597890et_nat]: ((~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: ((~ (! [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ B)) <= (member_nat @ D @ C)))) <= (A = (produc7507926704131184380et_nat @ B @ C))))) <= (in_range @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2468_in__range_Oelims_I2_J)). 39.62/11.62 thf(529,plain,((! [A:produc3658429121746597890et_nat]: (~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: (~ (! [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ B)) | ~ (member_nat @ D @ C))) | ~ (A = (produc7507926704131184380et_nat @ B @ C)))) | ~ (in_range @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 39.62/11.62 thf(186,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_inf_Ocobounded1)). 39.62/11.62 thf(1153,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 39.62/11.62 thf(87,axiom,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2302_Collect__restrict)). 39.62/11.62 thf(810,plain,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 39.62/11.62 thf(410,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ C @ A) @ B) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_le__infI2)). 39.62/11.62 thf(1868,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ C @ A) @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 39.62/11.62 thf(206,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((! [F:heap_e7401611519738050253t_unit,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ F @ (sup_sup_set_nat @ E @ G))) <= ((relH @ E @ D @ F) & (in_range @ (produc7507926704131184380et_nat @ F @ E)) & (A @ (produc7507926704131184380et_nat @ F @ G)) & ((inf_inf_set_nat @ E @ G) = bot_bot_set_nat))) & (in_range @ (produc7507926704131184380et_nat @ D @ E))) <= (C = (produc7507926704131184380et_nat @ D @ E))))) <= (~ (wand_raw @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2483_wand__raw_Oelims_I3_J)). 39.62/11.62 thf(1223,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((! [F:heap_e7401611519738050253t_unit,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ F @ (sup_sup_set_nat @ E @ G))) | ~ ((relH @ E @ D @ F) & (in_range @ (produc7507926704131184380et_nat @ F @ E)) & (A @ (produc7507926704131184380et_nat @ F @ G)) & ((inf_inf_set_nat @ E @ G) = bot_bot_set_nat))) & (in_range @ (produc7507926704131184380et_nat @ D @ E))) | ~ (C = (produc7507926704131184380et_nat @ D @ E)))) | (wand_raw @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 39.62/11.62 thf(151,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) = (! [C:nat]: ((member_nat @ C @ A) => (~ (member_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_disjoint__iff)). 39.62/11.62 thf(1042,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) = (! [C:nat]: ((member_nat @ C @ A) => (~ (member_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 39.62/11.62 thf(299,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_inf__sup__aci_I8_J)). 39.62/11.62 thf(1519,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 39.62/11.62 thf(318,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)) <= (ord_less_eq_set_nat @ C @ D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_sup__mono)). 39.62/11.62 thf(1580,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 39.62/11.62 thf(175,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2394_minf_I4_J)). 39.62/11.62 thf(1123,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 39.62/11.62 thf(192,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_Un__left__absorb)). 39.62/11.62 thf(1174,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 39.62/11.62 thf(288,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_1322_Orderings_Oorder__eq__iff)). 39.62/11.62 thf(1487,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)],[288])). 39.62/11.62 thf(204,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_1288_order_Otrans)). 39.62/11.62 thf(1217,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)],[204])). 39.62/11.62 thf(490,axiom,((entails = (^ [A:assn,B:assn]: ! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (rep_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2864_entails__def)). 39.62/11.62 thf(2147,plain,(((entails) = (^ [A:assn,B:assn]: ! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (rep_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 39.62/11.62 thf(53,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1679_dual__order_Ostrict__implies__not__eq)). 39.62/11.62 thf(693,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 39.62/11.62 thf(35,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2057_leI)). 39.62/11.62 thf(630,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 39.62/11.62 thf(331,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ B) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_le__infI1)). 39.62/11.62 thf(1619,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 39.62/11.62 thf(492,axiom,((! [A:assn,B:$o,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = ((B) & (rep_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2451_mod__pure__star__dist)). 39.62/11.62 thf(2150,plain,((! [A:assn,B:$o,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = ((B) & (rep_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 39.62/11.62 thf(485,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:assn]: ((relH @ A @ B @ C) => ((rep_assn @ D @ (produc7507926704131184380et_nat @ B @ A)) = (rep_assn @ D @ (produc7507926704131184380et_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mod__relH)). 39.62/11.62 thf(2132,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:assn]: ((relH @ A @ B @ C) => ((rep_assn @ D @ (produc7507926704131184380et_nat @ B @ A)) = (rep_assn @ D @ (produc7507926704131184380et_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 39.62/11.62 thf(63,axiom,((! [A:option3562590408128118217it_nat]: ((A != none_P2651198173097904984it_nat) => (~ (! [B:produc3260487557148687353it_nat]: (A != (some_P7913643980934408916it_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2563_option_Oexhaust)). 39.62/11.62 thf(729,plain,((! [A:option3562590408128118217it_nat]: ((~ (A = none_P2651198173097904984it_nat)) => (~ (! [B:produc3260487557148687353it_nat]: ~ (A = (some_P7913643980934408916it_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 39.62/11.62 thf(267,axiom,((! [A:produc3260487557148687353it_nat]: ~ (! [B:a,C:produc6653097349344004940it_nat]: (A != (produc9178034014595674355it_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_old_Oprod_Oexhaust)). 39.62/11.62 thf(1423,plain,((! [A:produc3260487557148687353it_nat]: ~ (! [B:a,C:produc6653097349344004940it_nat]: ~ (A = (produc9178034014595674355it_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 39.62/11.62 thf(426,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ D)) <= (ord_less_eq_set_nat @ C @ D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_Int__mono)). 39.62/11.62 thf(1938,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ D)) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 39.62/11.62 thf(312,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat,D:$o]: (((times_assn_raw @ A @ B @ C) = D) => (~ (! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((C = (produc7507926704131184380et_nat @ E @ F)) => (D = (~ (? [G:set_nat,H:set_nat]: (((inf_inf_set_nat @ G @ H) = bot_bot_set_nat) & (B @ (produc7507926704131184380et_nat @ E @ H)) & (A @ (produc7507926704131184380et_nat @ E @ G)) & (F = (sup_sup_set_nat @ G @ H)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_times__assn__raw_Oelims_I1_J)). 39.62/11.62 thf(1555,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat,D:$o]: (((times_assn_raw @ (A) @ (B) @ C) = D) => (~ (! [E:heap_e7401611519738050253t_unit,F:set_nat]: ((C = (produc7507926704131184380et_nat @ E @ F)) => (D = (~ (? [G:set_nat,H:set_nat]: (((inf_inf_set_nat @ G @ H) = bot_bot_set_nat) & (B @ (produc7507926704131184380et_nat @ E @ H)) & (A @ (produc7507926704131184380et_nat @ E @ G)) & (F = (sup_sup_set_nat @ G @ H)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 39.62/11.62 thf(45,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2248_nat__less__le)). 39.62/11.62 thf(665,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 39.62/11.62 thf(201,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_inf_Ocobounded2)). 39.62/11.62 thf(1210,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 39.62/11.62 thf(12,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1527_subset__eq)). 39.62/11.62 thf(551,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 39.62/11.62 thf(368,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((((inf_inf_set_nat @ C @ B) = (inf_inf_set_nat @ D @ B)) => ((inf_inf_set_nat @ C @ A) = (inf_inf_set_nat @ D @ A))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2225_inter__eq__subsetI)). 39.62/11.62 thf(1740,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((((inf_inf_set_nat @ C @ B) = (inf_inf_set_nat @ D @ B)) => ((inf_inf_set_nat @ C @ A) = (inf_inf_set_nat @ D @ A))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 39.62/11.62 thf(141,axiom,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) = (! [C:nat]: ((member_nat @ C @ B) => (ord_less_nat @ C @ (lim_Product_unit @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2470_in__range_Osimps)). 39.62/11.62 thf(1012,plain,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) = (! [C:nat]: ((member_nat @ C @ B) => (ord_less_nat @ C @ (lim_Product_unit @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 39.62/11.62 thf(467,axiom,((! [A:assn,B:produc3658429121746597890et_nat,C:assn]: (((entails @ A @ C) => (rep_assn @ C @ B)) <= (rep_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2867_ent__fwd)). 39.62/11.62 thf(2068,plain,((! [A:assn,B:produc3658429121746597890et_nat,C:assn]: (((entails @ A @ C) => (rep_assn @ C @ B)) | ~ (rep_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 39.62/11.62 thf(393,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ B @ A) = A) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_Int__absorb1)). 39.62/11.62 thf(1819,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ B @ A) = A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 39.62/11.62 thf(23,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ B))))) = (! [D:nat]: ((C @ D) <= (member_nat @ D @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2515_subset__Collect__iff)). 39.62/11.62 thf(583,plain,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ B))))) = (! [D:nat]: ((C @ D) | ~ (member_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 39.62/11.62 thf(3,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_eq_nat @ C @ A))) <= ((B @ A) <= (! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1850_exists__leI)). 39.62/11.62 thf(522,plain,((! [A:nat,B:(nat > $o)]: (? [C:nat]: ((B @ C) & (ord_less_eq_nat @ C @ A)) | ~ ((B @ A) | ~ (! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 39.62/11.62 thf(106,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ B @ C)) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_UnI1)). 39.62/11.62 thf(889,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ B @ C)) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 39.62/11.62 thf(502,axiom,((times_times_assn = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_assn__times__comm)). 39.62/11.62 thf(2179,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 39.62/11.62 thf(399,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_sup_Oleft__idem)). 39.62/11.62 thf(1836,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 39.62/11.62 thf(382,axiom,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: (((heap_Time_execute_a @ A @ B) = none_P2651198173097904984it_nat) <= (! [C:a,D:produc6653097349344004940it_nat]: ((heap_Time_execute_a @ A @ B) != (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2636_Heap__cases)). 39.62/11.62 thf(1787,plain,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: (((heap_Time_execute_a @ A @ B) = none_P2651198173097904984it_nat) | ~ (! [C:a,D:produc6653097349344004940it_nat]: ~ ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 39.62/11.62 thf(503,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:assn]: ((B = (abs_assn @ A)) <= (! [C:produc3658429121746597890et_nat]: ((A @ C) = (rep_assn @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2584_Abs__assn__eqI_I2_J)). 39.62/11.62 thf(2181,plain,((! [A:(produc3658429121746597890et_nat > $o),B:assn]: ((B = (abs_assn @ (A))) | ~ (! [C:produc3658429121746597890et_nat]: ((A @ C) = (rep_assn @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 39.62/11.62 thf(21,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1859_linorder__le__less__linear)). 39.62/11.62 thf(578,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 39.62/11.62 thf(54,axiom,((! [A:produc3658429121746597890et_nat,B:$o]: (((in_range @ A) = B) => (~ (! [C:heap_e7401611519738050253t_unit,D:set_nat]: ((B = (~ (! [E:nat]: ((member_nat @ E @ D) => (ord_less_nat @ E @ (lim_Product_unit @ C)))))) <= (A = (produc7507926704131184380et_nat @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2469_in__range_Oelims_I1_J)). 39.62/11.62 thf(697,plain,((! [A:produc3658429121746597890et_nat,B:$o]: (((in_range @ A) = B) => (~ (! [C:heap_e7401611519738050253t_unit,D:set_nat]: ((B = (~ (! [E:nat]: ((member_nat @ E @ D) => (ord_less_nat @ E @ (lim_Product_unit @ C)))))) | ~ (A = (produc7507926704131184380et_nat @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 39.62/11.62 thf(442,axiom,((! [A:set_nat,B:set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ A @ B)) = ((B = bot_bot_set_nat) & (A = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_bot__eq__sup__iff)). 39.62/11.62 thf(1983,plain,((! [A:set_nat,B:set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ A @ B)) = ((B = bot_bot_set_nat) & (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 39.62/11.62 thf(432,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((inf_inf_set_nat @ D @ A) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ D @ C))) <= (A = (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1387_boolean__algebra__cancel_Oinf2)). 39.62/11.62 thf(1953,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((inf_inf_set_nat @ D @ A) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ D @ C))) | ~ (A = (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 39.62/11.62 thf(387,axiom,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) = (? [D:heap_e7401611519738050253t_unit,E:set_nat,F:set_nat]: (((inf_inf_set_nat @ E @ F) = bot_bot_set_nat) & (rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) & (rep_assn @ B @ (produc7507926704131184380et_nat @ D @ F)) & (C = (produc7507926704131184380et_nat @ D @ (sup_sup_set_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_mod__star__conv)). 39.62/11.62 thf(1804,plain,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) = (? [D:heap_e7401611519738050253t_unit,E:set_nat,F:set_nat]: (((inf_inf_set_nat @ E @ F) = bot_bot_set_nat) & (rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) & (rep_assn @ B @ (produc7507926704131184380et_nat @ D @ F)) & (C = (produc7507926704131184380et_nat @ D @ (sup_sup_set_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 39.62/11.62 thf(236,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_inf_Oleft__idem)). 39.62/11.62 thf(1328,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 39.62/11.62 thf(174,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1688_order__less__asym)). 39.62/11.62 thf(1121,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 39.62/11.62 thf(307,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_sup__left__commute)). 39.62/11.62 thf(1540,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 39.62/11.62 thf(259,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_Int__empty__right)). 39.62/11.62 thf(1397,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ bot_bot_set_nat) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 39.62/11.62 thf(494,axiom,((! [A:produc3658429121746597890et_nat]: ~ (rep_assn @ bot_bot_assn @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_mod__false)). 39.62/11.62 thf(2157,plain,((! [A:produc3658429121746597890et_nat]: ~ (rep_assn @ bot_bot_assn @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 39.62/11.62 thf(183,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1979_dual__order_Ostrict__trans1)). 39.62/11.62 thf(1143,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 39.62/11.62 thf(404,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_Int__lower2)). 39.62/11.62 thf(1851,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 39.62/11.62 thf(377,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) => (~ ((ord_less_eq_set_nat @ A @ B) => (~ (ord_less_eq_set_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_le__infE)). 39.62/11.62 thf(1772,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) => (~ ((ord_less_eq_set_nat @ A @ B) => (~ (ord_less_eq_set_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 39.62/11.62 thf(216,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_inf__sup__distrib1)). 39.62/11.62 thf(1259,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 39.62/11.62 thf(292,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_Int__Un__distrib)). 39.62/11.62 thf(1498,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 39.62/11.62 thf(320,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Int__Un__eq_I2_J)). 39.62/11.62 thf(1587,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 39.62/11.62 thf(181,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1929_order__less__imp__le)). 39.62/11.62 thf(1138,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 39.62/11.62 thf(361,axiom,((! [A:set_nat,B:set_nat]: ((B = (sup_sup_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_sup_OorderE)). 39.62/11.62 thf(1719,plain,((! [A:set_nat,B:set_nat]: ((B = (sup_sup_set_nat @ B @ A)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 39.62/11.62 thf(351,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_sup_Oabsorb__iff2)). 39.62/11.62 thf(1683,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 39.62/11.62 thf(189,axiom,((! [A:$o]: (((pure_assn @ A) = bot_bot_assn) = (~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2447_pure__assn__eq__false__iff)). 39.62/11.62 thf(1160,plain,((! [A:$o]: (((pure_assn @ A) = bot_bot_assn) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 39.62/11.62 thf(455,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Un__Int__eq_I3_J)). 39.62/11.62 thf(2023,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 39.62/11.62 thf(249,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_1351_linorder__linear)). 39.62/11.62 thf(1361,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)],[249])). 39.62/11.62 thf(110,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2063_leD)). 39.62/11.62 thf(901,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 39.62/11.62 thf(39,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) <= (ord_less_nat @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2358_pinf_I1_J)). 39.62/11.62 thf(642,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) | ~ (ord_less_nat @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 39.62/11.62 thf(203,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_Int__left__commute)). 39.62/11.62 thf(1214,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 39.62/11.62 thf(478,axiom,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ A @ (times_times_assn @ C @ B)) <= (dvd_dvd_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8071_dvd__mult)). 39.62/11.62 thf(2108,plain,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ A @ (times_times_assn @ C @ B)) | ~ (dvd_dvd_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 39.62/11.62 thf(25,axiom,((! [A:$o]: (((pure_assn @ A) = one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2950_pure__assn__eq__emp__iff)). 39.62/11.62 thf(590,plain,((! [A:$o]: (((pure_assn @ A) = one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 39.62/11.62 thf(340,axiom,((! [A:assn,B:$o,C:assn]: ((entails @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = ((B) => (entails @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2858_ent__pure__pre__iff)). 39.62/11.62 thf(1644,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)],[340])). 39.62/11.62 thf(56,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ B @ (wand_assn @ A @ C)) <= (entails @ (times_times_assn @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2882_ent__wandI)). 39.62/11.62 thf(706,plain,((! [A:assn,B:assn,C:assn]: ((entails @ B @ (wand_assn @ A @ C)) | ~ (entails @ (times_times_assn @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 39.62/11.62 thf(264,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_le__infI)). 39.62/11.62 thf(1414,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 39.62/11.62 thf(509,axiom,((times_times_assn = (^ [A:assn,B:assn]: (abs_assn @ (times_assn_raw @ (rep_assn @ A) @ (rep_assn @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2504_times__assn__def)). 39.62/11.62 thf(2196,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (abs_assn @ (times_assn_raw @ (rep_assn @ A) @ (rep_assn @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 39.62/11.62 thf(401,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1200_Int__greatest)). 39.62/11.62 thf(1842,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 39.62/11.62 thf(383,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((~ (times_assn_raw @ A @ B @ C)) => (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (? [F:set_nat,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ D @ G)) & (A @ (produc7507926704131184380et_nat @ D @ F)) & ((inf_inf_set_nat @ F @ G) = bot_bot_set_nat) & (E = (sup_sup_set_nat @ F @ G)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_times__assn__raw_Oelims_I3_J)). 39.62/11.62 thf(1791,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((~ (times_assn_raw @ (A) @ (B) @ C)) => (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (? [F:set_nat,G:set_nat]: ((B @ (produc7507926704131184380et_nat @ D @ G)) & (A @ (produc7507926704131184380et_nat @ D @ F)) & ((inf_inf_set_nat @ F @ G) = bot_bot_set_nat) & (E = (sup_sup_set_nat @ F @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 39.62/11.62 thf(500,axiom,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ top_top_assn) @ B) => (~ (! [C:produc3658429121746597890et_nat]: (((~ (rep_assn @ A @ C)) <= (ord_less_eq_set_nat @ (produc8586169260539613262et_nat @ C) @ (produc8586169260539613262et_nat @ B))) <= ((produc1824681642469235216et_nat @ C) = (produc1824681642469235216et_nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9387_mod__star__trueE_H)). 39.62/11.62 thf(2172,plain,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ top_top_assn) @ B) => (~ (! [C:produc3658429121746597890et_nat]: (~ (rep_assn @ A @ C) | ~ (ord_less_eq_set_nat @ (produc8586169260539613262et_nat @ C) @ (produc8586169260539613262et_nat @ B)) | ~ ((produc1824681642469235216et_nat @ C) = (produc1824681642469235216et_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 39.62/11.62 thf(329,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (sup_sup_set_nat @ B @ C)) => ((sup_sup_set_nat @ D @ A) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1400_boolean__algebra__cancel_Osup2)). 39.62/11.62 thf(1612,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((A = (sup_sup_set_nat @ B @ C)) => ((sup_sup_set_nat @ D @ A) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 39.62/11.62 thf(150,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1650_dual__order_Oirrefl)). 39.62/11.62 thf(1039,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 39.62/11.62 thf(187,axiom,((top_top_assn = (abs_assn @ in_range))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9253_top__assn__def)). 39.62/11.62 thf(1155,plain,((top_top_assn = (abs_assn @ (in_range)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 39.62/11.62 thf(369,axiom,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) => (relH @ B @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2461_relH__refl)). 39.62/11.62 thf(1744,plain,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ B)) => (relH @ B @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 39.62/11.62 thf(227,axiom,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ((heap_Time_success_a @ A @ B) => (~ (! [C:a,D:produc6653097349344004940it_nat]: ((heap_Time_execute_a @ A @ B) != (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2600_successE)). 39.62/11.62 thf(1297,plain,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ((heap_Time_success_a @ A @ B) => (~ (! [C:a,D:produc6653097349344004940it_nat]: ~ ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 39.62/11.62 thf(275,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1404_bot_Oextremum)). 39.62/11.62 thf(1451,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 39.62/11.62 thf(303,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)) <= (ord_less_eq_set_nat @ C @ D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1213_Un__mono)). 39.62/11.62 thf(1530,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ D)) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 39.62/11.62 thf(493,axiom,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ((hoare_hoare_triple_a @ A @ B @ C) <= (! [D:produc3658429121746597890et_nat]: ((hoare_hoare_triple_a @ A @ B @ C) <= (rep_assn @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_hoare__triple__preI)). 39.62/11.62 thf(2153,plain,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ((hoare_hoare_triple_a @ A @ B @ (C)) | ~ (! [D:produc3658429121746597890et_nat]: ((hoare_hoare_triple_a @ A @ B @ (C)) | ~ (rep_assn @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 39.62/11.62 thf(41,axiom,((inf_inf_set_nat = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (member_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1800_Int__def)). 39.62/11.62 thf(654,plain,(((inf_inf_set_nat) = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (member_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 39.62/11.62 thf(311,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_374_star__or__dist2)). 39.62/11.62 thf(1552,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)],[311])). 39.62/11.62 thf(424,axiom,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Un__empty)). 39.62/11.62 thf(1932,plain,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 39.62/11.62 thf(158,axiom,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_emptyE)). 39.62/11.62 thf(1060,plain,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 39.62/11.62 thf(385,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (ord_less_eq_set_nat @ (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C)) @ (inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_distrib__inf__le)). 39.62/11.62 thf(1799,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (ord_less_eq_set_nat @ (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C)) @ (inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 39.62/11.62 thf(429,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_inf_Oabsorb__iff1)). 39.62/11.62 thf(1947,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 39.62/11.62 thf(463,axiom,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) => (? [D:produc3658429121746597890et_nat,E:produc3658429121746597890et_nat]: ((rep_assn @ B @ E) & (rep_assn @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mod__starD)). 39.62/11.62 thf(2052,plain,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) => (? [D:produc3658429121746597890et_nat,E:produc3658429121746597890et_nat]: ((rep_assn @ B @ E) & (rep_assn @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 39.62/11.62 thf(76,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2277_less__not__refl)). 39.62/11.62 thf(779,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 39.62/11.62 thf(487,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_89_assn__times__assoc)). 39.62/11.62 thf(2140,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)],[487])). 39.62/11.62 thf(29,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1961_order_Ostrict__implies__order)). 39.62/11.62 thf(605,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 39.62/11.62 thf(301,axiom,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2875_ent__disjI2__direct)). 39.62/11.62 thf(1525,plain,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 39.62/11.62 thf(169,axiom,(((^ [A:assn]: (A)) = (times_times_assn @ one_one_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3135_lambda__one)). 39.62/11.62 thf(1099,plain,(((^ [A:assn]: (A)) = (times_times_assn @ one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 39.62/11.62 thf(131,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_1640_linorder__cases)). 39.62/11.62 thf(985,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)],[131])). 39.62/11.62 thf(185,axiom,((! [A:heap_e7401611519738050253t_unit,B:set_nat,C:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ (sup_sup_set_nat @ B @ C))) = ((in_range @ (produc7507926704131184380et_nat @ A @ C)) & (in_range @ (produc7507926704131184380et_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2452_in__range__dist__union)). 39.62/11.62 thf(1150,plain,((! [A:heap_e7401611519738050253t_unit,B:set_nat,C:set_nat]: ((in_range @ (produc7507926704131184380et_nat @ A @ (sup_sup_set_nat @ B @ C))) = ((in_range @ (produc7507926704131184380et_nat @ A @ C)) & (in_range @ (produc7507926704131184380et_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 39.62/11.62 thf(284,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_1268_order__class_Oorder__eq__iff)). 39.62/11.62 thf(1478,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)],[284])). 39.62/11.62 thf(345,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_1302_dual__order_Oeq__iff)). 39.62/11.62 thf(1668,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)],[345])). 39.62/11.62 thf(439,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ C @ A) @ B) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_inf_OcoboundedI2)). 39.62/11.62 thf(1974,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (inf_inf_set_nat @ C @ A) @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 39.62/11.62 thf(450,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ B @ C) => (entails @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2860_ent__trans)). 39.62/11.62 thf(2006,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ B @ C) => (entails @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 39.62/11.62 thf(60,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_1683_linorder__neqE)). 39.62/11.62 thf(721,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)],[60])). 39.62/11.62 thf(232,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1228_Un__upper2)). 39.62/11.62 thf(1318,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 39.62/11.62 thf(354,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ C) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_le__inf__iff)). 39.62/11.62 thf(1695,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ C) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 39.62/11.62 thf(43,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) = (! [C:nat]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1587_Collect__mono__iff)). 39.62/11.62 thf(657,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((A @ C) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 39.62/11.62 thf(191,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat,F:set_nat]: ((inf_inf_set_nat @ D @ (sup_sup_set_nat @ E @ F)) = (sup_sup_set_nat @ (inf_inf_set_nat @ D @ E) @ (inf_inf_set_nat @ D @ F)))) => ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_distrib__imp1)). 39.62/11.62 thf(1170,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat,F:set_nat]: ((inf_inf_set_nat @ D @ (sup_sup_set_nat @ E @ F)) = (sup_sup_set_nat @ (inf_inf_set_nat @ D @ E) @ (inf_inf_set_nat @ D @ F)))) => ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 39.62/11.62 thf(280,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_sup_Oabsorb1)). 39.62/11.62 thf(1466,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 39.62/11.62 thf(49,axiom,((bot_bot_assn != one_one_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2951_assn__basic__inequalities_I3_J)). 39.62/11.62 thf(674,plain,((~ (bot_bot_assn = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 39.62/11.62 thf(343,axiom,((hoare_hoare_triple_a = (^ [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:a,G:heap_e7401611519738050253t_unit]: ((ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)) & (relH @ (collect_nat @ (^ [H:nat]: (~ (member_nat @ H @ E) & (ord_less_nat @ H @ (lim_Product_unit @ D))))) @ D @ G) & (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G))) & ? [H:nat]: ((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2229_hoare__triple__def)). 39.62/11.62 thf(1663,plain,(((hoare_hoare_triple_a) = (^ [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:a,G:heap_e7401611519738050253t_unit]: ((ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)) & (relH @ (collect_nat @ (^ [H:nat]: (~ (member_nat @ H @ E) & (ord_less_nat @ H @ (lim_Product_unit @ D))))) @ D @ G) & (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G))) & ? [H:nat]: ((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 39.62/11.62 thf(190,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_inf__sup__aci_I7_J)). 39.62/11.62 thf(1167,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 39.62/11.62 thf(122,axiom,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (uminus_uminus_assn @ A) @ B) = (~ (rep_assn @ A @ B) & (in_range @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4882_mod__not__dist)). 39.62/11.62 thf(953,plain,((! [A:assn,B:produc3658429121746597890et_nat]: ((rep_assn @ (uminus_uminus_assn @ A) @ B) = (~ (rep_assn @ A @ B) & (in_range @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 39.62/11.62 thf(82,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_1761_linorder__less__linear)). 39.62/11.62 thf(794,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)],[82])). 39.62/11.62 thf(514,axiom,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) => (~ ((? [D:produc3658429121746597890et_nat]: (rep_assn @ A @ D)) => (! [D:produc3658429121746597890et_nat]: ~ (rep_assn @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_mod__starE)). 39.62/11.62 thf(2208,plain,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ (times_times_assn @ A @ B) @ C) => (~ ((? [D:produc3658429121746597890et_nat]: (rep_assn @ A @ D)) => (! [D:produc3658429121746597890et_nat]: ~ (rep_assn @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 39.62/11.62 thf(86,axiom,((! [A:produc3658429121746597890et_nat]: ((~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: ((! [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ B)) <= (member_nat @ D @ C))) <= (A = (produc7507926704131184380et_nat @ B @ C))))) <= (~ (in_range @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2467_in__range_Oelims_I3_J)). 39.62/11.62 thf(805,plain,((! [A:produc3658429121746597890et_nat]: (~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: (! [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ B)) | ~ (member_nat @ D @ C)) | ~ (A = (produc7507926704131184380et_nat @ B @ C)))) | (in_range @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 39.62/11.62 thf(465,axiom,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: (((rep_assn @ B @ C) <= (rep_assn @ A @ C)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2866_entailsD)). 39.62/11.62 thf(2057,plain,((! [A:assn,B:assn,C:produc3658429121746597890et_nat]: ((rep_assn @ B @ C) | ~ (rep_assn @ A @ C) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 39.62/11.62 thf(72,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__mem__eq)). 39.62/11.62 thf(765,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 39.62/11.62 thf(296,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Int__Un__eq_I3_J)). 39.62/11.62 thf(1510,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 39.62/11.62 thf(355,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_1273_ord__eq__le__trans)). 39.62/11.62 thf(1698,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)],[355])). 39.62/11.62 thf(286,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_sup_Oabsorb__iff1)). 39.62/11.62 thf(1483,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 39.62/11.62 thf(94,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_1660_order_Ostrict__trans)). 39.62/11.62 thf(856,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)],[94])). 39.62/11.62 thf(66,axiom,((top_top_assn != one_one_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9231_assn__basic__inequalities_I1_J)). 39.62/11.62 thf(745,plain,((~ (top_top_assn = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 39.62/11.62 thf(19,axiom,((! [A:nat,B:nat]: (((A != B) => (ord_less_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1923_order__le__neq__trans)). 39.62/11.62 thf(573,plain,((! [A:nat,B:nat]: (((~ (A = B)) => (ord_less_nat @ A @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 39.62/11.62 thf(254,axiom,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_old_Oprod_Oinject)). 39.62/11.62 thf(1374,plain,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 39.62/11.62 thf(184,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1771_order__less__imp__not__eq2)). 39.62/11.62 thf(1146,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 39.62/11.62 thf(373,axiom,((! [A:produc3260487557148687353it_nat,B:produc3260487557148687353it_nat]: (((some_P7913643980934408916it_nat @ A) = (some_P7913643980934408916it_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1468_option_Oinject)). 39.62/11.62 thf(1754,plain,((! [A:produc3260487557148687353it_nat,B:produc3260487557148687353it_nat]: (((some_P7913643980934408916it_nat @ A) = (some_P7913643980934408916it_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 39.62/11.62 thf(457,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_sup_OcoboundedI2)). 39.62/11.62 thf(2033,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 39.62/11.62 thf(491,axiom,((rep_assn @ (times_times_assn @ p @ r) @ (produc7507926704131184380et_nat @ h2 @ as))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_A_K_AR_092_060close_062)). 39.62/11.62 thf(2149,plain,((rep_assn @ (times_times_assn @ p @ r) @ (produc7507926704131184380et_nat @ h2 @ as))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 39.62/11.62 thf(228,axiom,((! [A:(set_nat > (set_nat > set_nat)),B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ D @ (A @ D @ E))) => ((((sup_sup_set_nat @ B @ C) = (A @ B @ C)) <= (! [D:set_nat,E:set_nat,F:set_nat]: (((ord_less_eq_set_nat @ (A @ E @ F) @ D) <= (ord_less_eq_set_nat @ F @ D)) <= (ord_less_eq_set_nat @ E @ D)))) <= (! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ E @ (A @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_sup__unique)). 39.62/11.62 thf(1301,plain,((! [A:(set_nat > (set_nat > set_nat)),B:set_nat,C:set_nat]: ((! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ D @ (A @ D @ E))) => (((sup_sup_set_nat @ B @ C) = (A @ B @ C)) | ~ (! [D:set_nat,E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (A @ E @ F) @ D) | ~ (ord_less_eq_set_nat @ F @ D) | ~ (ord_less_eq_set_nat @ E @ D))) | ~ (! [D:set_nat,E:set_nat]: (ord_less_eq_set_nat @ E @ (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 39.62/11.62 thf(323,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_1283_order__antisym)). 39.62/11.62 thf(1595,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)],[323])). 39.62/11.62 thf(335,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_sup__ge1)). 39.62/11.62 thf(1631,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 39.62/11.62 thf(64,axiom,((! [A:assn,B:assn]: (((uminus_uminus_assn @ A) = (uminus_uminus_assn @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4835_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff)). 39.62/11.62 thf(733,plain,((! [A:assn,B:assn]: (((uminus_uminus_assn @ A) = (uminus_uminus_assn @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 39.62/11.62 thf(90,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1973_dual__order_Ostrict__trans2)). 39.62/11.62 thf(819,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 39.62/11.62 thf(16,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_1692_linorder__neq__iff)). 39.62/11.62 thf(562,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)],[16])). 39.62/11.62 thf(139,axiom,((sup_sup_set_nat = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: ((member_nat @ C @ B) | (member_nat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1831_Un__def)). 39.62/11.62 thf(1007,plain,(((sup_sup_set_nat) = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: ((member_nat @ C @ B) | (member_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 39.62/11.62 thf(462,axiom,((! [A:produc3658429121746597890et_nat]: ~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: (A != (produc7507926704131184380et_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_one__assn__raw_Ocases)). 39.62/11.62 thf(2048,plain,((! [A:produc3658429121746597890et_nat]: ~ (! [B:heap_e7401611519738050253t_unit,C:set_nat]: ~ (A = (produc7507926704131184380et_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 39.62/11.62 thf(381,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_inf_Oleft__commute)). 39.62/11.62 thf(1784,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 39.62/11.62 thf(74,axiom,((! [A:assn,B:assn]: (entails @ (times_times_assn @ A @ (wand_assn @ A @ B)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2883_ent__mp)). 39.62/11.62 thf(772,plain,((! [A:assn,B:assn]: (entails @ (times_times_assn @ A @ (wand_assn @ A @ B)) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 39.62/11.62 thf(372,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_inf__sup__ord_I2_J)). 39.62/11.62 thf(1752,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 39.62/11.62 thf(305,axiom,((! [A:set_nat,B:set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ A @ B)) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_sup__bot_Oneutr__eq__iff)). 39.62/11.62 thf(1535,plain,((! [A:set_nat,B:set_nat]: ((bot_bot_set_nat = (sup_sup_set_nat @ A @ B)) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 39.62/11.62 thf(101,axiom,((wand_assn = (^ [A:assn,B:assn]: (abs_assn @ (wand_raw @ (rep_assn @ A) @ (rep_assn @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2494_wand__assn__def)). 39.62/11.62 thf(875,plain,(((wand_assn) = (^ [A:assn,B:assn]: (abs_assn @ (wand_raw @ (rep_assn @ A) @ (rep_assn @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 39.62/11.62 thf(92,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ D @ B) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (! [F:nat]: (((ord_less_eq_nat @ A @ F) & (ord_less_nat @ F @ E)) => (C @ F)))) & ! [E:nat]: (((ord_less_nat @ E @ D) & (ord_less_eq_nat @ A @ E)) => (C @ E)) & (ord_less_eq_nat @ A @ D)))) <= (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2324_complete__interval)). 39.62/11.62 thf(826,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ D @ B) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (! [F:nat]: (((ord_less_eq_nat @ A @ F) & (ord_less_nat @ F @ E)) => (C @ F)))) & ! [E:nat]: (((ord_less_nat @ E @ D) & (ord_less_eq_nat @ A @ E)) => (C @ E)) & (ord_less_eq_nat @ A @ D)))) | ~ (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 39.62/11.62 thf(215,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_2873_ent__disjI2_H)). 39.62/11.62 thf(1256,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)],[215])). 39.62/11.62 thf(10,axiom,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ((heap_Time_success_a @ A @ B) <= ((heap_Time_execute_a @ A @ B) != none_P2651198173097904984it_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2619_successI)). 39.62/11.62 thf(545,plain,((! [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ((heap_Time_success_a @ A @ B) | ((heap_Time_execute_a @ A @ B) = none_P2651198173097904984it_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 39.62/11.62 thf(508,axiom,((! [A:assn]: ((times_times_assn @ A @ bot_bot_assn) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_star__false__right)). 39.62/11.62 thf(2193,plain,((! [A:assn]: ((times_times_assn @ A @ bot_bot_assn) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 39.62/11.62 thf(518,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_3558_power__mult__distrib)). 39.62/11.62 thf(2220,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)],[518])). 39.62/11.62 thf(357,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) => (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1414_bot_Oextremum__uniqueI)). 39.62/11.62 thf(1707,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) => (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 39.62/11.62 thf(253,axiom,((top_top_assn != bot_bot_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9230_assn__basic__inequalities_I5_J)). 39.62/11.62 thf(1371,plain,((~ (top_top_assn = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 39.62/11.62 thf(230,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Int__Un__eq_I4_J)). 39.62/11.62 thf(1312,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 39.62/11.62 thf(337,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_Un__Int__distrib)). 39.62/11.62 thf(1635,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 39.62/11.62 thf(157,axiom,((heap_Time_success_a = (^ [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ((heap_Time_execute_a @ A @ B) != none_P2651198173097904984it_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2618_success__def)). 39.62/11.62 thf(1058,plain,(((heap_Time_success_a) = (^ [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit]: ~ ((heap_Time_execute_a @ A @ B) = none_P2651198173097904984it_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 39.62/11.62 thf(166,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((? [D:nat]: ((member_nat @ D @ (sup_sup_set_nat @ A @ B)) & (C @ D))) = (? [D:nat]: ((C @ D) & (member_nat @ D @ A)) | ? [D:nat]: ((member_nat @ D @ B) & (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_bex__Un)). 39.62/11.62 thf(1092,plain,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((? [D:nat]: ((member_nat @ D @ (sup_sup_set_nat @ A @ B)) & (C @ D))) = (? [D:nat]: ((C @ D) & (member_nat @ D @ A)) | ? [D:nat]: ((member_nat @ D @ B) & (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 39.62/11.62 thf(498,axiom,((! [A:assn,B:produc3658429121746597890et_nat]: ((~ (! [C:produc3658429121746597890et_nat]: ~ (rep_assn @ A @ C))) <= (rep_assn @ (times_times_assn @ A @ top_top_assn) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9252_mod__star__trueE)). 39.62/11.62 thf(2166,plain,((! [A:assn,B:produc3658429121746597890et_nat]: (~ (! [C:produc3658429121746597890et_nat]: ~ (rep_assn @ A @ C)) | ~ (rep_assn @ (times_times_assn @ A @ top_top_assn) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 39.62/11.62 thf(55,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1645_dual__order_Oasym)). 39.62/11.62 thf(704,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 39.62/11.62 thf(338,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_Un__assoc)). 39.62/11.62 thf(1638,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 39.62/11.62 thf(247,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_Un__absorb)). 39.62/11.62 thf(1356,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 39.62/11.62 thf(31,axiom,((! [A:nat,B:set_nat,C:set_nat,D:(nat > $o)]: ((member_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C))))) => (D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2295_prop__restrict)). 39.62/11.62 thf(611,plain,((! [A:nat,B:set_nat,C:set_nat,D:(nat > $o)]: ((member_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C))))) => (D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 39.62/11.62 thf(79,axiom,((! [A:nat,B:set_nat,C:set_nat]: (((member_nat @ A @ C) <= (~ (member_nat @ A @ B))) <= (member_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_UnE)). 39.62/11.62 thf(787,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ C) | (member_nat @ A @ B) | ~ (member_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 39.62/11.62 thf(209,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_sup__absorb2)). 39.62/11.62 thf(1239,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 39.62/11.62 thf(447,axiom,((inf_inf_set_nat = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_inf_Ocommute)). 39.62/11.62 thf(1997,plain,(((inf_inf_set_nat) = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 39.62/11.62 thf(348,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_inf_OcoboundedI1)). 39.62/11.62 thf(1675,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 39.62/11.62 thf(8,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_1999_order_Ostrict__iff__not)). 39.62/11.62 thf(540,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)],[8])). 39.62/11.62 thf(133,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_2041_antisym__conv2)). 39.62/11.62 thf(990,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)],[133])). 39.62/11.62 thf(290,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_sup__bot_Oleft__neutral)). 39.62/11.62 thf(1492,plain,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 39.62/11.62 thf(362,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1422_boolean__algebra_Odisj__zero__right)). 39.62/11.62 thf(1722,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 39.62/11.62 thf(481,axiom,((! [A:$o,B:heap_e7401611519738050253t_unit]: ((rep_assn @ (pure_assn @ A) @ (produc7507926704131184380et_nat @ B @ bot_bot_set_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2432_mod__h__bot__iff_I1_J)). 39.62/11.62 thf(2116,plain,((! [A:$o,B:heap_e7401611519738050253t_unit]: ((rep_assn @ (pure_assn @ A) @ (produc7507926704131184380et_nat @ B @ bot_bot_set_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 39.62/11.62 thf(437,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_inf__greatest)). 39.62/11.62 thf(1969,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) => (ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 39.62/11.62 thf(96,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) = (B @ C))) => ((collect_nat @ A) = (collect_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Collect__cong)). 39.62/11.62 thf(863,plain,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) = (B @ C))) => ((collect_nat @ (A)) = (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 39.62/11.62 thf(405,axiom,((inf_inf_set_nat = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_inf__commute)). 39.62/11.62 thf(1853,plain,(((inf_inf_set_nat) = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 39.62/11.62 thf(262,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_2287_le__antisym)). 39.62/11.62 thf(1408,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)],[262])). 39.62/11.62 thf(78,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_1664_not__less__iff__gr__or__eq)). 39.62/11.62 thf(784,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)],[78])). 39.62/11.62 thf(172,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2011_order_Ostrict__trans1)). 39.62/11.62 thf(1117,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 39.62/11.62 thf(153,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) => (~ ((member_nat @ A @ B) => (~ (member_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_IntE)). 39.62/11.62 thf(1048,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) => (~ ((member_nat @ A @ B) => (~ (member_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 39.62/11.62 thf(65,axiom,((! [A:nat,B:(nat > $o),C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((B @ D) <= (! [E:nat]: ((B @ E) <= (ord_less_nat @ D @ E)))))) => (B @ C)) <= (! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2242_nat__descend__induct)). 39.62/11.62 thf(736,plain,((! [A:nat,B:(nat > $o),C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((B @ D) | ~ (! [E:nat]: ((B @ E) | ~ (ord_less_nat @ D @ E)))))) => (B @ C)) | ~ (! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 39.62/11.62 thf(103,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ B) <= (member_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_IntD1)). 39.62/11.62 thf(880,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ B) | ~ (member_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 39.62/11.62 thf(386,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((~ ((~ (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ C))) <= (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_sup_OboundedE)). 39.62/11.62 thf(1801,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (~ (~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ C)) | ~ (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 39.62/11.62 thf(162,axiom,((! [A:nat,B:set_nat,C:set_nat]: (((member_nat @ A @ C) <= (~ (member_nat @ A @ B))) => (member_nat @ A @ (sup_sup_set_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_UnCI)). 39.62/11.62 thf(1080,plain,((! [A:nat,B:set_nat,C:set_nat]: (((member_nat @ A @ C) | (member_nat @ A @ B)) => (member_nat @ A @ (sup_sup_set_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 39.62/11.62 thf(240,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_inf__le2)). 39.62/11.62 thf(1339,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 39.62/11.62 thf(484,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:assn]: (((abs_assn @ A) = B) <= (! [C:produc3658429121746597890et_nat]: ((A @ C) = (rep_assn @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2583_Abs__assn__eqI_I1_J)). 39.62/11.62 thf(2129,plain,((! [A:(produc3658429121746597890et_nat > $o),B:assn]: (((abs_assn @ (A)) = B) | ~ (! [C:produc3658429121746597890et_nat]: ((A @ C) = (rep_assn @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 39.62/11.62 thf(89,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((collect_nat @ (^ [C:nat]: ((A @ C) & (B @ C)))) = (inf_inf_set_nat @ (collect_nat @ A) @ (collect_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1820_Collect__conj__eq)). 39.62/11.62 thf(816,plain,((! [A:(nat > $o),B:(nat > $o)]: ((collect_nat @ (^ [C:nat]: ((A @ C) & (B @ C)))) = (inf_inf_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 39.62/11.62 thf(479,axiom,((! [A:assn,B:assn]: (((rep_assn @ A) = (rep_assn @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Rep__assn__inject)). 39.62/11.62 thf(2111,plain,((! [A:assn,B:assn]: (((rep_assn @ A) = (rep_assn @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 39.62/11.62 thf(365,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ (sup_sup_assn @ B @ C)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2872_ent__disjI1_H)). 39.62/11.62 thf(1731,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ (sup_sup_assn @ B @ C)) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 39.62/11.62 thf(125,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1669_dual__order_Ostrict__trans)). 39.62/11.62 thf(964,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 39.62/11.62 thf(242,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_sup_Ocobounded2)). 39.62/11.62 thf(1344,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 39.62/11.62 thf(278,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ C) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_inf_Obounded__iff)). 39.62/11.62 thf(1460,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = ((ord_less_eq_set_nat @ A @ C) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 39.62/11.62 thf(47,axiom,((! [A:(nat > $o)]: (((collect_nat @ A) = bot_bot_set_nat) = (! [B:nat]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Collect__empty__eq)). 39.62/11.62 thf(668,plain,((! [A:(nat > $o)]: (((collect_nat @ (A)) = bot_bot_set_nat) = (! [B:nat]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 39.62/11.62 thf(193,axiom,((! [A:heap_e7401611519738050253t_unit]: (in_range @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2450_in__range__empty)). 39.62/11.62 thf(1177,plain,((! [A:heap_e7401611519738050253t_unit]: (in_range @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 39.62/11.62 thf(116,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1697_order__less__asym_H)). 39.62/11.62 thf(932,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 39.62/11.62 thf(146,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1610_gt__ex)). 39.62/11.62 thf(1029,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 39.62/11.62 thf(108,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2280_less__irrefl__nat)). 39.62/11.62 thf(895,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 39.62/11.62 thf(470,axiom,((! [A:$o,B:$o]: ((times_times_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) & (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2445_merge__pure__star)). 39.62/11.62 thf(2075,plain,((! [A:$o,B:$o]: ((times_times_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) & (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 39.62/11.62 thf(73,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1674_order_Ostrict__implies__not__eq)). 39.62/11.62 thf(768,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 39.62/11.62 thf(211,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_Un__empty__left)). 39.62/11.62 thf(1245,plain,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 39.62/11.62 thf(98,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) => (member_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_IntD2)). 39.62/11.62 thf(868,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (inf_inf_set_nat @ B @ C)) => (member_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 39.62/11.62 thf(104,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_2005_order_Ostrict__trans2)). 39.62/11.62 thf(883,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)],[104])). 39.62/11.62 thf(142,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) => (B @ C))) => (ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1540_Collect__mono)). 39.62/11.62 thf(1015,plain,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) => (B @ C))) => (ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 39.62/11.62 thf(378,axiom,((! [A:set_nat,B:set_nat]: ((A = (sup_sup_set_nat @ A @ B)) => (ord_less_eq_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_sup_OorderI)). 39.62/11.62 thf(1775,plain,((! [A:set_nat,B:set_nat]: ((A = (sup_sup_set_nat @ A @ B)) => (ord_less_eq_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 39.62/11.62 thf(475,axiom,((rep_assn @ p @ (produc7507926704131184380et_nat @ h2 @ as1))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_M1)). 39.62/11.62 thf(2101,plain,((rep_assn @ p @ (produc7507926704131184380et_nat @ h2 @ as1))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 39.62/11.62 thf(213,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ B) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_le__supI)). 39.62/11.62 thf(1250,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ B) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 39.62/11.62 thf(313,axiom,((inf_inf_set_nat = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_inf__sup__aci_I1_J)). 39.62/11.62 thf(1562,plain,(((inf_inf_set_nat) = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 39.62/11.62 thf(114,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => (((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D)))) <= (! [D:nat]: (A @ D @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1655_linorder__less__wlog)). 39.62/11.62 thf(912,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) | ~ (! [D:nat]: (A @ D @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 39.62/11.62 thf(1,conjecture,((rep_assn @ (times_times_assn @ (q @ r2) @ r) @ (produc7507926704131184380et_nat @ h @ (hoare_new_addrs @ h2 @ as @ h)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 39.62/11.62 thf(2,negated_conjecture,((~ (rep_assn @ (times_times_assn @ (q @ r2) @ r) @ (produc7507926704131184380et_nat @ h @ (hoare_new_addrs @ h2 @ as @ h))))),inference(neg_conjecture,[status(cth)],[1])). 39.62/11.62 thf(521,plain,((~ (rep_assn @ (times_times_assn @ (q @ r2) @ r) @ (produc7507926704131184380et_nat @ h @ (hoare_new_addrs @ h2 @ as @ h))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 39.62/11.62 thf(515,axiom,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((hoare_new_addrs @ A @ B @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_new__addr__refl)). 39.62/11.62 thf(2212,plain,((! [A:heap_e7401611519738050253t_unit,B:set_nat]: ((hoare_new_addrs @ A @ B @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 39.62/11.62 thf(124,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1631_ord__less__eq__trans)). 39.62/11.62 thf(959,plain,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 39.62/11.62 thf(148,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_1702_order__less__trans)). 39.62/11.62 thf(1034,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)],[148])). 39.62/11.62 thf(319,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1347_order__eq__refl)). 39.62/11.62 thf(1583,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 39.62/11.62 thf(389,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (relH @ A @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_relH__sym)). 39.62/11.62 thf(1809,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (relH @ A @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 39.62/11.62 thf(474,axiom,((! [A:assn,B:assn,C:assn]: ((A = (times_times_assn @ B @ C)) => (dvd_dvd_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8061_dvdI)). 39.62/11.62 thf(2096,plain,((! [A:assn,B:assn,C:assn]: ((A = (times_times_assn @ B @ C)) => (dvd_dvd_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 39.62/11.62 thf(199,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ B @ C)) @ (inf_inf_set_nat @ C @ A)) = (inf_inf_set_nat @ (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ B @ C)) @ (sup_sup_set_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_Un__Int__crazy)). 39.62/11.62 thf(1203,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ B @ C)) @ (inf_inf_set_nat @ C @ A)) = (inf_inf_set_nat @ (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ B @ C)) @ (sup_sup_set_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 39.62/11.62 thf(51,axiom,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1521_subsetD)). 39.62/11.62 thf(680,plain,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 39.62/11.62 thf(11,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((collect_nat @ (^ [C:nat]: ((A @ C) | (B @ C)))) = (sup_sup_set_nat @ (collect_nat @ A) @ (collect_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1849_Collect__disj__eq)). 39.62/11.62 thf(548,plain,((! [A:(nat > $o),B:(nat > $o)]: ((collect_nat @ (^ [C:nat]: ((A @ C) | (B @ C)))) = (sup_sup_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 39.62/11.62 thf(88,axiom,((! [A:set_nat]: ((A != bot_bot_set_nat) => (~ (! [B:nat]: ~ (member_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2223_set__notEmptyE)). 39.62/11.62 thf(812,plain,((! [A:set_nat]: ((~ (A = bot_bot_set_nat)) => (~ (! [B:nat]: ~ (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 39.62/11.62 thf(33,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F))))) <= (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2362_pinf_I2_J)). 39.62/11.62 thf(617,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F)))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) | ~ (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 39.62/11.62 thf(282,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_sup_Obounded__iff)). 39.62/11.62 thf(1472,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (ord_less_eq_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 39.62/11.62 thf(143,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_2281_nat__less__induct)). 39.62/11.62 thf(1018,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)],[143])). 39.62/11.62 thf(433,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_le__iff__inf)). 39.62/11.62 thf(1958,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 39.62/11.62 thf(13,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1766_order__less__imp__not__eq)). 39.62/11.62 thf(553,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 39.62/11.62 thf(195,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2284_le__refl)). 39.62/11.62 thf(1181,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 39.62/11.62 thf(421,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:set_nat]: (((relH @ D @ B @ C) <= (ord_less_eq_set_nat @ D @ A)) <= (relH @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1250_relH__subset)). 39.62/11.62 thf(1905,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:set_nat]: ((relH @ D @ B @ C) | ~ (ord_less_eq_set_nat @ D @ A) | ~ (relH @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 39.62/11.62 thf(266,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_sup__inf__distrib2)). 39.62/11.62 thf(1420,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 39.62/11.62 thf(221,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1444_boolean__algebra_Oconj__disj__distrib2)). 39.62/11.62 thf(1277,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 39.62/11.62 thf(482,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_2771_ab__semigroup__mult__class_Omult_Oleft__commute)). 39.62/11.62 thf(2124,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)],[482])). 39.62/11.62 thf(402,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_sup__inf__absorb)). 39.62/11.62 thf(1845,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 39.62/11.62 thf(22,axiom,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2922_mult_Oright__neutral)). 39.62/11.62 thf(580,plain,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 39.62/11.62 thf(38,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_2402_minf_I7_J)). 39.62/11.62 thf(640,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)],[38])). 39.62/11.62 thf(145,axiom,((! [A:nat,B:set_nat]: ((B != bot_bot_set_nat) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2218_memb__imp__not__empty)). 39.62/11.62 thf(1025,plain,((! [A:nat,B:set_nat]: (~ (B = bot_bot_set_nat) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 39.62/11.62 thf(161,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]: ((((A @ F) & (C @ F)) = ((B @ F) & (D @ F))) <= (ord_less_nat @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2382_minf_I1_J)). 39.62/11.62 thf(1070,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((((A @ F) & (C @ F)) = ((B @ F) & (D @ F))) | ~ (ord_less_nat @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 39.62/11.62 thf(127,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1949_order__le__less)). 39.62/11.62 thf(971,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 39.62/11.62 thf(341,axiom,((! [A:$o,B:$o]: ((sup_sup_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) | (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2446_merge__pure__or)). 39.62/11.62 thf(1647,plain,((! [A:$o,B:$o]: ((sup_sup_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) | (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 39.62/11.62 thf(427,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Un__Int__eq_I2_J)). 39.62/11.62 thf(1941,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 39.62/11.62 thf(252,axiom,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_prod_Oinject)). 39.62/11.62 thf(1368,plain,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 39.62/11.62 thf(219,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_inf__sup__ord_I3_J)). 39.62/11.62 thf(1267,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 39.62/11.62 thf(495,axiom,((! [A:assn]: ((abs_assn @ (rep_assn @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2535_Rep__assn__inverse)). 39.62/11.62 thf(2160,plain,((! [A:assn]: ((abs_assn @ (rep_assn @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 39.62/11.62 thf(134,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1621_order_Oasym)). 39.62/11.62 thf(993,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 39.62/11.62 thf(58,axiom,((! [A:set_nat,B:set_nat]: ((! [C:nat]: ((~ (member_nat @ C @ B)) <= (member_nat @ C @ A))) => ((inf_inf_set_nat @ A @ B) = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1491_disjointI)). 39.62/11.62 thf(712,plain,((! [A:set_nat,B:set_nat]: ((! [C:nat]: (~ (member_nat @ C @ B) | ~ (member_nat @ C @ A))) => ((inf_inf_set_nat @ A @ B) = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 39.62/11.62 thf(14,axiom,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_all__not__in__conv)). 39.62/11.62 thf(557,plain,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 39.62/11.62 thf(298,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2285_le__trans)). 39.62/11.62 thf(1516,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 39.62/11.62 thf(324,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_sup__bot__right)). 39.62/11.62 thf(1598,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 39.62/11.62 thf(466,axiom,((~ (! [A:set_nat,B:set_nat]: ((((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) => ((~ (rep_assn @ r @ (produc7507926704131184380et_nat @ h2 @ B))) <= (rep_assn @ p @ (produc7507926704131184380et_nat @ h2 @ A)))) <= (as = (sup_sup_set_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062as1_Aas2_O_A_092_060lbrakk_062as_A_061_Aas1_A_092_060union_062_Aas2_059_Aas1_A_092_060inter_062_Aas2_A_061_A_123_125_059_A_Ih_M_Aas1_J_A_092_060Turnstile_062_AP_059_A_Ih_M_Aas2_J_A_092_060Turnstile_062_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 39.62/11.62 thf(2060,plain,((~ (! [A:set_nat,B:set_nat]: ((((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) => (~ (rep_assn @ r @ (produc7507926704131184380et_nat @ h2 @ B)) | ~ (rep_assn @ p @ (produc7507926704131184380et_nat @ h2 @ A)))) | ~ (as = (sup_sup_set_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 39.62/11.62 thf(260,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((C = D) => (ord_less_eq_nat @ A @ D)) <= (ord_less_eq_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2201_ord__eq__le__eq__trans)). 39.62/11.62 thf(1400,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) => (ord_less_eq_nat @ A @ D)) | ~ (ord_less_eq_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 39.62/11.62 thf(315,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C))) = (ord_less_eq_set_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1255_Un__Int__assoc__eq)). 39.62/11.62 thf(1566,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C))) = (ord_less_eq_set_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 39.62/11.62 thf(488,axiom,((! [A:assn,B:assn]: ((! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (rep_assn @ B @ C))) => (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2865_entailsI)). 39.62/11.62 thf(2143,plain,((! [A:assn,B:assn]: ((! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (rep_assn @ B @ C))) => (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 39.62/11.62 thf(452,axiom,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ((! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:a,G:heap_e7401611519738050253t_unit,H:nat]: (((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H)))) & (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G))) & (relH @ (collect_nat @ (^ [I:nat]: (~ (member_nat @ I @ E) & (ord_less_nat @ I @ (lim_Product_unit @ D))))) @ D @ G) & (ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)))))) => (hoare_hoare_triple_a @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2231_hoare__tripleI)). 39.62/11.62 thf(2012,plain,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn)]: ((! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:a,G:heap_e7401611519738050253t_unit,H:nat]: (((heap_Time_execute_a @ B @ D) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ F @ (produc584006145561248582it_nat @ G @ H)))) & (rep_assn @ (C @ F) @ (produc7507926704131184380et_nat @ G @ (hoare_new_addrs @ D @ E @ G))) & (relH @ (collect_nat @ (^ [I:nat]: (~ (member_nat @ I @ E) & (ord_less_nat @ I @ (lim_Product_unit @ D))))) @ D @ G) & (ord_less_eq_nat @ (lim_Product_unit @ D) @ (lim_Product_unit @ G)))))) => (hoare_hoare_triple_a @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 39.62/11.62 thf(155,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_2378_pinf_I7_J)). 39.62/11.62 thf(1053,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)],[155])). 39.62/11.62 thf(360,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_inf_Oabsorb1)). 39.62/11.62 thf(1716,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 39.62/11.62 thf(497,axiom,((rep_assn @ (q @ r2) @ (produc7507926704131184380et_nat @ h @ (hoare_new_addrs @ h2 @ as1 @ h)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MDL)). 39.62/11.62 thf(2165,plain,((rep_assn @ (q @ r2) @ (produc7507926704131184380et_nat @ h @ (hoare_new_addrs @ h2 @ as1 @ h)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 39.62/11.62 thf(391,axiom,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ B @ A) = B) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1238_Un__absorb2)). 39.62/11.62 thf(1813,plain,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ B @ A) = B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 39.62/11.62 thf(81,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ C @ B)) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_UnI2)). 39.62/11.62 thf(791,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (sup_sup_set_nat @ C @ B)) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 39.62/11.62 thf(59,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_2282_infinite__descent)). 39.62/11.62 thf(717,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)],[59])). 39.62/11.62 thf(217,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_2870_ent__disjI1)). 39.62/11.62 thf(1262,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)],[217])). 39.62/11.62 thf(441,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) => (~ ((ord_less_eq_set_nat @ A @ C) => (~ (ord_less_eq_set_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_le__supE)). 39.62/11.62 thf(1980,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) => (~ ((ord_less_eq_set_nat @ A @ C) => (~ (ord_less_eq_set_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 39.62/11.62 thf(306,axiom,((heap_Time_effect_a = (^ [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:a,E:nat]: ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ D @ (produc584006145561248582it_nat @ C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2466_effect__def)). 39.62/11.62 thf(1538,plain,(((heap_Time_effect_a) = (^ [A:heap_Time_Heap_a,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit,D:a,E:nat]: ((heap_Time_execute_a @ A @ B) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ D @ (produc584006145561248582it_nat @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 39.62/11.62 thf(461,axiom,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: (((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:heap_e7401611519738050253t_unit,G:a,H:nat]: ((rep_assn @ (C @ G) @ (produc7507926704131184380et_nat @ F @ (hoare_new_addrs @ D @ E @ F))) & (heap_Time_effect_a @ B @ D @ F @ G @ H)))) <= (hoare_hoare_triple_a @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2433_hoare__triple__effect)). 39.62/11.62 thf(2044,plain,((! [A:assn,B:heap_Time_Heap_a,C:(a > assn),D:heap_e7401611519738050253t_unit,E:set_nat]: (((rep_assn @ A @ (produc7507926704131184380et_nat @ D @ E)) => (? [F:heap_e7401611519738050253t_unit,G:a,H:nat]: ((rep_assn @ (C @ G) @ (produc7507926704131184380et_nat @ F @ (hoare_new_addrs @ D @ E @ F))) & (heap_Time_effect_a @ B @ D @ F @ G @ H)))) | ~ (hoare_hoare_triple_a @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 39.62/11.62 thf(177,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2318_pinf_I6_J)). 39.62/11.62 thf(1130,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 39.62/11.62 thf(224,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_Int__lower1)). 39.62/11.62 thf(1285,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 39.62/11.62 thf(205,axiom,((! [A:set_nat,B:set_nat,C:heap_e7401611519738050253t_unit]: ((ord_less_eq_set_nat @ A @ B) => ((in_range @ (produc7507926704131184380et_nat @ C @ B)) => (in_range @ (produc7507926704131184380et_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2462_in__range__subset)). 39.62/11.62 thf(1220,plain,((! [A:set_nat,B:set_nat,C:heap_e7401611519738050253t_unit]: ((ord_less_eq_set_nat @ A @ B) => ((in_range @ (produc7507926704131184380et_nat @ C @ B)) => (in_range @ (produc7507926704131184380et_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 39.62/11.62 thf(112,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2310_minf_I6_J)). 39.62/11.62 thf(907,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 39.62/11.62 thf(164,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) = (! [C:nat]: ((member_nat @ C @ A) => (! [D:nat]: ((member_nat @ D @ B) => (C != D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_disjoint__iff__not__equal)). 39.62/11.62 thf(1085,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = bot_bot_set_nat) = (! [C:nat]: ((member_nat @ C @ A) => (! [D:nat]: ((member_nat @ D @ B) => (~ (C = D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 39.62/11.62 thf(20,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B != A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1985_dual__order_Ostrict__iff__order)). 39.62/11.62 thf(576,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (B = A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 39.62/11.62 thf(464,axiom,((relH @ as2 @ h2 @ h)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062relH_Aas2_Ah_Ah_H_092_060close_062)). 39.62/11.62 thf(2056,plain,((relH @ as2 @ h2 @ h)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 39.62/11.62 thf(182,axiom,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3062_mult_Ocomm__neutral)). 39.62/11.62 thf(1140,plain,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 39.62/11.62 thf(346,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_1293_order__trans)). 39.62/11.62 thf(1670,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)],[346])). 39.62/11.62 thf(95,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 @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2243_less__mono__imp__le__mono)). 39.62/11.62 thf(859,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 @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 39.62/11.62 thf(330,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_empty__subsetI)). 39.62/11.62 thf(1617,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 39.62/11.62 thf(308,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_Int__assoc)). 39.62/11.62 thf(1543,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 39.62/11.62 thf(375,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = (inf_inf_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_inf_OorderI)). 39.62/11.62 thf(1766,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = (inf_inf_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 39.62/11.62 thf(42,axiom,((relH @ (collect_nat @ (^ [A:nat]: ((ord_less_nat @ A @ (lim_Product_unit @ h2)) & ~ (member_nat @ A @ as1)))) @ h2 @ h)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1504_RH1)). 39.62/11.62 thf(656,plain,((relH @ (collect_nat @ (^ [A:nat]: ((ord_less_nat @ A @ (lim_Product_unit @ h2)) & ~ (member_nat @ A @ as1)))) @ h2 @ h)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 39.62/11.62 thf(144,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1991_dual__order_Oorder__iff__strict)). 39.62/11.62 thf(1023,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 39.62/11.62 thf(246,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_inf__left__commute)). 39.62/11.62 thf(1353,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ B @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 39.62/11.62 thf(27,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1943_order__less__le)). 39.62/11.62 thf(600,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 39.62/11.62 thf(287,axiom,((as = (sup_sup_set_nat @ as1 @ as2))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__092_060open_062as_A_061_Aas1_A_092_060union_062_Aas2_092_060close_062)). 39.62/11.62 thf(1485,plain,((as = (sup_sup_set_nat @ as1 @ as2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 39.62/11.62 thf(438,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_inf__le1)). 39.62/11.62 thf(1972,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (inf_inf_set_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 39.62/11.62 thf(371,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_sup__bot__left)). 39.62/11.62 thf(1749,plain,((! [A:set_nat]: ((sup_sup_set_nat @ bot_bot_set_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 39.62/11.62 thf(268,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1307_dual__order_Oantisym)). 39.62/11.62 thf(1427,plain,((! [A:nat,B:nat]: ((B = A) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 39.62/11.62 thf(294,axiom,((! [A:assn,B:$o]: ((entails @ A @ (pure_assn @ B)) = ((entails @ A @ one_one_assn) & ! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2889_ent__pure__post__iff__sng)). 39.62/11.62 thf(1504,plain,((! [A:assn,B:$o]: ((entails @ A @ (pure_assn @ B)) = ((entails @ A @ one_one_assn) & ! [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) => (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 39.62/11.62 thf(62,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_1652_exists__least__iff)). 39.62/11.62 thf(727,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)],[62])). 39.62/11.62 thf(400,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_inf__right__idem)). 39.62/11.62 thf(1839,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 39.62/11.62 thf(34,axiom,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_empty__iff)). 39.62/11.62 thf(627,plain,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 39.62/11.62 thf(471,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_3563_power__commutes)). 39.62/11.62 thf(2088,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)],[471])). 39.62/11.62 thf(436,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_Int__Un__distrib2)). 39.62/11.62 thf(1966,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 39.62/11.62 thf(352,axiom,((~ (! [A:a,B:heap_e7401611519738050253t_unit]: (((rep_assn @ (q @ A) @ (produc7507926704131184380et_nat @ B @ (hoare_new_addrs @ h2 @ as1 @ B))) => ((relH @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (lim_Product_unit @ h2)) & ~ (member_nat @ C @ as1)))) @ h2 @ B) => (~ (ord_less_eq_nat @ (lim_Product_unit @ h2) @ (lim_Product_unit @ B))))) <= (? [C:nat]: ((heap_Time_execute_a @ c @ h2) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ A @ (produc584006145561248582it_nat @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1467__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062r_Ah_H_At_O_A_092_060lbrakk_062execute_Ac_Ah_A_061_ASome_A_Ir_M_Ah_H_M_At_J_059_A_Ih_H_M_Anew__addrs_Ah_Aas1_Ah_H_J_A_092_060Turnstile_062_AQ_Ar_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_Ah_Ah_H_059_Alim_Ah_A_092_060le_062_Alim_Ah_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 39.62/11.62 thf(1685,plain,((~ (! [A:a,B:heap_e7401611519738050253t_unit]: (((rep_assn @ (q @ A) @ (produc7507926704131184380et_nat @ B @ (hoare_new_addrs @ h2 @ as1 @ B))) => ((relH @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (lim_Product_unit @ h2)) & ~ (member_nat @ C @ as1)))) @ h2 @ B) => (~ (ord_less_eq_nat @ (lim_Product_unit @ h2) @ (lim_Product_unit @ B))))) | ~ (? [C:nat]: ((heap_Time_execute_a @ c @ h2) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ A @ (produc584006145561248582it_nat @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 39.62/11.62 thf(430,axiom,((hoare_hoare_triple_a @ p @ c @ q)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_assms)). 39.62/11.62 thf(1949,plain,((hoare_hoare_triple_a @ p @ c @ (q))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 39.62/11.62 thf(48,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1905_order__less__le__trans)). 39.62/11.62 thf(671,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 39.62/11.62 thf(111,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2390_minf_I3_J)). 39.62/11.62 thf(903,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 39.62/11.62 thf(516,axiom,((! [A:assn,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ B @ bot_bot_set_nat)) = (rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mod__h__bot__indep)). 39.62/11.62 thf(2215,plain,((! [A:assn,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((rep_assn @ A @ (produc7507926704131184380et_nat @ B @ bot_bot_set_nat)) = (rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 39.62/11.62 thf(70,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2354_verit__comp__simplify1_I1_J)). 39.62/11.62 thf(759,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 39.62/11.62 thf(380,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_sup__inf__distrib1)). 39.62/11.62 thf(1781,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 39.62/11.62 thf(506,axiom,((! [A:assn,B:assn,C:heap_e7401611519738050253t_unit]: ((rep_assn @ (times_times_assn @ A @ B) @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) = ((rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) & (rep_assn @ B @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mod__h__bot__iff_I5_J)). 39.62/11.62 thf(2187,plain,((! [A:assn,B:assn,C:heap_e7401611519738050253t_unit]: ((rep_assn @ (times_times_assn @ A @ B) @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) = ((rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) & (rep_assn @ B @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 39.62/11.62 thf(188,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_Int__left__absorb)). 39.62/11.62 thf(1157,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 39.62/11.62 thf(398,axiom,((uminus_uminus_assn = (^ [A:assn]: (abs_assn @ (^ [B:produc3658429121746597890et_nat]: (~ (rep_assn @ A @ B) & (in_range @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5339_uminus__assn__def)). 39.62/11.62 thf(1834,plain,(((uminus_uminus_assn) = (^ [A:assn]: (abs_assn @ (^ [B:produc3658429121746597890et_nat]: (~ (rep_assn @ A @ B) & (in_range @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 39.62/11.62 thf(520,axiom,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ (times_times_assn @ A @ B) @ C) => (dvd_dvd_assn @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8081_dvd__mult__left)). 39.62/11.62 thf(2226,plain,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ (times_times_assn @ A @ B) @ C) => (dvd_dvd_assn @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 39.62/11.62 thf(276,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_2288_nat__le__linear)). 39.62/11.62 thf(1453,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)],[276])). 39.62/11.62 thf(409,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_inf_Oabsorb__iff2)). 39.62/11.62 thf(1866,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 39.62/11.62 thf(468,axiom,((rep_assn @ r @ (produc7507926704131184380et_nat @ h @ as2))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062)). 39.62/11.62 thf(2071,plain,((rep_assn @ r @ (produc7507926704131184380et_nat @ h @ as2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 39.62/11.62 thf(366,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_inf_OboundedI)). 39.62/11.62 thf(1734,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (inf_inf_set_nat @ B @ C)) | ~ (ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 39.62/11.62 thf(388,axiom,(((inf_inf_set_nat @ (hoare_new_addrs @ h2 @ as1 @ h) @ as2) = bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_DJN)). 39.62/11.62 thf(1807,plain,(((inf_inf_set_nat @ (hoare_new_addrs @ h2 @ as1 @ h) @ as2) = bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 39.62/11.62 thf(321,axiom,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_Un__empty__right)). 39.62/11.62 thf(1590,plain,((! [A:set_nat]: ((sup_sup_set_nat @ A @ bot_bot_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 39.62/11.62 thf(235,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2349_verit__comp__simplify1_I2_J)). 39.62/11.62 thf(1326,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 39.62/11.62 thf(214,axiom,((! [A:(produc3260487557148687353it_nat > $o),B:produc3260487557148687353it_nat]: ((A @ B) <= (! [C:a,D:heap_e7401611519738050253t_unit,E:nat]: (A @ (produc9178034014595674355it_nat @ C @ (produc584006145561248582it_nat @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_prod__induct3)). 39.62/11.62 thf(1253,plain,((! [A:(produc3260487557148687353it_nat > $o),B:produc3260487557148687353it_nat]: ((A @ B) | ~ (! [C:a,D:heap_e7401611519738050253t_unit,E:nat]: (A @ (produc9178034014595674355it_nat @ C @ (produc584006145561248582it_nat @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 39.62/11.62 thf(170,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1917_order__neq__le__trans)). 39.62/11.62 thf(1101,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 39.62/11.62 thf(40,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2374_pinf_I5_J)). 39.62/11.62 thf(652,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 39.62/11.62 thf(449,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_1375_linorder__le__cases)). 39.62/11.62 thf(2004,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)],[449])). 39.62/11.62 thf(456,axiom,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) => (~ ((B != D) <= (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Pair__inject)). 39.62/11.62 thf(2026,plain,((! [A:a,B:produc6653097349344004940it_nat,C:a,D:produc6653097349344004940it_nat]: (((produc9178034014595674355it_nat @ A @ B) = (produc9178034014595674355it_nat @ C @ D)) => (~ (~ (B = D) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 39.62/11.62 thf(36,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_2276_nat__neq__iff)). 39.62/11.62 thf(632,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)],[36])). 39.62/11.62 thf(394,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2286_eq__imp__le)). 39.62/11.62 thf(1822,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 39.62/11.62 thf(135,axiom,((! [A:set_nat]: ((? [B:nat]: (member_nat @ B @ A)) = (A != bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_ex__in__conv)). 39.62/11.62 thf(995,plain,((! [A:set_nat]: ((? [B:nat]: (member_nat @ B @ A)) = (~ (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 39.62/11.62 thf(241,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_inf__assoc)). 39.62/11.62 thf(1341,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 39.62/11.62 thf(67,axiom,((! [A:set_nat,B:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ B)) = (! [C:nat]: ((member_nat @ C @ A) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1781_subset__Collect__conv)). 39.62/11.62 thf(748,plain,((! [A:set_nat,B:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (B))) = (! [C:nat]: ((member_nat @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 39.62/11.62 thf(451,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_le__supI2)). 39.62/11.62 thf(2009,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 39.62/11.62 thf(510,axiom,((! [A:assn,B:assn,C:$o]: ((entails @ A @ (times_times_assn @ B @ (pure_assn @ C))) = ((entails @ A @ B) & ! [D:produc3658429121746597890et_nat]: ((rep_assn @ A @ D) => (C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2855_ent__pure__post__iff)). 39.62/11.62 thf(2198,plain,((! [A:assn,B:assn,C:$o]: ((entails @ A @ (times_times_assn @ B @ (pure_assn @ C))) = ((entails @ A @ B) & ! [D:produc3658429121746597890et_nat]: ((rep_assn @ A @ D) => (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 39.62/11.62 thf(202,axiom,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2874_ent__disjI1__direct)). 39.62/11.62 thf(1212,plain,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 39.62/11.62 thf(327,axiom,((inf_inf_set_nat = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_Int__commute)). 39.62/11.62 thf(1607,plain,(((inf_inf_set_nat) = (^ [A:set_nat,B:set_nat]: (inf_inf_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 39.62/11.62 thf(297,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_inf_Oright__idem)). 39.62/11.62 thf(1513,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ B) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 39.62/11.62 thf(446,axiom,((! [A:produc3658429121746597890et_nat]: ((rep_assn @ top_top_assn @ A) = (in_range @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9235_mod__true)). 39.62/11.62 thf(1994,plain,((! [A:produc3658429121746597890et_nat]: ((rep_assn @ top_top_assn @ A) = (in_range @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 39.62/11.62 thf(152,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ B) <= (member_nat @ C @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1516_in__mono)). 39.62/11.62 thf(1045,plain,((! [A:set_nat,B:set_nat,C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 39.62/11.62 thf(46,axiom,((ord_less_eq_set_nat @ as2 @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as1) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1511__092_060open_062as2_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062)). 39.62/11.62 thf(667,plain,((ord_less_eq_set_nat @ as2 @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as1) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 39.62/11.62 thf(226,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_sup__left__idem)). 39.62/11.62 thf(1294,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 39.62/11.62 thf(418,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_inf_Oassoc)). 39.62/11.62 thf(1893,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ A @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 39.62/11.62 thf(458,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = A) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_Int__absorb2)). 39.62/11.62 thf(2036,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 39.62/11.62 thf(229,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_1259_nle__le)). 39.62/11.62 thf(1309,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)],[229])). 39.62/11.62 thf(272,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B) <= (ord_less_eq_set_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1218_Un__least)). 39.62/11.62 thf(1444,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B) | ~ (ord_less_eq_set_nat @ C @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 39.62/11.62 thf(271,axiom,((! [A:assn]: (entails @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2861_ent__refl)). 39.62/11.62 thf(1442,plain,((! [A:assn]: (entails @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 39.62/11.62 thf(422,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((~ (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ C @ B)) => (((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))))))) <= ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1263_le__cases3)). 39.62/11.62 thf(1908,plain,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => ((~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ B)) => ((~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))))))) | ~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 39.62/11.62 thf(244,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_373_star__or__dist1)). 39.62/11.62 thf(1348,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)],[244])). 39.62/11.62 thf(476,axiom,(((heap_Time_execute_a @ c @ h2) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ r2 @ (produc584006145561248582it_nat @ h @ t))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_EX)). 39.62/11.62 thf(2102,plain,(((heap_Time_execute_a @ c @ h2) = (some_P7913643980934408916it_nat @ (produc9178034014595674355it_nat @ r2 @ (produc584006145561248582it_nat @ h @ t))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 39.62/11.62 thf(349,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_Int__absorb)). 39.62/11.62 thf(1678,plain,((! [A:set_nat]: ((inf_inf_set_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 39.62/11.62 thf(126,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2279_less__not__refl3)). 39.62/11.62 thf(967,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 39.62/11.62 thf(168,axiom,(((('?') @ option3562590408128118217it_nat) = (^ [A:(option3562590408128118217it_nat > $o)]: (? [B:produc3260487557148687353it_nat]: (A @ (some_P7913643980934408916it_nat @ B)) | (A @ none_P2651198173097904984it_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2566_split__option__ex)). 39.62/11.62 thf(1097,plain,(((('?') @ option3562590408128118217it_nat) = (^ [A:(option3562590408128118217it_nat > $o)]: (? [B:produc3260487557148687353it_nat]: (A @ (some_P7913643980934408916it_nat @ B)) | (A @ none_P2651198173097904984it_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 39.62/11.62 thf(309,axiom,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_sup__eq__bot__iff)). 39.62/11.62 thf(1546,plain,((! [A:set_nat,B:set_nat]: (((sup_sup_set_nat @ A @ B) = bot_bot_set_nat) = ((A = bot_bot_set_nat) & (B = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 39.62/11.62 thf(333,axiom,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_inf__bot__left)). 39.62/11.62 thf(1625,plain,((! [A:set_nat]: ((inf_inf_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 39.62/11.62 thf(443,axiom,((! [A:assn,B:assn]: ((entails @ A @ B) => ((A = B) <= (entails @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2862_ent__iffI)). 39.62/11.62 thf(1986,plain,((! [A:assn,B:assn]: ((entails @ A @ B) => ((A = B) | ~ (entails @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 39.62/11.62 thf(212,axiom,((sup_sup_set_nat = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_inf__sup__aci_I5_J)). 39.62/11.62 thf(1248,plain,(((sup_sup_set_nat) = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 39.62/11.62 thf(374,axiom,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: ((~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (~ (? [F:set_nat,G:set_nat]: ((E = (sup_sup_set_nat @ F @ G)) & (B @ (produc7507926704131184380et_nat @ D @ G)) & (A @ (produc7507926704131184380et_nat @ D @ F)) & ((inf_inf_set_nat @ F @ G) = bot_bot_set_nat))))))) <= (times_assn_raw @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_times__assn__raw_Oelims_I2_J)). 39.62/11.62 thf(1757,plain,((! [A:(produc3658429121746597890et_nat > $o),B:(produc3658429121746597890et_nat > $o),C:produc3658429121746597890et_nat]: (~ (! [D:heap_e7401611519738050253t_unit,E:set_nat]: ((C = (produc7507926704131184380et_nat @ D @ E)) => (~ (? [F:set_nat,G:set_nat]: ((E = (sup_sup_set_nat @ F @ G)) & (B @ (produc7507926704131184380et_nat @ D @ G)) & (A @ (produc7507926704131184380et_nat @ D @ F)) & ((inf_inf_set_nat @ F @ G) = bot_bot_set_nat)))))) | ~ (times_assn_raw @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 39.62/11.62 thf(285,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_inf__sup__aci_I4_J)). 39.62/11.62 thf(1480,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (inf_inf_set_nat @ A @ B)) = (inf_inf_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 39.62/11.62 thf(517,axiom,((! [A:heap_e7401611519738050253t_unit]: (rep_assn @ top_top_assn @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9257_mod__h__bot__iff_I2_J)). 39.62/11.62 thf(2218,plain,((! [A:heap_e7401611519738050253t_unit]: (rep_assn @ top_top_assn @ (produc7507926704131184380et_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 39.62/11.62 thf(179,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2322_verit__comp__simplify1_I3_J)). 39.62/11.62 thf(1133,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 39.62/11.62 thf(363,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Un__Int__eq_I4_J)). 39.62/11.62 thf(1725,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 39.62/11.62 thf(222,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ B) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_sup_OboundedI)). 39.62/11.62 thf(1280,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ B) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ C) @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 39.62/11.62 thf(322,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_inf__sup__ord_I4_J)). 39.62/11.62 thf(1593,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 39.62/11.62 thf(256,axiom,((! [A:$o,B:$o]: (((pure_assn @ A) = (pure_assn @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2444_pure__assn__eq__conv)). 39.62/11.62 thf(1380,plain,((! [A:$o,B:$o]: (((pure_assn @ A) = (pure_assn @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 39.62/11.62 thf(302,axiom,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (in_range @ (produc7507926704131184380et_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2460_relH__in__rangeI_I1_J)). 39.62/11.62 thf(1527,plain,((! [A:set_nat,B:heap_e7401611519738050253t_unit,C:heap_e7401611519738050253t_unit]: ((relH @ A @ B @ C) => (in_range @ (produc7507926704131184380et_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 39.62/11.62 thf(347,axiom,((sup_sup_assn = (^ [A:assn,B:assn]: (abs_assn @ (^ [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) | (rep_assn @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2597_sup__assn__def)). 39.62/11.62 thf(1673,plain,(((sup_sup_assn) = (^ [A:assn,B:assn]: (abs_assn @ (^ [C:produc3658429121746597890et_nat]: ((rep_assn @ A @ C) | (rep_assn @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 39.62/11.62 thf(250,axiom,((! [A:assn,B:assn,C:heap_e7401611519738050253t_unit]: ((rep_assn @ (sup_sup_assn @ A @ B) @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) = ((rep_assn @ B @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) | (rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_mod__h__bot__iff_I7_J)). 39.62/11.62 thf(1363,plain,((! [A:assn,B:assn,C:heap_e7401611519738050253t_unit]: ((rep_assn @ (sup_sup_assn @ A @ B) @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) = ((rep_assn @ B @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)) | (rep_assn @ A @ (produc7507926704131184380et_nat @ C @ bot_bot_set_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 39.62/11.62 thf(505,axiom,((rep_assn @ r @ (produc7507926704131184380et_nat @ h2 @ as2))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_M2)). 39.62/11.62 thf(2186,plain,((rep_assn @ r @ (produc7507926704131184380et_nat @ h2 @ as2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 39.62/11.62 thf(358,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_sup_Oabsorb2)). 39.62/11.62 thf(1710,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((sup_sup_set_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 39.62/11.62 thf(472,axiom,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ B) => ((entails @ C @ D) => (entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2868_ent__star__mono)). 39.62/11.62 thf(2091,plain,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ B) => ((entails @ C @ D) => (entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 39.62/11.62 thf(243,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1248_subset__Un__eq)). 39.62/11.62 thf(1346,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 39.62/11.62 thf(105,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_2283_linorder__neqE__nat)). 39.62/11.62 thf(886,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)],[105])). 39.62/11.62 thf(511,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_2761_mult_Oassoc)). 39.62/11.62 thf(2201,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)],[511])). 39.62/11.62 thf(84,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_2033_less__le__not__le)). 39.62/11.62 thf(801,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)],[84])). 39.62/11.62 thf(444,axiom,((! [A:nat,B:nat,C:nat]: (((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_1312_dual__order_Otrans)). 39.62/11.62 thf(1989,plain,((! [A:nat,B:nat,C:nat]: (((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)],[444])). 39.62/11.62 thf(392,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_inf__sup__aci_I6_J)). 39.62/11.62 thf(1816,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 39.62/11.62 thf(291,axiom,((! [A:assn,B:assn,C:assn]: (((entails @ (sup_sup_assn @ A @ C) @ B) <= (entails @ C @ B)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2869_ent__disjE)). 39.62/11.62 thf(1495,plain,((! [A:assn,B:assn,C:assn]: ((entails @ (sup_sup_assn @ A @ C) @ B) | ~ (entails @ C @ B) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 39.62/11.62 thf(519,axiom,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ A @ B) => (dvd_dvd_assn @ A @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8076_dvd__mult2)). 39.62/11.62 thf(2223,plain,((! [A:assn,B:assn,C:assn]: ((dvd_dvd_assn @ A @ B) => (dvd_dvd_assn @ A @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 39.62/11.62 thf(37,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_2245_less__or__eq__imp__le)). 39.62/11.62 thf(635,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)],[37])). 39.62/11.62 thf(91,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1616_less__imp__neq)). 39.62/11.62 thf(822,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 39.62/11.62 thf(359,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_inf__absorb2)). 39.62/11.62 thf(1713,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((inf_inf_set_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 39.62/11.62 thf(415,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_dual__order_Orefl)). 39.62/11.62 thf(1885,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 39.62/11.62 thf(173,axiom,((relH @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))) @ h2 @ h)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1510__092_060open_062relH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_Ah_Ah_H_092_060close_062)). 39.62/11.62 thf(1120,plain,((relH @ (collect_nat @ (^ [A:nat]: (~ (member_nat @ A @ as) & (ord_less_nat @ A @ (lim_Product_unit @ h2))))) @ h2 @ h)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 39.62/11.62 thf(30,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2370_pinf_I4_J)). 39.62/11.62 thf(607,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 39.62/11.62 thf(208,axiom,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = A) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_inf__absorb1)). 39.62/11.62 thf(1236,plain,((! [A:set_nat,B:set_nat]: (((inf_inf_set_nat @ A @ B) = A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 39.62/11.62 thf(483,axiom,((times_times_assn = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2766_ab__semigroup__mult__class_Omult_Ocommute)). 39.62/11.62 thf(2127,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 39.62/11.62 thf(396,axiom,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Int__Un__eq_I1_J)). 39.62/11.62 thf(1829,plain,((! [A:set_nat,B:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 39.62/11.62 thf(440,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inf__sup__absorb)). 39.62/11.62 thf(1977,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 39.62/11.62 thf(413,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_sup_Ocobounded1)). 39.62/11.62 thf(1880,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 39.62/11.62 thf(138,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((! [D:nat]: ((C @ D) <= (member_nat @ D @ (sup_sup_set_nat @ A @ B)))) = (! [D:nat]: ((C @ D) <= (member_nat @ D @ A)) & ! [D:nat]: ((member_nat @ D @ B) => (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_ball__Un)). 39.62/11.62 thf(1004,plain,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((! [D:nat]: ((C @ D) | ~ (member_nat @ D @ (sup_sup_set_nat @ A @ B)))) = (! [D:nat]: ((C @ D) | ~ (member_nat @ D @ A)) & ! [D:nat]: ((member_nat @ D @ B) => (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 39.62/11.62 thf(237,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1430_boolean__algebra_Oconj__disj__distrib)). 39.62/11.62 thf(1331,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ (inf_inf_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 39.62/11.62 thf(85,axiom,((hoare_new_addrs = (^ [A:heap_e7401611519738050253t_unit,B:set_nat,C:heap_e7401611519738050253t_unit]: (sup_sup_set_nat @ B @ (collect_nat @ (^ [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ C)) & (ord_less_eq_nat @ (lim_Product_unit @ A) @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2197_new__addrs__def)). 39.62/11.62 thf(803,plain,(((hoare_new_addrs) = (^ [A:heap_e7401611519738050253t_unit,B:set_nat,C:heap_e7401611519738050253t_unit]: (sup_sup_set_nat @ B @ (collect_nat @ (^ [D:nat]: ((ord_less_nat @ D @ (lim_Product_unit @ C)) & (ord_less_eq_nat @ (lim_Product_unit @ A) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 39.62/11.62 thf(233,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1437_boolean__algebra_Odisj__conj__distrib)). 39.62/11.62 thf(1320,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ A @ (inf_inf_set_nat @ B @ C)) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ (sup_sup_set_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 39.62/11.62 thf(140,axiom,((! [A:nat,B:set_nat,C:set_nat]: (((member_nat @ A @ C) => (member_nat @ A @ (inf_inf_set_nat @ B @ C))) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_IntI)). 39.62/11.62 thf(1009,plain,((! [A:nat,B:set_nat,C:set_nat]: (((member_nat @ A @ C) => (member_nat @ A @ (inf_inf_set_nat @ B @ C))) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 39.62/11.62 thf(350,axiom,((sup_sup_set_nat = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_sup__commute)). 39.62/11.62 thf(1681,plain,(((sup_sup_set_nat) = (^ [A:set_nat,B:set_nat]: (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 39.62/11.62 thf(279,axiom,((! [A:set_nat,B:set_nat,C:heap_e7401611519738050253t_unit,D:heap_e7401611519738050253t_unit]: ((relH @ (sup_sup_set_nat @ A @ B) @ C @ D) = ((relH @ B @ C @ D) & (relH @ A @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_relH__dist__union)). 39.62/11.62 thf(1463,plain,((! [A:set_nat,B:set_nat,C:heap_e7401611519738050253t_unit,D:heap_e7401611519738050253t_unit]: ((relH @ (sup_sup_set_nat @ A @ B) @ C @ D) = ((relH @ B @ C @ D) & (relH @ A @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 39.62/11.62 thf(403,axiom,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Un__Int__eq_I1_J)). 39.62/11.62 thf(1848,plain,((! [A:set_nat,B:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 39.62/11.62 thf(376,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_Un__Int__distrib2)). 39.62/11.62 thf(1769,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (inf_inf_set_nat @ A @ B) @ C) = (inf_inf_set_nat @ (sup_sup_set_nat @ A @ C) @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 39.62/11.62 thf(165,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2366_pinf_I3_J)). 39.62/11.62 thf(1088,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 39.62/11.62 thf(274,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_sup__ge2)). 39.62/11.62 thf(1449,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ A @ (sup_sup_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 39.62/11.62 thf(57,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_1633_less__induct)). 39.62/11.62 thf(708,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)],[57])). 39.62/11.62 thf(501,axiom,((dvd_dvd_assn = (^ [A:assn,B:assn]: ? [C:assn]: (B = (times_times_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8066_dvd__def)). 39.62/11.62 thf(2177,plain,(((dvd_dvd_assn) = (^ [A:assn,B:assn]: ? [C:assn]: (B = (times_times_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 39.62/11.62 thf(265,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_sup_Oassoc)). 39.62/11.62 thf(1417,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 39.62/11.62 thf(428,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_sup__assoc)). 39.62/11.62 thf(1944,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 39.62/11.62 thf(119,axiom,(((('!') @ option3562590408128118217it_nat) = (^ [A:(option3562590408128118217it_nat > $o)]: ((A @ none_P2651198173097904984it_nat) & ! [B:produc3260487557148687353it_nat]: (A @ (some_P7913643980934408916it_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2569_split__option__all)). 39.62/11.62 thf(940,plain,(((('!') @ option3562590408128118217it_nat) = (^ [A:(option3562590408128118217it_nat > $o)]: ((A @ none_P2651198173097904984it_nat) & ! [B:produc3260487557148687353it_nat]: (A @ (some_P7913643980934408916it_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 39.62/11.62 thf(513,axiom,((! [A:assn,B:assn]: (dvd_dvd_assn @ A @ (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8101_dvd__triv__right)). 39.62/11.62 thf(2206,plain,((! [A:assn,B:assn]: (dvd_dvd_assn @ A @ (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 39.62/11.62 thf(367,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_inf__sup__distrib2)). 39.62/11.62 thf(1737,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((inf_inf_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ (inf_inf_set_nat @ A @ C) @ (inf_inf_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 39.62/11.62 thf(149,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2246_le__eq__less__or__eq)). 39.62/11.62 thf(1037,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 39.62/11.62 thf(15,axiom,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((B @ C) & (member_nat @ C @ A)))) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1557_Collect__subset)). 39.62/11.62 thf(560,plain,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((B @ C) & (member_nat @ C @ A)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 39.62/11.62 thf(3069,plain,(($false)),inference(cvc4,[status(thm)],[1665,1501,1337,1469,1633,2072,1899,1315,1083,1179,2163,892,2094,1411,909,1031,1950,1549,977,762,2104,683,1882,1068,1522,1569,1728,873,1533,597,1437,1855,1200,2114,1269,614,1692,677,533,2184,945,1063,2042,1999,797,538,2146,1507,930,1095,1001,1127,1391,782,2020,973,1935,1359,1601,1475,1887,1746,898,565,1366,2136,1703,1628,1287,570,1430,2039,1660,1871,751,1826,1992,1132,542,1055,724,1860,1264,587,1323,1577,1455,1832,934,1191,1922,853,2169,1609,1641,1963,1232,870,1890,1875,1778,1489,756,789,1811,1334,1136,1858,937,1960,1051,2017,1183,1283,1377,866,1796,1394,1351,660,998,988,1405,527,1564,602,981,1896,877,2190,1447,956,1622,774,1104,1242,1604,1206,942,2204,529,1153,810,1868,1223,1042,1519,1580,1123,1174,1487,1217,2147,693,630,1619,2150,2132,729,1423,1938,1555,665,1210,551,1740,1012,2068,1819,583,522,889,2179,1836,1787,2181,578,697,1983,1953,1804,1328,1121,1540,1397,2157,1143,1851,1772,1259,1498,1587,1138,1719,1683,1160,2023,1361,901,642,1214,2108,590,1644,706,1414,2196,1842,1791,2172,1612,1039,1155,1744,1297,1451,1530,2153,654,1552,1932,1060,1799,1947,2052,779,2140,605,1525,1099,985,1150,1478,1668,1974,2006,721,1318,1695,657,1170,1466,674,1663,1167,953,794,2208,805,2057,765,1510,1698,1483,856,745,573,1374,1146,1754,2033,2149,1301,1595,1631,733,819,562,1007,2048,1784,772,1752,1535,875,826,1256,545,2193,2220,1707,1371,1312,1635,1058,1092,2166,704,1638,1356,611,787,1239,1997,1675,540,990,1492,1722,2116,1969,863,1853,1408,784,1117,1048,736,880,1801,1080,1339,2129,816,2111,1731,964,1344,1460,668,1177,932,1029,895,2075,768,1245,868,883,1015,1775,2101,1250,1562,912,521,2212,959,1034,1583,1809,2096,1203,680,548,812,617,1472,1018,1958,553,1181,1905,1420,1277,2124,1845,580,640,1025,1070,971,1647,1941,1368,1267,2160,993,712,557,1516,1598,2060,1400,1566,2143,2012,1053,1716,2165,1813,791,717,1262,1980,1538,2044,1130,1285,1220,907,1085,576,2056,1140,1670,859,1617,1543,1766,656,1023,1353,600,1485,1972,1749,1427,1504,727,1839,627,2088,1966,1685,1949,671,903,2215,759,1781,2187,1157,1834,2226,1453,1866,2071,1734,1807,1590,1326,1253,1101,652,2004,2026,632,1822,995,1341,748,2009,2198,1212,1607,1513,1994,1045,667,1294,1893,2036,1309,1444,1442,1908,1348,2102,1678,967,1097,1546,1625,1986,1248,1757,1480,2218,1133,1725,1280,1593,1380,1527,1673,1363,2186,1710,2091,1346,886,2201,801,1989,1816,1495,2223,635,822,1713,1885,1120,607,1236,2127,1829,1977,1880,1004,1331,803,1320,1009,1681,1463,1848,1769,1088,1449,708,2177,1417,1944,940,2206,1737,1037,560])). 39.62/11.62 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.62/11.62 % [INFO] Killing All external provers ... 39.62/11.68 EOF