0.00/0.00 % Leo-III: Strategy 1 (for '60') 39.32/11.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 39.32/11.36 % [INFO] Parsing done (321ms). 39.32/11.36 % [INFO] Running in sequential loop mode. 39.32/11.36 % [CONFIG] Using configuration: timeout(60) with strategy 39.32/11.36 % [INFO] eprover registered as external prover. 39.32/11.36 % [INFO] cvc4 registered as external prover. 39.32/11.36 % [INFO] Parsing finished. Scanning for conjecture ... 39.32/11.36 % [INFO] Found a conjecture and 1198 axioms. Running axiom selection ... 39.32/11.36 % [INFO] Axiom selection finished. Selected 1198 axioms (removed 0 axioms). 39.32/11.36 % [INFO] Problem is higher-order (TPTP THF). 39.32/11.36 % [INFO] Type checking passed. Searching for refutation ... 39.32/11.36 % External prover 'cvc4' found a proof! 39.32/11.36 % [INFO] Killing All external provers ... 39.32/11.36 % Time passed: 10772ms (effective reasoning time: 10077ms) 39.32/11.36 % Solved by strategy 39.32/11.36 % Axioms used in derivation (1198): fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_822_mult__strict__left__mono, fact_269_double__number__of__Bit0, fact_865_real__mult__less__mono2, fact_925_dvd_Oless__irrefl, fact_547_nat__number__of__Pls, fact_999_trans__le__add1, fact_946_eq__diff__iff, fact_78_nat__numeral__1__eq__1, fact_327_zdvd__antisym__nonneg, fact_1168_zmult2__lemma__aux4, fact_997_le__iff__add, fact_47_zpower__zpower, fact_505_int__pos__lt__two__imp__zero__or__one, fact_959_zero__less__diff, fact_559_less__0__number__of, fact_325_power__eq__imp__eq__base, fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_1039_dvd__imp__le, fact_598_unique__quotient__lemma__neg, fact_613_number__of__diff, fact_846_mult__pos__pos, fact_454_zero__less__power2, fact_88_zle__add1__eq__le, fact_439_zero__power2, fact_770_split__mult__neg__le, fact_740_mult__dvd__mono, fact_118_mem__def, fact_7_zadd__power2, fact_434_le__special_I1_J, fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_528_rel__simps_I13_J, fact_457_power__commutes, fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_742_dvd__mult, fact_753_dvd__add, fact_1178_mod__less__divisor, fact_296_power__less__power__Suc, fact_329_dvd__power__same, fact_214_semiring__mult__number__of, fact_884_diff__0__eq__0, fact_772_split__mult__neg__le, fact_287_semiring__one__add__one__is__two, fact_763_divides__add__revr, fact_1005_add__leE, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_321_power__le__dvd, fact_136_eq__number__of, fact_152_rel__simps_I4_J, fact_766_nat__mult__eq__one, fact_368_zero__less__power, fact_1117_pow__divides__eq__int, fact_162_less__special_I4_J, fact_678_dvd__refl, fact_1145_zcong__zmod, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_278_mult__2, fact_928_nat__add__left__commute, fact_139_number__of__reorient, fact_248_add__number__of__eq, fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_395_semiring__numeral__0__eq__0, fact_757_one__dvd, fact_564_zcong__trans, fact_702_no__zero__divisors, fact_799_mult__nonneg__nonpos2, fact_74_less__eq__number__of__int__code, fact_754_dvd__add, fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_201_mult__Pls, fact_363_zero__le__power, fact_164_less__special_I2_J, fact_257_mult__numeral__1, fact_733_dvd__mult__left, fact_365_power__mono, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_355_add__0__iff, fact_393_number__of__Pls, fact_135_eq__number__of, fact_283_mult__2__right, fact_478_sum__power2__le__zero__iff, fact_657_zprime__zdvd__zmult__better, fact_207_zmult__1__right, fact_160_power__even__eq, fact_1053_nat__diff__add__eq1, fact_1153_zdiff__zmod__right, fact_1156_zmod__zdvd__zmod, fact_590_zcong__iff__lin, fact_899_dvd_Oless__asym_H, fact_218_semiring__add__number__of, fact_282_semiring__mult__2__right, fact_479_not__sum__power2__lt__zero, fact_686_real__less__def, fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_1172_neq__one__mod__two, fact_441_zero__eq__power2, fact_354_add__0__iff, fact_1095_MultInv__prop2, fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_374_power__less__imp__less__base, fact_313_power__eq__0__iff, fact_930_nat__add__left__cancel, fact_399_bin__less__0__simps_I1_J, fact_50_le__number__of__eq__not__less, fact_220_left__distrib__number__of, fact_995_le__add2, fact_407_power__Suc__less, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_331_dvd__power__same, fact_370_zero__less__power, fact_756_one__dvd, fact_328_zdvd__mult__cancel, fact_514_nat__zero__less__power__iff, fact_1114_d22set__g__1, fact_835_zero__less__mult__pos2, fact_146_zadd__left__commute, fact_842_mult__pos__neg2, fact_384_even__less__0__iff, fact_216_semiring__add__number__of, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_237_add__numeral__0__right, fact_32_one__add__one__is__two, fact_421_number__of__Bit0, fact_554_one__less__power, fact_1035_mult__less__cancel2, fact_979_add__less__mono1, fact_252_add__Bit0__Bit1, fact_171_crossproduct__eq, fact_862_real__mult__le__cancel__iff1, fact_921_dvd_Oless__le__not__le, fact_746_dvd__mult2, fact_1118_gcd__lcm__complete__lattice__nat_Otop__le, fact_1033_mult__less__mono2, fact_638_zcong__eq__trans, fact_808_mult__le__0__iff, fact_361_zadd__0__right, fact_1129_pow__divides__eq__nat, fact_801_mult__nonneg__nonpos2, fact_1096_wset__mem__inv__mem, fact_850_mult__less__cancel__left__pos, fact_1063_zdvd__mono, fact_1007_le__diff__conv, fact_266_semiring__norm_I110_J, fact_159_power__even__eq, fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_927_nat__add__commute, fact_1047_nat__mult__eq__cancel1, fact_1060_is__sum2sq__def, fact_965_le__0__eq, fact_71_less__eq__int__code_I13_J, fact_662_zcong__zprime__prod__zero, fact_1022_mult__le__mono1, fact_629_zcong__def, fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_797_mult__nonpos__nonneg, fact_974_not__add__less1, fact_953_gr0I, fact_378_power__decreasing, fact_9_power2__sum, fact_367_power__mono, fact_975_not__add__less2, fact_1056_nat__diff__add__eq2, fact_1001_add__le__mono1, fact_932_diff__add__inverse2, fact_765_divides__mul__r, fact_618_zcong__zdiff, fact_165_less__special_I2_J, fact_785_comm__mult__left__mono, fact_357_double__eq__0__iff, fact_1191_StandardRes__prop1, fact_73_less__number__of__int__code, fact_1094_MultInv__prop2a, fact_199_rel__simps_I38_J, fact_463_power__add, fact_225_right__distrib__number__of, fact_853_mult__less__cancel__right__disj, fact_614_diff__bin__simps_I1_J, fact_222_left__distrib__number__of, fact_40_zle__antisym, fact_333_field__power__not__zero, fact_1068_zcong__zless__unique, fact_397_semiring__numeral__0__eq__0, fact_712_zero__neq__one, fact_145_zadd__assoc, fact_977_trans__less__add1, fact_1146_zdvd__zmod__imp__zdvd, fact_567_mult__nat__number__of, fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_739_mult__dvd__mono, fact_372_zdvd__reduce, fact_1195_mod__lemma, fact_531_rel__simps_I6_J, fact_687_divides__antisym, fact_913_dvd__antisym, fact_821_mult__strict__left__mono, fact_1017_add__mult__distrib, fact_887_diffs0__imp__equal, fact_578_zcong__zmult__self, fact_251_add__Bit1__Bit0, fact_869_exp__eq__1, fact_784_mult__right__mono__neg, fact_549_rel__simps_I25_J, fact_684_real__zero__not__eq__one, fact_38_zless__linear, fact_658_Int2_Ozcong__zero, fact_494_power__strict__increasing__iff, fact_845_mult__pos__neg, fact_987_less__imp__le__nat, fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_871_two__realpow__ge__one, fact_243_number__of__mult, fact_294_power__less__power__Suc, fact_37_zless__le, fact_72_rel__simps_I31_J, fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_910_dvd_Oord__eq__less__trans, fact_163_less__special_I4_J, fact_951_diff__mult__distrib, fact_558_dvd__power, fact_761_real__mult__right__cancel, fact_460_power__mult__distrib, fact_339_power__strict__mono, fact_980_add__less__mono, fact_550_rel__simps_I11_J, fact_1018_add__mult__distrib2, fact_396_semiring__numeral__0__eq__0, fact_918_dvd_Oantisym__conv, fact_260_semiring__numeral__1__eq__1, fact_1044_nat__less__add__iff2, fact_1032_nat__diff__split__asm, fact_500_power__strict__increasing, fact_324_power__eq__imp__eq__base, fact_272_power3__eq__cube, fact_782_mult__left__mono__neg, fact_577_zcong__scalar, fact_677_linorder__neqE__linordered__idom, fact_261_semiring__numeral__1__eq__1, fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_878_less__zeroE, fact_443_zero__le__power2, fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_653_zcong__not__zero, fact_312_power__eq__0__iff, fact_709_mult__zero__left, fact_420_le__nat__number__of, fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_450_power2__eq__imp__eq, fact_641_zcong__square__zless, fact_81_rel__simps_I5_J, fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_988_le__neq__implies__less, fact_376_power__less__imp__less__base, fact_575_zcong__zmult, fact_501_power__strict__increasing, fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_1133_SR__def, fact_503_s, fact_635_diff__bin__simps_I5_J, fact_14_power2__eq__square__number__of, fact_972_mult__cancel1, fact_425_power__one__right, fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_1041_mult__le__cancel1, fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_1104_int__le__induct, fact_636_diff__bin__simps_I6_J, fact_1125_gcd__lcm__complete__lattice__nat_Obot__less, fact_905_dvd_Oless__imp__not__less, fact_967_diff__is__0__eq_H, fact_719_combine__common__factor, fact_1010_add__diff__assoc, fact_601_q__neg__lemma, fact_1187_mod__less, fact_897_dvd_Oless__asym, fact_53_le__number__of, fact_569_order__le__neq__implies__less, fact_13_power2__eq__square__number__of, fact_498_power__less__imp__less__exp, fact_156_rel__simps_I27_J, fact_856_not__square__less__zero, fact_249_number__of__add, fact_789_mult__left__mono, fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_356_double__eq__0__iff, fact_481_sum__power2__gt__zero__iff, fact_75_zadd__strict__right__mono, fact_1120_gcd__lcm__complete__lattice__nat_Oless__top, fact_403_pos__zmult__pos, fact_143_zmult__commute, fact_669_realpow__two__sum__zero__iff, fact_539_eq__number__of__Pls__Min, fact_1090_MultInv__zcong__prop2, fact_544_power__0, fact_597_zdiv__mono2__neg__lemma, fact_1080_inv__less__p__minus__1, fact_748_dvd__triv__right, fact_1184_StandardRes__def, fact_255_number__of__Bit1, fact_338_power__strict__mono, fact_861_real__mult__less__iff1, fact_1093_Int2_Oaux____1, fact_147_zadd__commute, fact_828_mult__neg__neg, fact_616_zdiff__zmult__distrib2, fact_509_self__quotient__aux2, fact_689_real__mult__commute, fact_857_pos__add__strict, fact_944_diff__le__mono, fact_39_zle__trans, fact_998_nat__add__left__cancel__le, fact_537_rel__simps_I23_J, fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_1052_nat__le__add__iff1, fact_840_mult__pos__neg2, fact_508_zprime__def, fact_771_split__mult__neg__le, fact_904_dvd_Oless__imp__not__eq, fact_989_less__or__eq__imp__le, fact_1162_neg__mod__conj, fact_524_rel__simps_I42_J, fact_1151_zmod__self, fact_970_mult__0__right, fact_149_less__int__code_I15_J, fact_760_dvd__diff, fact_1011_le__diff__conv2, fact_656_zcong__zero__equiv__div, fact_1012_le__add__diff__inverse2, fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_1110_d22set__eq__wset, fact_362_zero__le__power, fact_685_less__eq__real__def, fact_35_zle__refl, fact_1003_add__leD2, fact_939_eq__imp__le, fact_172_crossproduct__eq, fact_532_rel__simps_I8_J, fact_743_dvd__mult, fact_51_less__number__of, fact_1142_zmod__eq__dvd__iff, fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_562_zcong__sym, fact_1136_zdvd__iff__zmod__eq__0__number__of, fact_690_real__mult__1, fact_244_number__of__mult, fact_1097_wset__inv__mem__mem, fact_0_tpos, fact_825_mult__strict__right__mono, fact_1059_number__of1, fact_1155_zmod__minus1__right, fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_360_zadd__0, fact_67_rel__simps_I2_J, fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_488_power__increasing, fact_1152_zmod__zero, fact_326_zdvd__not__zless, fact_580_power__m1__even, fact_277_semiring__mult__2, fact_55_zadd__zless__mono, fact_671_convex__bound__lt, fact_711_mult__zero__left, fact_311_power__eq__0__iff, fact_876_le0, fact_639_mult__sum2sq, fact_414_sum__squares__le__zero__iff, fact_358_Pls__def, fact_1049_nat__mult__dvd__cancel__disj, fact_722_comm__semiring__class_Odistrib, fact_495_power__strict__increasing__iff, fact_223_right__distrib__number__of, fact_486_one__le__power, fact_545_power__0, fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_382_power__strict__decreasing, fact_591_power__0__left__number__of, fact_48_le__number__of__eq__not__less, fact_935_Nat_Odiff__cancel, fact_82_less__eq__int__code_I15_J, fact_813_zero__le__square, fact_651_zdiff__power3, fact_1083_MultInv__zcong__prop1, fact_392_semiring__norm_I112_J, fact_1105_int__less__induct, fact_239_mult__number__of__left, fact_1188_mod__less__eq__dividend, fact_625_diff__bin__simps_I10_J, fact_1135_zmod__number__of__Bit1, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1170_zmult2__lemma__aux2, fact_489_power__increasing, fact_931_nat__add__right__cancel, fact_151_rel__simps_I10_J, fact_885_minus__nat_Odiff__0, fact_235_add__numeral__0, fact_773_split__mult__pos__le, fact_497_power__less__imp__less__exp, fact_962_Nat_Oadd__0__right, fact_650_zdiff__power2, fact_960_add__eq__self__zero, fact_584_power__eq__0__iff__number__of, fact_33_one__add__one__is__two, fact_471_power__mult, fact_1175_zmod__eq__0D, fact_259_mult__numeral__1__right, fact_741_dvd__mult, fact_649_power2__diff, fact_1002_add__le__mono, fact_473_power2__less__imp__less, fact_623_left__diff__distrib__number__of, fact_1025_nat__mult__eq__1__iff, fact_723_comm__semiring__class_Odistrib, fact_615_diff__bin__simps_I7_J, fact_612_number__of__diff, fact_792_mult__right__mono, fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_69_rel__simps_I14_J, fact_205_add__Bit0__Bit0, fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_573_IntPrimes_Ozcong__zero, fact_777_mult__mono, fact_644_zcong__zmult__prop1, fact_827_mult__neg__neg, fact_1031_nat__diff__split, fact_262_semiring__numeral__1__eq__1, fact_802_mult__nonneg__nonpos, fact_161_power__even__eq, fact_844_mult__pos__neg, fact_1004_add__leD1, fact_90_is__mult__sum2sq, fact_1070_Wilson__Russ, fact_633_zle__diff1__eq, fact_340_power__strict__mono, fact_654_zdvd__bounds, fact_933_diff__add__inverse, fact_270_double__number__of__Bit0, fact_1106_d22set__induct__old, fact_170_crossproduct__eq, fact_1115_d22set__mem, fact_240_mult__number__of__left, fact_592_power__0__left__number__of, fact_405_odd__nonzero, fact_660_neg__one__power, fact_926_dvd__diff__nat, fact_868_divides__rev, fact_1055_nat__le__add__iff2, fact_510_self__quotient__aux1, fact_1081_MultInv__prop1, fact_916_dvd_Ole__neq__trans, fact_805_mult__nonneg__nonneg, fact_1103_wset__mem, fact_879_diff__commute, fact_153_rel__simps_I22_J, fact_198_rel__simps_I44_J, fact_1082_inv__not__0, fact_676_linorder__neqE__linordered__idom, fact_727_add__diff__add, fact_1150_zmod__simps_I3_J, fact_964_diff__add__0, fact_859_divides__ge, fact_288_p0, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_732_dvd__mult__left, fact_593_power__0__left__number__of, fact_383_even__less__0__iff, fact_949_nat__mult__assoc, fact_595_zcong__zless__0, fact_318_dvd__power__le, fact_795_mult__nonpos__nonpos, fact_675_real__le__eq__diff, fact_954_gr__implies__not0, fact_800_mult__nonneg__nonpos2, fact_919_dvd_Oeq__refl, fact_852_mult__less__cancel__left__disj, fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1180_mod__geq, fact_314_le__imp__power__dvd, fact_566_nat__number__of__mult__left, fact_520_Bit1__Min, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_1008_le__add__diff, fact_738_mult__dvd__mono, fact_375_power__less__imp__less__base, fact_377_power__decreasing, fact_1147_zdvd__zmod, fact_535_rel__simps_I26_J, fact_679_dvd__refl, fact_1167_zmult2__lemma__aux3, fact_298_power__gt1__lemma, fact_265_semiring__norm_I110_J, fact_866_real__two__squares__add__zero__iff, fact_872_realpow__pos__nth, fact_1086_MultInv__prop3, fact_459_power__commutes, fact_1101_wset__g__1, fact_433_le__special_I1_J, fact_692_realpow__minus__mult, fact_428_odd__less__0, fact_491_power__inject__exp, fact_890_less__not__refl2, fact_337_zdvd__imp__le, fact_1020_mult__le__mono, 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fact_83_rel__simps_I33_J, fact_705_mult__eq__0__iff, fact_468_power__one, fact_303_power__increasing__iff, fact_487_one__le__power, fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_570_order__le__neq__implies__less, fact_814_mult__strict__left__mono__neg, fact_831_mult__neg__pos, fact_504_Euler_Oaux____1, fact_776_mult__mono, fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_1072_inv__inv, fact_451_power2__less__0, fact_330_dvd__power__same, fact_157_rel__simps_I21_J, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_1064_number__of2, fact_280_semiring__mult__2__right, fact_65_less__eq__int__code_I16_J, fact_929_nat__add__assoc, fact_150_rel__simps_I16_J, fact_394_number__of__Pls, fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_796_mult__nonpos__nonneg, fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_617_zdiff__zmult__distrib, fact_413_sum__squares__le__zero__iff, fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_914_dvd_Oord__le__eq__trans, fact_11_power2__sum, fact_993_dvd__diffD1, fact_581_power__m1__even, fact_485_one__le__power, fact_1174_pos__zmod__mult__2, fact_506_even__power__le__0__imp__0, fact_1027_nat__1__eq__mult__iff, fact_619_zdvd__zdiffD, fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_86_zless__imp__add1__zle, fact_683_dvd__trans, fact_834_zero__less__mult__pos2, fact_527_not__real__square__gt__zero, fact_561_eq__0__number__of, fact_1109_mono__nat__linear__lb, fact_1193_StandardRes__SR__prop, fact_1183_le__mod__geq, fact_483_zero__le__even__power_H, fact_475_sum__power2__ge__zero, fact_181_crossproduct__noteq, fact_60_nat__mult__2, fact_1197_StandardRes__prop2, fact_652_zcong__less__eq, fact_1069_norR__mem__unique__aux, fact_322_power__le__dvd, fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J, fact_627_less__bin__lemma, fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_477_sum__power2__le__zero__iff, fact_431_less__special_I3_J, fact_297_power__gt1__lemma, fact_755_dvd__add, fact_1029_nat__dvd__not__less, fact_693_realpow__minus__mult, fact_195_rel__simps_I39_J, fact_1057_nat__eq__add__iff2, fact_696_power__eq__if, fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_1173_zmod__minus1, fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_279_mult__2, fact_883_real__le__antisym, fact_819_comm__mult__strict__left__mono, fact_411_sum__squares__ge__zero, fact_499_power__less__imp__less__exp, fact_720_combine__common__factor, fact_217_semiring__add__number__of, fact_729_dvd__mult__right, fact_540_power__dvd__imp__le, fact_54_le__number__of, fact_1091_MultInv__zcong__prop3, fact_1189_StandardRes__eq__zcong, fact_546_power__0, fact_204_add__Pls, fact_140_rel__simps_I51_J, fact_1185_mod__mult__distrib, fact_381_power__strict__decreasing, fact_815_mult__strict__left__mono__neg, fact_1149_zmod__zmult1__eq, fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_6_qf1pt, fact_824_mult__strict__right__mono, fact_794_mult__nonpos__nonpos, fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_268_mult__Bit1, fact_968_diff__is__0__eq, fact_826_mult__strict__right__mono, fact_389_add__scale__eq__noteq, fact_628_xzgcda__linear__aux1, fact_482_sum__power2__gt__zero__iff, fact_246_add__number__of__left, fact_985_nat__less__le, fact_983_add__diff__inverse, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_966_less__eq__nat_Osimps_I1_J, fact_364_zero__le__power, fact_250_number__of__add, fact_423_power__one__right, fact_704_mult__eq__0__iff, fact_991_diff__less__mono, fact_1038_mult__eq__self__implies__10, fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_788_mult__left__mono, fact_780_mult__mono_H, fact_490_power__increasing, fact_1159_pos__mod__conj, fact_695_mult__eq__if, fact_728_add__diff__add, fact_36_zle__linear, fact_28_add__special_I2_J, fact_1192_StandardRes__ubound, fact_1108_int__gr__induct, fact_519_rel__simps_I43_J, fact_737_dvdI, fact_816_mult__strict__right__mono__neg, fact_717_one__neq__zero, fact_518_rel__simps_I47_J, fact_923_dvd_Ole__less, fact_1034_mult__less__mono1, fact_210_zadd__zmult__distrib, fact_749_dvd__triv__right, fact_940_le__trans, fact_680_dvd__refl, fact_902_dvd_Oless__imp__triv, fact_169_le__special_I2_J, fact_768_nat__power__eq__0__iff, fact_701_no__zero__divisors, fact_775_mult__mono, fact_493_power__inject__exp, fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_817_mult__strict__right__mono__neg, fact_202_mult__Bit0, fact_521_rel__simps_I37_J, fact_1030_add__gr__0, fact_335_power__0__left, fact_8_zadd__power3, fact_1019_nat__dvd__1__iff__1, fact_316_le__imp__power__dvd, fact_643_zcong__id, fact_1111_ex__least__nat__le, fact_1113_d22set__le__swap, fact_402_int__0__less__1, fact_417_not__sum__squares__lt__zero, fact_1132_mult__left__cancel, fact_300_power__le__imp__le__exp, fact_366_power__mono, fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_758_one__dvd, fact_958_diff__less, fact_973_mult__cancel2, fact_1071_zfact_Osimps, fact_247_add__number__of__eq, fact_242_arith__simps_I32_J, fact_267_one__is__num__one, fact_502_power__strict__increasing, fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_315_le__imp__power__dvd, fact_16_one__power2, fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N, fact_369_zero__less__power, fact_299_power__gt1__lemma, fact_1045_nat__mult__eq__cancel__disj, fact_551_pos__zmult__eq__1__iff__lemma, fact_1077_inv__not__1, fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_1046_left__add__mult__distrib, fact_1066_incr__mult__lemma, fact_895_diff__less__mono2, fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_1190_StandardRes__prop3, fact_769_divides__exp, fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_213_semiring__mult__number__of, fact_76_zadd__left__mono, fact_576_zcong__scalar2, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_292_real__sum__squared__expand, fact_1036_mult__less__cancel1, fact_631_add__number__of__diff1, fact_1100_wset__less, fact_848_mult__pos__pos, fact_698_divisors__zero, fact_241_arith__simps_I32_J, fact_523_rel__simps_I45_J, fact_1099_wset__subset 39.32/11.36 % No. of inferences in proof: 2400 39.32/11.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10772 ms resp. 10077 ms w/o parsing 39.32/11.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.32/11.36 thf(int_type, type, int: $tType). 39.32/11.36 thf(nat_type, type, nat: $tType). 39.32/11.36 thf(real_type, type, real: $tType). 39.32/11.36 thf(product_prod_int_int_type, type, product_prod_int_int: $tType). 39.32/11.36 thf(div_mod_int_type, type, div_mod_int: (int > (int > int))). 39.32/11.36 thf(div_mod_nat_type, type, div_mod_nat: (nat > (nat > nat))). 39.32/11.36 thf(minus_minus_int_type, type, minus_minus_int: (int > (int > int))). 39.32/11.36 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 39.32/11.36 thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))). 39.32/11.36 thf(one_one_int_type, type, one_one_int: int). 39.32/11.36 thf(one_one_nat_type, type, one_one_nat: nat). 39.32/11.36 thf(one_one_real_type, type, one_one_real: real). 39.32/11.36 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 39.32/11.36 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 39.32/11.36 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 39.32/11.36 thf(times_times_int_type, type, times_times_int: (int > (int > int))). 39.32/11.36 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 39.32/11.36 thf(times_times_real_type, type, times_times_real: (real > (real > real))). 39.32/11.36 thf(zero_zero_int_type, type, zero_zero_int: int). 39.32/11.36 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 39.32/11.36 thf(zero_zero_real_type, type, zero_zero_real: real). 39.32/11.36 thf(multInv_type, type, multInv: (int > (int > int))). 39.32/11.36 thf(d22set_type, type, d22set: (int > (int > $o))). 39.32/11.36 thf(zfact_type, type, zfact: (int > int)). 39.32/11.36 thf(zcong_type, type, zcong: (int > (int > (int > $o)))). 39.32/11.36 thf(zprime_type, type, zprime: (int > $o)). 39.32/11.36 thf(bit0_type, type, bit0: (int > int)). 39.32/11.36 thf(bit1_type, type, bit1: (int > int)). 39.32/11.36 thf(min_type, type, min: int). 39.32/11.36 thf(pls_type, type, pls: int). 39.32/11.36 thf(number_number_of_int_type, type, number_number_of_int: (int > int)). 39.32/11.36 thf(number_number_of_nat_type, type, number_number_of_nat: (int > nat)). 39.32/11.36 thf(number267125858f_real_type, type, number267125858f_real: (int > real)). 39.32/11.36 thf(ord_less_int_type, type, ord_less_int: (int > (int > $o))). 39.32/11.36 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 39.32/11.36 thf(ord_less_real_type, type, ord_less_real: (real > (real > $o))). 39.32/11.36 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 39.32/11.36 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 39.32/11.36 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 39.32/11.36 thf(power_power_int_type, type, power_power_int: (int > (nat > int))). 39.32/11.36 thf(power_power_nat_type, type, power_power_nat: (nat > (nat > nat))). 39.32/11.36 thf(power_power_real_type, type, power_power_real: (real > (nat > real))). 39.32/11.36 thf(product_Pair_int_int_type, type, product_Pair_int_int: (int > (int > product_prod_int_int))). 39.32/11.36 thf(legendre_type, type, legendre: (int > (int > int))). 39.32/11.36 thf(quadRes_type, type, quadRes: (int > (int > $o))). 39.32/11.36 thf(sr_type, type, sr: (int > (int > $o))). 39.32/11.36 thf(standardRes_type, type, standardRes: (int > (int > int))). 39.32/11.36 thf(dvd_dvd_int_type, type, dvd_dvd_int: (int > (int > $o))). 39.32/11.36 thf(dvd_dvd_nat_type, type, dvd_dvd_nat: (nat > (nat > $o))). 39.32/11.36 thf(dvd_dvd_real_type, type, dvd_dvd_real: (real > (real > $o))). 39.32/11.36 thf(collect_int_type, type, collect_int: ((int > $o) > (int > $o))). 39.32/11.36 thf(twoSqu919416604sum2sq_type, type, twoSqu919416604sum2sq: (int > $o)). 39.32/11.36 thf(twoSqu2057625106sum2sq_type, type, twoSqu2057625106sum2sq: (product_prod_int_int > int)). 39.32/11.36 thf(inv_type, type, inv: (int > (int > int))). 39.32/11.36 thf(wset_type, type, wset: (int > (int > (int > $o)))). 39.32/11.36 thf(member_int_type, type, member_int: (int > ((int > $o) > $o))). 39.32/11.36 thf(m_type, type, m: int). 39.32/11.36 thf(s1_type, type, s1: int). 39.32/11.36 thf(s_type, type, s: int). 39.32/11.36 thf(t_type, type, t: int). 39.32/11.36 thf(47,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ A @ (times_times_nat @ B @ (times_times_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 39.32/11.36 thf(1322,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ A @ (times_times_nat @ B @ (times_times_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 39.32/11.36 thf(1081,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (number267125858f_real @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_one__add__one__is__two)). 39.32/11.36 thf(4262,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (number267125858f_real @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081])). 39.32/11.36 thf(466,axiom,((! [A:int,B:nat]: (((times_times_int @ (power_power_int @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_int @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_realpow__minus__mult)). 39.32/11.36 thf(2463,plain,((! [A:int,B:nat]: (((times_times_int @ (power_power_int @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_int @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 39.32/11.36 thf(500,axiom,((! [A:real,B:real,C:int]: ((times_times_real @ (minus_minus_real @ A @ B) @ (number267125858f_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (number267125858f_real @ C)) @ (times_times_real @ B @ (number267125858f_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_left__diff__distrib__number__of)). 39.32/11.36 thf(2559,plain,((! [A:real,B:real,C:int]: ((times_times_real @ (minus_minus_real @ A @ B) @ (number267125858f_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (number267125858f_real @ C)) @ (times_times_real @ B @ (number267125858f_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 39.32/11.36 thf(494,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_zero__le__power)). 39.32/11.36 thf(2544,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 39.32/11.36 thf(966,axiom,((! [A:int]: ((number_number_of_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_number__of__is__id)). 39.32/11.36 thf(3927,plain,((! [A:int]: ((number_number_of_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])). 39.32/11.36 thf(580,axiom,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) = (ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_even__less__0__iff)). 39.32/11.36 thf(2822,plain,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) = (ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 39.32/11.36 thf(523,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = (times_times_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 39.32/11.36 thf(2630,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = (times_times_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 39.32/11.36 thf(1059,axiom,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_mult__2)). 39.32/11.36 thf(4201,plain,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059])). 39.32/11.36 thf(462,axiom,((! [A:int,B:int]: ((member_int @ B @ (wset @ B @ A)) <= (ord_less_int @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_wset__mem__mem)). 39.32/11.36 thf(2452,plain,((! [A:int,B:int]: ((member_int @ B @ (wset @ B @ A)) | ~ (ord_less_int @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 39.32/11.36 thf(1186,axiom,((! [A:int,B:int]: ((number_number_of_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_number__of__add)). 39.32/11.36 thf(4560,plain,((! [A:int,B:int]: ((number_number_of_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186])). 39.32/11.36 thf(978,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 39.32/11.36 thf(3962,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[978])). 39.32/11.36 thf(53,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_not__add__less1)). 39.32/11.36 thf(1337,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 39.32/11.36 thf(191,axiom,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (bit0 @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_bin__less__0__simps_I3_J)). 39.32/11.36 thf(1718,plain,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (bit0 @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 39.32/11.36 thf(516,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_power__dvd__imp__le)). 39.32/11.36 thf(2612,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 39.32/11.36 thf(100,axiom,((! [A:real,B:nat,C:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (power_power_real @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 39.32/11.36 thf(1469,plain,((! [A:real,B:nat,C:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (power_power_real @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 39.32/11.36 thf(407,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (div_mod_int @ B @ A) @ B) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_zmod__le__nonneg__dividend)). 39.32/11.36 thf(2306,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (div_mod_int @ B @ A) @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 39.32/11.36 thf(1190,axiom,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_semiring__mult__2__right)). 39.32/11.36 thf(4571,plain,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190])). 39.32/11.36 thf(1029,axiom,(((minus_minus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min)) = (plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096)). 39.32/11.36 thf(4101,plain,(((minus_minus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min)) = (plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])). 39.32/11.36 thf(643,axiom,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_int @ min @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_rel__simps_I9_J)). 39.32/11.36 thf(3008,plain,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_int @ min @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])). 39.32/11.36 thf(95,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_power__0)). 39.32/11.36 thf(1454,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 39.32/11.36 thf(159,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 39.32/11.36 thf(1633,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 39.32/11.36 thf(567,axiom,((! [A:nat,B:(nat > $o)]: (((? [C:nat]: (! [D:nat]: ((ord_less_nat @ D @ C) => (~ (B @ D))) & (B @ C) & (ord_less_eq_nat @ C @ A))) <= (B @ A)) <= (~ (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_ex__least__nat__le)). 39.32/11.36 thf(2778,plain,((! [A:nat,B:(nat > $o)]: (? [C:nat]: (! [D:nat]: ((ord_less_nat @ D @ C) => (~ (B @ D))) & (B @ C) & (ord_less_eq_nat @ C @ A)) | ~ (B @ A) | (B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])). 39.32/11.36 thf(296,axiom,((! [A:nat,B:nat,C:nat]: ((((power_power_nat @ C @ A) = (power_power_nat @ C @ B)) = (A = B)) <= (ord_less_nat @ one_one_nat @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_power__inject__exp)). 39.32/11.36 thf(1995,plain,((! [A:nat,B:nat,C:nat]: ((((power_power_nat @ C @ A) = (power_power_nat @ C @ B)) = (A = B)) | ~ (ord_less_nat @ one_one_nat @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 39.32/11.36 thf(967,axiom,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (twoSqu2057625106sum2sq @ (product_Pair_int_int @ A @ B)) @ (twoSqu2057625106sum2sq @ (product_Pair_int_int @ C @ D))) = (twoSqu2057625106sum2sq @ (product_Pair_int_int @ (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) @ (minus_minus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_mult__sum2sq)). 39.32/11.36 thf(3930,plain,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (twoSqu2057625106sum2sq @ (product_Pair_int_int @ A @ B)) @ (twoSqu2057625106sum2sq @ (product_Pair_int_int @ C @ D))) = (twoSqu2057625106sum2sq @ (product_Pair_int_int @ (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) @ (minus_minus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[967])). 39.32/11.36 thf(1051,axiom,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (power_power_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_two__realpow__ge__one)). 39.32/11.36 thf(4169,plain,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (power_power_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051])). 39.32/11.36 thf(873,axiom,((! [A:int,B:int]: ((A = B) = ((bit0 @ A) = (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_rel__simps_I48_J)). 39.32/11.36 thf(3666,plain,((! [A:int,B:int]: ((A = B) = ((bit0 @ A) = (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[873])). 39.32/11.36 thf(195,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ B @ A)) <= (ord_less_eq_int @ A @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_mult__right__mono__neg)). 39.32/11.36 thf(1729,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ B @ A)) | ~ (ord_less_eq_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 39.32/11.36 thf(447,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_zero__less__mult__pos)). 39.32/11.36 thf(2412,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 39.32/11.36 thf(600,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_878_less__zeroE)). 39.32/11.36 thf(2876,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])). 39.32/11.36 thf(15,axiom,((! [A:nat,B:real,C:nat,D:real]: ((dvd_dvd_real @ (power_power_real @ B @ C) @ D) => ((ord_less_eq_nat @ A @ C) => (dvd_dvd_real @ (power_power_real @ B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_power__le__dvd)). 39.32/11.36 thf(1237,plain,((! [A:nat,B:real,C:nat,D:real]: ((dvd_dvd_real @ (power_power_real @ B @ C) @ D) => ((ord_less_eq_nat @ A @ C) => (dvd_dvd_real @ (power_power_real @ B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 39.32/11.36 thf(1093,axiom,((! [A:nat]: ((times_times_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_semiring__mult__2__right)). 39.32/11.36 thf(4290,plain,((! [A:nat]: ((times_times_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093])). 39.32/11.36 thf(804,axiom,(((power_power_int @ one_one_int @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__power2)). 39.32/11.36 thf(3477,plain,(((power_power_int @ one_one_int @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 39.32/11.36 thf(941,axiom,((! [A:int]: ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_odd__nonzero)). 39.32/11.36 thf(3863,plain,((! [A:int]: ~ ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[941])). 39.32/11.36 thf(240,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B))) <= (ord_less_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_add__less__mono)). 39.32/11.36 thf(1850,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B))) | ~ (ord_less_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 39.32/11.36 thf(478,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((ord_less_int @ A @ (minus_minus_int @ C @ one_one_int)) <= (member_int @ A @ (wset @ B @ C)))) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_wset__less)). 39.32/11.36 thf(2499,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((ord_less_int @ A @ (minus_minus_int @ C @ one_one_int)) | ~ (member_int @ A @ (wset @ B @ C)))) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 39.32/11.36 thf(283,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (ord_less_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_nat__mult__less__cancel1)). 39.32/11.36 thf(1956,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (ord_less_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 39.32/11.36 thf(280,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_mult__le__mono)). 39.32/11.36 thf(1950,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 39.32/11.36 thf(177,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_zero__less__mult__pos2)). 39.32/11.36 thf(1686,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ A)) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 39.32/11.36 thf(385,axiom,((! [A:nat,B:int,C:nat,D:int]: ((dvd_dvd_int @ (power_power_int @ B @ C) @ D) => ((ord_less_eq_nat @ A @ C) => (dvd_dvd_int @ (power_power_int @ B @ A) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_power__le__dvd)). 39.32/11.36 thf(2250,plain,((! [A:nat,B:int,C:nat,D:int]: ((dvd_dvd_int @ (power_power_int @ B @ C) @ D) => ((ord_less_eq_nat @ A @ C) => (dvd_dvd_int @ (power_power_int @ B @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 39.32/11.36 thf(203,axiom,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (bit1 @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_bin__less__0__simps_I4_J)). 39.32/11.36 thf(1750,plain,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (bit1 @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 39.32/11.36 thf(632,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_dvd__diffD1)). 39.32/11.36 thf(2976,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) | ~ (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])). 39.32/11.36 thf(374,axiom,((! [A:int,B:real,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (number267125858f_real @ A) @ B) @ (times_times_real @ (number267125858f_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_right__distrib__number__of)). 39.32/11.36 thf(2210,plain,((! [A:int,B:real,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (number267125858f_real @ A) @ B) @ (times_times_real @ (number267125858f_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 39.32/11.36 thf(1068,axiom,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_sum__squares__eq__zero__iff)). 39.32/11.36 thf(4226,plain,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068])). 39.32/11.36 thf(253,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ C @ (times_times_nat @ (times_times_nat @ A @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 39.32/11.36 thf(1882,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ C @ (times_times_nat @ (times_times_nat @ A @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 39.32/11.36 thf(833,axiom,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit1 @ pls))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_mult__numeral__1__right)). 39.32/11.36 thf(3549,plain,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit1 @ pls))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 39.32/11.36 thf(153,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int)) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_mult__pos__neg2)). 39.32/11.36 thf(1618,plain,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 39.32/11.36 thf(75,axiom,((! [A:int,B:int,C:int]: ((zcong @ A @ C @ B) <= ((div_mod_int @ A @ B) = (div_mod_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_Residues_Oaux)). 39.32/11.36 thf(1401,plain,((! [A:int,B:int,C:int]: ((zcong @ A @ C @ B) | ~ ((div_mod_int @ A @ B) = (div_mod_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 39.32/11.36 thf(961,axiom,((! [A:int]: ((ord_less_eq_int @ A @ (bit1 @ pls)) = (ord_less_eq_int @ (number_number_of_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__special_I4_J)). 39.32/11.36 thf(3912,plain,((! [A:int]: ((ord_less_eq_int @ A @ (bit1 @ pls)) = (ord_less_eq_int @ (number_number_of_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[961])). 39.32/11.36 thf(592,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((E != zero_zero_real) => (((C = D) & (A != B)) => ((plus_plus_real @ C @ (times_times_real @ E @ A)) != (plus_plus_real @ D @ (times_times_real @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_add__scale__eq__noteq)). 39.32/11.36 thf(2854,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((~ (E = zero_zero_real)) => (((C = D) & ~ (A = B)) => (~ ((plus_plus_real @ C @ (times_times_real @ E @ A)) = (plus_plus_real @ D @ (times_times_real @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])). 39.32/11.36 thf(105,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_add__leE)). 39.32/11.36 thf(1486,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 39.32/11.36 thf(428,axiom,((! [A:nat]: ((A = one_one_nat) = (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique)). 39.32/11.36 thf(2363,plain,((! [A:nat]: ((A = one_one_nat) = (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 39.32/11.36 thf(878,axiom,((! [A:int,B:int]: ((twoSqu919416604sum2sq @ B) => ((twoSqu919416604sum2sq @ A) => (twoSqu919416604sum2sq @ (times_times_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_is__mult__sum2sq)). 39.32/11.36 thf(3680,plain,((! [A:int,B:int]: ((twoSqu919416604sum2sq @ B) => ((twoSqu919416604sum2sq @ A) => (twoSqu919416604sum2sq @ (times_times_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])). 39.32/11.36 thf(326,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = zero_zero_nat)) = ((times_times_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_mult__is__0)). 39.32/11.36 thf(2077,plain,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = zero_zero_nat)) = ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 39.32/11.36 thf(1009,axiom,((! [A:nat,B:int,C:nat,D:int]: ((zcong @ (power_power_int @ B @ C) @ one_one_int @ D) => (zcong @ (power_power_int @ B @ (times_times_nat @ C @ A)) @ one_one_int @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_zcong__zpower__zmult)). 39.32/11.36 thf(4043,plain,((! [A:nat,B:int,C:nat,D:int]: ((zcong @ (power_power_int @ B @ C) @ one_one_int @ D) => (zcong @ (power_power_int @ B @ (times_times_nat @ C @ A)) @ one_one_int @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])). 39.32/11.36 thf(341,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_mult__cancel1)). 39.32/11.36 thf(2117,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 39.32/11.36 thf(144,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ C @ (minus_minus_int @ A @ B)) = (zcong @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_zcong__def)). 39.32/11.36 thf(1596,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ C @ (minus_minus_int @ A @ B)) = (zcong @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 39.32/11.36 thf(77,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_add__diff__add)). 39.32/11.36 thf(1406,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 39.32/11.36 thf(378,axiom,((! [A:nat,B:nat,C:int]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (number_number_of_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (number_number_of_nat @ C)) @ (times_times_nat @ B @ (number_number_of_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_left__distrib__number__of)). 39.32/11.36 thf(2231,plain,((! [A:nat,B:nat,C:int]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (number_number_of_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (number_number_of_nat @ C)) @ (times_times_nat @ B @ (number_number_of_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 39.32/11.36 thf(520,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ C @ A) => (dvd_dvd_nat @ B @ A)) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_dvd__trans)). 39.32/11.36 thf(2622,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ C @ A) => (dvd_dvd_nat @ B @ A)) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 39.32/11.36 thf(939,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_zmult__1__right)). 39.32/11.36 thf(3858,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[939])). 39.32/11.36 thf(908,axiom,((? [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & ! [B:int]: (((ord_less_int @ B @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ B @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (ord_less_eq_int @ zero_zero_int @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1)). 39.32/11.36 thf(3762,plain,((? [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & ! [B:int]: (((ord_less_int @ B @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ B @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (ord_less_eq_int @ zero_zero_int @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[908])). 39.32/11.36 thf(1173,axiom,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_number__of2)). 39.32/11.36 thf(4515,plain,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173])). 39.32/11.36 thf(91,axiom,((zero_zero_real = (number267125858f_real @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_semiring__norm_I112_J)). 39.32/11.36 thf(1443,plain,((zero_zero_real = (number267125858f_real @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 39.32/11.36 thf(566,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_mult__right__mono)). 39.32/11.36 thf(2776,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 39.32/11.36 thf(224,axiom,((! [A:int,B:int,C:int]: ((zcong @ A @ B @ C) = (zcong @ (div_mod_int @ A @ C) @ (div_mod_int @ B @ C) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_zcong__zmod)). 39.32/11.36 thf(1808,plain,((! [A:int,B:int,C:int]: ((zcong @ A @ B @ C) = (zcong @ (div_mod_int @ A @ C) @ (div_mod_int @ B @ C) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 39.32/11.36 thf(534,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) & (B != zero_zero_nat)) = ((power_power_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_nat__power__eq__0__iff)). 39.32/11.36 thf(2659,plain,((! [A:nat,B:nat]: (((A = zero_zero_nat) & ~ (B = zero_zero_nat)) = ((power_power_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 39.32/11.36 thf(783,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 39.32/11.36 thf(3417,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 39.32/11.36 thf(487,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ B @ A) @ (times_times_nat @ B @ (power_power_nat @ B @ A))) <= (ord_less_nat @ one_one_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_power__less__power__Suc)). 39.32/11.36 thf(2527,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ B @ A) @ (times_times_nat @ B @ (power_power_nat @ B @ A))) | ~ (ord_less_nat @ one_one_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 39.32/11.36 thf(694,axiom,((! [A:nat,B:nat]: (((times_times_nat @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_realpow__minus__mult)). 39.32/11.36 thf(3153,plain,((! [A:nat,B:nat]: (((times_times_nat @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])). 39.32/11.36 thf(799,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (times_times_int @ (number_number_of_int @ B) @ C)) = (times_times_int @ (number_number_of_int @ (times_times_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_mult__number__of__left)). 39.32/11.36 thf(3460,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (times_times_int @ (number_number_of_int @ B) @ C)) = (times_times_int @ (number_number_of_int @ (times_times_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 39.32/11.36 thf(83,axiom,((! [A:int,B:int]: ((standardRes @ A @ B) = (div_mod_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_StandardRes__def)). 39.32/11.36 thf(1422,plain,((! [A:int,B:int]: ((standardRes @ A @ B) = (div_mod_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 39.32/11.36 thf(621,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) <= (member_int @ A @ (d22set @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_d22set__le)). 39.32/11.36 thf(2947,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (member_int @ A @ (d22set @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 39.32/11.36 thf(134,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ C @ B)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_mult__less__cancel__left__disj)). 39.32/11.36 thf(1569,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ C @ B)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 39.32/11.36 thf(977,axiom,((! [A:int]: (((div_mod_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) != zero_zero_int) = ((div_mod_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_neq__one__mod__two)). 39.32/11.36 thf(3959,plain,((! [A:int]: ((~ ((div_mod_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = zero_zero_int)) = ((div_mod_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])). 39.32/11.36 thf(384,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_dvd__mult__cancel)). 39.32/11.36 thf(2248,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 39.32/11.36 thf(538,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_minus__nat_Odiff__0)). 39.32/11.36 thf(2671,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])). 39.32/11.36 thf(960,axiom,((one_one_real = (number267125858f_real @ (bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_semiring__norm_I110_J)). 39.32/11.36 thf(3910,plain,((one_one_real = (number267125858f_real @ (bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])). 39.32/11.36 thf(397,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ A) => (~ (zcong @ B @ zero_zero_int @ A))) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_zcong__not__zero)). 39.32/11.36 thf(2282,plain,((! [A:int,B:int]: (((ord_less_int @ B @ A) => (~ (zcong @ B @ zero_zero_int @ A))) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 39.32/11.36 thf(142,axiom,((! [A:nat,B:int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_zero__less__power)). 39.32/11.36 thf(1591,plain,((! [A:nat,B:int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 39.32/11.36 thf(340,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (times_times_real @ B @ A)) = (times_times_real @ (plus_plus_real @ B @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 39.32/11.36 thf(2114,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ (times_times_real @ B @ A)) = (times_times_real @ (plus_plus_real @ B @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 39.32/11.36 thf(585,axiom,((! [A:int,B:int,C:int]: ((zprime @ C) => ((ord_less_int @ zero_zero_int @ B) => ((zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C) => ((zcong @ B @ zero_zero_int @ C) | (zcong @ A @ zero_zero_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_zcong__zprime__prod__zero)). 39.32/11.36 thf(2837,plain,((! [A:int,B:int,C:int]: ((zprime @ C) => ((ord_less_int @ zero_zero_int @ B) => ((zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C) => ((zcong @ B @ zero_zero_int @ C) | (zcong @ A @ zero_zero_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])). 39.32/11.36 thf(1064,axiom,(((number_number_of_int @ (bit1 @ pls)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_semiring__numeral__1__eq__1)). 39.32/11.36 thf(4215,plain,(((number_number_of_int @ (bit1 @ pls)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064])). 39.32/11.36 thf(435,axiom,((! [A:int,B:int]: ((((zcong @ B @ zero_zero_int @ A) => (B = zero_zero_int)) <= (ord_less_int @ B @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_Int2_Ozcong__zero)). 39.32/11.36 thf(2380,plain,((! [A:int,B:int]: (((zcong @ B @ zero_zero_int @ A) => (B = zero_zero_int)) | ~ (ord_less_int @ B @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 39.32/11.36 thf(773,axiom,((! [A:int]: ((ord_less_eq_int @ one_one_int @ (number_number_of_int @ A)) = (ord_less_eq_int @ (bit1 @ pls) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_le__special_I2_J)). 39.32/11.36 thf(3382,plain,((! [A:int]: ((ord_less_eq_int @ one_one_int @ (number_number_of_int @ A)) = (ord_less_eq_int @ (bit1 @ pls) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])). 39.32/11.36 thf(1158,axiom,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_power__one)). 39.32/11.36 thf(4479,plain,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158])). 39.32/11.36 thf(543,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ (div_mod_int @ A @ B)) & (ord_less_eq_int @ (div_mod_int @ A @ B) @ zero_zero_int)) <= (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_neg__mod__conj)). 39.32/11.36 thf(2686,plain,((! [A:int,B:int]: (((ord_less_int @ B @ (div_mod_int @ A @ B)) & (ord_less_eq_int @ (div_mod_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 39.32/11.36 thf(43,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_order__le__neq__implies__less)). 39.32/11.36 thf(1310,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 39.32/11.36 thf(767,axiom,((! [A:int]: ((power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_int @ (times_times_int @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power3__eq__cube)). 39.32/11.36 thf(3365,plain,((! [A:int]: ((power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_int @ (times_times_int @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])). 39.32/11.36 thf(1066,axiom,((! [A:int]: ((plus_plus_int @ (number_number_of_int @ pls) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__numeral__0)). 39.32/11.36 thf(4220,plain,((! [A:int]: ((plus_plus_int @ (number_number_of_int @ pls) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066])). 39.32/11.36 thf(411,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((dvd_dvd_int @ B @ C) <= (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_zdvd__mult__cancel)). 39.32/11.36 thf(2316,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((dvd_dvd_int @ B @ C) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 39.32/11.36 thf(914,axiom,(((number267125858f_real @ (bit1 @ pls)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_numeral__1__eq__1)). 39.32/11.36 thf(3781,plain,(((number267125858f_real @ (bit1 @ pls)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])). 39.32/11.36 thf(746,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_mult__0)). 39.32/11.36 thf(3313,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 39.32/11.36 thf(282,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_dvd__triv__right)). 39.32/11.36 thf(1954,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 39.32/11.36 thf(350,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_not__less0)). 39.32/11.36 thf(2146,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 39.32/11.36 thf(109,axiom,((! [A:int,B:int]: ((A != B) => ((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_linorder__neqE__linordered__idom)). 39.32/11.36 thf(1497,plain,((! [A:int,B:int]: ((~ (A = B)) => ((ord_less_int @ B @ A) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 39.32/11.36 thf(646,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ zero_zero_nat) => ((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_mult__neg__pos)). 39.32/11.36 thf(3017,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ zero_zero_nat) => ((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])). 39.32/11.36 thf(1025,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 39.32/11.36 thf(4090,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])). 39.32/11.36 thf(166,axiom,((! [A:int,B:int]: ((((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B))) = (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_mult__le__0__iff)). 39.32/11.36 thf(1655,plain,((! [A:int,B:int]: ((((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B))) = (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 39.32/11.36 thf(658,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_less__eq__nat_Osimps_I1_J)). 39.32/11.36 thf(3049,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])). 39.32/11.36 thf(902,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_zadd__0)). 39.32/11.36 thf(3745,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])). 39.32/11.36 thf(689,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_neq0__conv)). 39.32/11.36 thf(3135,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 39.32/11.36 thf(971,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_power__mult)). 39.32/11.36 thf(3942,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])). 39.32/11.36 thf(868,axiom,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_int)) => (dvd_dvd_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_dvd__power)). 39.32/11.36 thf(3649,plain,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_int)) => (dvd_dvd_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[868])). 39.32/11.36 thf(1003,axiom,((! [A:int,B:nat]: (((number_number_of_nat @ A) = B) = (B = (number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_number__of__reorient)). 39.32/11.36 thf(4026,plain,((! [A:int,B:nat]: (((number_number_of_nat @ A) = B) = (B = (number_number_of_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003])). 39.32/11.36 thf(656,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_nat__diff__add__eq1)). 39.32/11.36 thf(3044,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 39.32/11.36 thf(30,axiom,((! [A:real]: (dvd_dvd_real @ A @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_dvd__0__right)). 39.32/11.36 thf(1275,plain,((! [A:real]: (dvd_dvd_real @ A @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 39.32/11.36 thf(348,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ (div_mod_int @ A @ B)) <= (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_neg__mod__bound)). 39.32/11.36 thf(2141,plain,((! [A:int,B:int]: ((ord_less_int @ B @ (div_mod_int @ A @ B)) | ~ (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 39.32/11.36 thf(49,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A))) <= (ord_less_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_mult__neg__neg)). 39.32/11.36 thf(1327,plain,((! [A:real,B:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A))) | ~ (ord_less_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 39.32/11.36 thf(883,axiom,((! [A:int]: ((zprime @ A) => (((ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ A) <= (A != (number_number_of_int @ (bit1 @ (bit1 @ pls))))) <= (A != (number_number_of_int @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_prime__g__5)). 39.32/11.36 thf(3693,plain,((! [A:int]: ((zprime @ A) => ((ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ A) | (A = (number_number_of_int @ (bit1 @ (bit1 @ pls)))) | (A = (number_number_of_int @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])). 39.32/11.36 thf(522,axiom,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_power__one__right)). 39.32/11.36 thf(2627,plain,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 39.32/11.36 thf(359,axiom,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ B) = (power_power_real @ C @ B)) => ((((ord_less_nat @ zero_zero_nat @ B) => (A = C)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_power__eq__imp__eq__base)). 39.32/11.36 thf(2168,plain,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ B) = (power_power_real @ C @ B)) => (((ord_less_nat @ zero_zero_nat @ B) => (A = C)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 39.32/11.36 thf(782,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => ((ord_less_eq_int @ pls @ A) => ((plus_plus_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)) = (number267125858f_real @ (plus_plus_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_semiring__add__number__of)). 39.32/11.36 thf(3414,plain,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => ((ord_less_eq_int @ pls @ A) => ((plus_plus_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)) = (number267125858f_real @ (plus_plus_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 39.32/11.36 thf(684,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 39.32/11.36 thf(3121,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 39.32/11.36 thf(1075,axiom,((! [A:int,B:int,C:int,D:int]: (((zprime @ D) => ((~ (zcong @ C @ zero_zero_int @ D)) => ((zcong @ (times_times_int @ A @ C) @ (times_times_int @ (times_times_int @ B @ (multInv @ D @ C)) @ C) @ D) => (zcong @ (times_times_int @ A @ C) @ B @ D)))) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_aux______2)). 39.32/11.36 thf(4247,plain,((! [A:int,B:int,C:int,D:int]: (((zprime @ D) => ((~ (zcong @ C @ zero_zero_int @ D)) => ((zcong @ (times_times_int @ A @ C) @ (times_times_int @ (times_times_int @ B @ (multInv @ D @ C)) @ C) @ D) => (zcong @ (times_times_int @ A @ C) @ B @ D)))) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075])). 39.32/11.36 thf(838,axiom,((! [A:nat]: ((power_power_int @ (number_number_of_int @ min) @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A)) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_power__m1__even)). 39.32/11.36 thf(3562,plain,((! [A:nat]: ((power_power_int @ (number_number_of_int @ min) @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A)) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])). 39.32/11.36 thf(112,axiom,((! [A:int,B:int]: ((zcong @ A @ zero_zero_int @ B) = (dvd_dvd_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_zcong__zero__equiv__div)). 39.32/11.36 thf(1507,plain,((! [A:int,B:int]: ((zcong @ A @ zero_zero_int @ B) = (dvd_dvd_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 39.32/11.36 thf(427,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C)) = (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_mult__less__cancel2)). 39.32/11.36 thf(2360,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C)) = (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 39.32/11.36 thf(732,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) => ((dvd_dvd_int @ A @ B) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_zdvd__zdiffD)). 39.32/11.36 thf(3276,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) => ((dvd_dvd_int @ A @ B) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])). 39.32/11.36 thf(506,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ zero_zero_int) => ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_mult__neg__neg)). 39.32/11.36 thf(2575,plain,((! [A:int,B:int]: ((ord_less_int @ B @ zero_zero_int) => ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 39.32/11.36 thf(234,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_less__imp__add__positive)). 39.32/11.36 thf(1835,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 39.32/11.36 thf(861,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((E != zero_zero_int) => (((C = D) & (A != B)) => ((plus_plus_int @ C @ (times_times_int @ E @ A)) != (plus_plus_int @ D @ (times_times_int @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_add__scale__eq__noteq)). 39.32/11.36 thf(3629,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((~ (E = zero_zero_int)) => (((C = D) & ~ (A = B)) => (~ ((plus_plus_int @ C @ (times_times_int @ E @ A)) = (plus_plus_int @ D @ (times_times_int @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[861])). 39.32/11.36 thf(422,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_add__leD2)). 39.32/11.36 thf(2348,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 39.32/11.36 thf(813,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_dvd__triv__left)). 39.32/11.36 thf(3502,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])). 39.32/11.36 thf(1021,axiom,((! [A:int]: ((ord_less_eq_int @ (bit1 @ A) @ pls) = (ord_less_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rel__simps_I29_J)). 39.32/11.36 thf(4079,plain,((! [A:int]: ((ord_less_eq_int @ (bit1 @ A) @ pls) = (ord_less_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021])). 39.32/11.36 thf(896,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ A) @ B) @ (times_times_int @ (number_number_of_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_right__diff__distrib__number__of)). 39.32/11.36 thf(3730,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ A) @ B) @ (times_times_int @ (number_number_of_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])). 39.32/11.36 thf(603,axiom,((! [A:nat,B:nat,C:real]: (((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) => (ord_less_nat @ A @ B)) <= (ord_less_real @ one_one_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_power__less__imp__less__exp)). 39.32/11.36 thf(2886,plain,((! [A:nat,B:nat,C:real]: (((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) => (ord_less_nat @ A @ B)) | ~ (ord_less_real @ one_one_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])). 39.32/11.36 thf(1046,axiom,((! [A:int,B:int,C:int,D:int]: ((zcong @ (times_times_int @ B @ A) @ (times_times_int @ C @ A) @ D) <= (zcong @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_zcong__scalar)). 39.32/11.36 thf(4156,plain,((! [A:int,B:int,C:int,D:int]: ((zcong @ (times_times_int @ B @ A) @ (times_times_int @ C @ A) @ D) | ~ (zcong @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046])). 39.32/11.36 thf(625,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_combine__common__factor)). 39.32/11.36 thf(2957,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])). 39.32/11.36 thf(755,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_add__less__mono1)). 39.32/11.36 thf(3335,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])). 39.32/11.36 thf(1011,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (((times_times_int @ B @ A) = one_one_int) = ((A = one_one_int) & (B = one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_pos__zmult__eq__1__iff)). 39.32/11.36 thf(4047,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (((times_times_int @ B @ A) = one_one_int) = ((A = one_one_int) & (B = one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])). 39.32/11.36 thf(1041,axiom,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_mult__2__right)). 39.32/11.36 thf(4142,plain,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041])). 39.32/11.36 thf(314,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_power__decreasing)). 39.32/11.36 thf(2046,plain,((! [A:real,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 39.32/11.36 thf(991,axiom,((! [A:int]: (ord_less_eq_int @ A @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_power2__ge__self)). 39.32/11.36 thf(3994,plain,((! [A:int]: (ord_less_eq_int @ A @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])). 39.32/11.36 thf(265,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ A @ C) => ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_Euler_Oaux2)). 39.32/11.36 thf(1914,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ A @ C) => ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 39.32/11.36 thf(561,axiom,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_int @ min @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_rel__simps_I8_J)). 39.32/11.36 thf(2763,plain,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_int @ min @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 39.32/11.36 thf(962,axiom,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ C @ B)) <= ((minus_minus_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_Int2_Oaux1)). 39.32/11.36 thf(3915,plain,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ C @ B)) | ~ ((minus_minus_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])). 39.32/11.36 thf(672,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (member_int @ B @ (d22set @ A))) <= (ord_less_int @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_d22set__mem)). 39.32/11.36 thf(3088,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (member_int @ B @ (d22set @ A))) | ~ (ord_less_int @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 39.32/11.36 thf(912,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((zcong @ (plus_plus_int @ C @ A) @ (plus_plus_int @ D @ B) @ E) <= (zcong @ A @ B @ E)) <= (zcong @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_zcong__zadd)). 39.32/11.36 thf(3777,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ (plus_plus_int @ C @ A) @ (plus_plus_int @ D @ B) @ E) | ~ (zcong @ A @ B @ E) | ~ (zcong @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])). 39.32/11.36 thf(744,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((~ (((ord_less_nat @ B @ C) & ~ (A @ zero_zero_nat)) | ? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))))) = (A @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_nat__diff__split__asm)). 39.32/11.36 thf(3308,plain,((! [A:(nat > $o),B:nat,C:nat]: ((~ (((ord_less_nat @ B @ C) & ~ (A @ zero_zero_nat)) | ? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))))) = (A @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])). 39.32/11.36 thf(302,axiom,((! [A:int,B:int,C:int]: ((((~ (zcong @ A @ zero_zero_int @ C) & ~ (zcong @ B @ zero_zero_int @ C)) => (~ (zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C))) <= (ord_less_int @ zero_zero_int @ B)) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_zcong__zprime__prod__zero__contra)). 39.32/11.36 thf(2010,plain,((! [A:int,B:int,C:int]: (((~ (zcong @ A @ zero_zero_int @ C) & ~ (zcong @ B @ zero_zero_int @ C)) => (~ (zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C))) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 39.32/11.36 thf(274,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ A) => ((zcong @ (times_times_int @ A @ A) @ one_one_int @ B) => ((zcong @ A @ one_one_int @ B) | (zcong @ A @ (minus_minus_int @ B @ one_one_int) @ B)))) <= (zprime @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_zcong__square)). 39.32/11.36 thf(1935,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ A) => ((zcong @ (times_times_int @ A @ A) @ one_one_int @ B) => ((zcong @ A @ one_one_int @ B) | (zcong @ A @ (minus_minus_int @ B @ one_one_int) @ B)))) | ~ (zprime @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 39.32/11.36 thf(973,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ (number_number_of_int @ C)) = (plus_plus_int @ (times_times_int @ A @ (number_number_of_int @ C)) @ (times_times_int @ B @ (number_number_of_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_left__distrib__number__of)). 39.32/11.36 thf(3947,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ (number_number_of_int @ C)) = (plus_plus_int @ (times_times_int @ A @ (number_number_of_int @ C)) @ (times_times_int @ B @ (number_number_of_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[973])). 39.32/11.36 thf(146,axiom,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_power__one__right)). 39.32/11.36 thf(1601,plain,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 39.32/11.36 thf(734,axiom,((! [A:int,B:nat,C:int]: ((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) => ((ord_less_int @ A @ C) <= (ord_less_eq_int @ zero_zero_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_power__less__imp__less__base)). 39.32/11.36 thf(3281,plain,((! [A:int,B:nat,C:int]: ((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) => ((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])). 39.32/11.36 thf(801,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ A) <= (A = (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_dvdI)). 39.32/11.36 thf(3466,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ A) | ~ (A = (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 39.32/11.36 thf(1058,axiom,((! [A:nat,B:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ (plus_plus_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_nat @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__sum)). 39.32/11.36 thf(4198,plain,((! [A:nat,B:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ (plus_plus_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_nat @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058])). 39.32/11.36 thf(328,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_zero__le__mult__iff)). 39.32/11.36 thf(2082,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 39.32/11.36 thf(1039,axiom,((! [A:real]: ((times_times_real @ A @ A) = (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 39.32/11.36 thf(4137,plain,((! [A:real]: ((times_times_real @ A @ A) = (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039])). 39.32/11.36 thf(193,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_add__le__mono1)). 39.32/11.36 thf(1724,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 39.32/11.36 thf(102,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_nat__add__left__commute)). 39.32/11.36 thf(1475,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 39.32/11.36 thf(443,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) <= (B != zero_zero_nat)) <= (dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_divides__rev)). 39.32/11.36 thf(2400,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) | (B = zero_zero_nat) | ~ (dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 39.32/11.36 thf(581,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ B @ A)) <= (ord_less_int @ A @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_mult__strict__right__mono__neg)). 39.32/11.36 thf(2825,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ B @ A)) | ~ (ord_less_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 39.32/11.36 thf(287,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 39.32/11.36 thf(1967,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 39.32/11.36 thf(946,axiom,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_power__0)). 39.32/11.36 thf(3878,plain,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[946])). 39.32/11.36 thf(346,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__add__diff__inverse)). 39.32/11.36 thf(2136,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 39.32/11.36 thf(116,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_int @ C @ B) => (ord_less_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C) @ (times_times_int @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_zmult2__lemma__aux4)). 39.32/11.36 thf(1518,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_int @ C @ B) => (ord_less_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C) @ (times_times_int @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 39.32/11.36 thf(12,axiom,((! [A:nat,B:nat,C:real,D:real]: (((dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ D @ B)) <= (ord_less_eq_nat @ A @ B)) <= (dvd_dvd_real @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_dvd__power__le)). 39.32/11.36 thf(1228,plain,((! [A:nat,B:nat,C:real,D:real]: ((dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ D @ B)) | ~ (ord_less_eq_nat @ A @ B) | ~ (dvd_dvd_real @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 39.32/11.36 thf(155,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ B) = (dvd_dvd_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) <= (C != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_zdvd__mono)). 39.32/11.36 thf(1623,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ B) = (dvd_dvd_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) | (C = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 39.32/11.36 thf(1076,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B))) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_power__decreasing)). 39.32/11.36 thf(4249,plain,((! [A:int,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076])). 39.32/11.36 thf(255,axiom,((! [A:int,B:int]: ((((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => ((inv @ B @ A) != (minus_minus_int @ B @ one_one_int))) <= (ord_less_int @ one_one_int @ A)) <= (zprime @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_inv__not__p__minus__1)). 39.32/11.36 thf(1887,plain,((! [A:int,B:int]: (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (~ ((inv @ B @ A) = (minus_minus_int @ B @ one_one_int)))) | ~ (ord_less_int @ one_one_int @ A) | ~ (zprime @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 39.32/11.36 thf(513,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ C @ A)) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_less__diff__iff)). 39.32/11.36 thf(2603,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 39.32/11.36 thf(1187,axiom,((! [A:int,B:int]: ((bit1 @ A) != (bit0 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rel__simps_I50_J)). 39.32/11.36 thf(4563,plain,((! [A:int,B:int]: ~ ((bit1 @ A) = (bit0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187])). 39.32/11.36 thf(207,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_mult__strict__left__mono)). 39.32/11.36 thf(1760,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 39.32/11.36 thf(392,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_power__mult)). 39.32/11.36 thf(2269,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 39.32/11.36 thf(549,axiom,((! [A:real,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((? [C:real]: (((power_power_real @ C @ B) = A) & ! [D:real]: (((ord_less_real @ zero_zero_real @ D) & ((power_power_real @ D @ B) = A)) => (D = C)) & (ord_less_real @ zero_zero_real @ C))) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_realpow__pos__nth__unique)). 39.32/11.36 thf(2708,plain,((! [A:real,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => (? [C:real]: (((power_power_real @ C @ B) = A) & ! [D:real]: (((ord_less_real @ zero_zero_real @ D) & ((power_power_real @ D @ B) = A)) => (D = C)) & (ord_less_real @ zero_zero_real @ C)) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 39.32/11.36 thf(479,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_power__strict__increasing)). 39.32/11.36 thf(2501,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 39.32/11.36 thf(467,axiom,((! [A:real,B:real]: (((A = zero_zero_real) & (B = zero_zero_real)) = ((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_real__two__squares__add__zero__iff)). 39.32/11.36 thf(2466,plain,((! [A:real,B:real]: (((A = zero_zero_real) & (B = zero_zero_real)) = ((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 39.32/11.36 thf(532,axiom,((! [A:nat]: ~ (~ (dvd_dvd_nat @ one_one_nat @ A) & (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot)). 39.32/11.36 thf(2654,plain,((! [A:nat]: ~ (~ (dvd_dvd_nat @ one_one_nat @ A) & (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])). 39.32/11.36 thf(157,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_dvd__mult__left)). 39.32/11.36 thf(1628,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 39.32/11.36 thf(78,axiom,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_not__square__less__zero)). 39.32/11.36 thf(1409,plain,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 39.32/11.36 thf(1072,axiom,((! [A:int,B:int]: ((times_times_int @ A @ B) = (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 39.32/11.36 thf(4238,plain,((! [A:int,B:int]: ((times_times_int @ A @ B) = (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072])). 39.32/11.36 thf(728,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ (div_mod_int @ A @ B)) & (ord_less_int @ (div_mod_int @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_pos__mod__conj)). 39.32/11.36 thf(3263,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ (div_mod_int @ A @ B)) & (ord_less_int @ (div_mod_int @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])). 39.32/11.36 thf(1145,axiom,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_realpow__two__sum__zero__iff)). 39.32/11.36 thf(4439,plain,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145])). 39.32/11.36 thf(786,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__eq__int__code_I14_J)). 39.32/11.36 thf(3425,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])). 39.32/11.36 thf(217,axiom,((! [A:nat,B:nat]: ((~ (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A))) <= (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_dvd_Oless__asym_H)). 39.32/11.36 thf(1792,plain,((! [A:nat,B:nat]: (~ (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)) | ~ (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 39.32/11.36 thf(86,axiom,((! [A:int]: (dvd_dvd_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_dvd__refl)). 39.32/11.36 thf(1430,plain,((! [A:int]: (dvd_dvd_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 39.32/11.36 thf(1018,axiom,(((ord_less_int @ one_one_int @ t) => (? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06)). 39.32/11.36 thf(4070,plain,(((ord_less_int @ one_one_int @ t) => (? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018])). 39.32/11.36 thf(1044,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_int @ one_one_int @ A) => (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_power__strict__increasing)). 39.32/11.36 thf(4151,plain,((! [A:int,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_int @ one_one_int @ A) => (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044])). 39.32/11.36 thf(857,axiom,((! [A:int]: ((times_times_int @ A @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cube__square)). 39.32/11.36 thf(3617,plain,((! [A:int]: ((times_times_int @ A @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[857])). 39.32/11.36 thf(244,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_diff__is__0__eq)). 39.32/11.36 thf(1860,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 39.32/11.36 thf(394,axiom,((! [A:int]: ((ord_less_int @ A @ pls) = (ord_less_real @ (number267125858f_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_less__special_I3_J)). 39.32/11.36 thf(2274,plain,((! [A:int]: ((ord_less_int @ A @ pls) = (ord_less_real @ (number267125858f_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 39.32/11.36 thf(807,axiom,((twoSqu919416604sum2sq @ (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_qf1pt)). 39.32/11.36 thf(3485,plain,((twoSqu919416604sum2sq @ (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 39.32/11.36 thf(44,axiom,((! [A:nat,B:int]: ((((number_number_of_nat @ B) = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A)) = (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ (number_number_of_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_zero__less__power__nat__eq__number__of)). 39.32/11.36 thf(1313,plain,((! [A:nat,B:int]: ((((number_number_of_nat @ B) = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A)) = (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ (number_number_of_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 39.32/11.36 thf(32,axiom,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_one__dvd)). 39.32/11.36 thf(1279,plain,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 39.32/11.36 thf(1086,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit0 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I14_J)). 39.32/11.36 thf(4275,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit0 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086])). 39.32/11.36 thf(781,axiom,((! [A:int]: (pls != (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rel__simps_I39_J)). 39.32/11.36 thf(3410,plain,((! [A:int]: ~ (pls = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])). 39.32/11.36 thf(366,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (div_mod_nat @ A @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_mod__le__divisor)). 39.32/11.36 thf(2185,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (div_mod_nat @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 39.32/11.36 thf(501,axiom,((! [A:nat,B:nat]: (((A = one_one_nat) = (dvd_dvd_nat @ (times_times_nat @ A @ B) @ B)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_dvd__mult__cancel2)). 39.32/11.36 thf(2562,plain,((! [A:nat,B:nat]: (((A = one_one_nat) = (dvd_dvd_nat @ (times_times_nat @ A @ B) @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 39.32/11.36 thf(1002,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 39.32/11.36 thf(4023,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])). 39.32/11.36 thf(475,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_zmult__zless__mono2)). 39.32/11.36 thf(2488,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 39.32/11.36 thf(233,axiom,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_not__square__less__zero)). 39.32/11.36 thf(1832,plain,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 39.32/11.36 thf(607,axiom,((! [A:int]: ((div_mod_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_zmod__zero)). 39.32/11.36 thf(2897,plain,((! [A:int]: ((div_mod_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 39.32/11.36 thf(1141,axiom,(((number_number_of_int @ pls) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_semiring__numeral__0__eq__0)). 39.32/11.36 thf(4428,plain,(((number_number_of_int @ pls) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141])). 39.32/11.36 thf(938,axiom,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_sum__power2__eq__zero__iff)). 39.32/11.36 thf(3855,plain,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[938])). 39.32/11.36 thf(450,axiom,((! [A:real,B:real,C:real,D:real]: (((B = D) | (A = C)) = ((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_crossproduct__eq)). 39.32/11.36 thf(2420,plain,((! [A:real,B:real,C:real,D:real]: (((B = D) | (A = C)) = ((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 39.32/11.36 thf(676,axiom,((! [A:nat,B:nat,C:int,D:int]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (power_power_int @ C @ A) @ (power_power_int @ D @ B))) <= (dvd_dvd_int @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_dvd__power__le)). 39.32/11.36 thf(3099,plain,((! [A:nat,B:nat,C:int,D:int]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (power_power_int @ C @ A) @ (power_power_int @ D @ B))) | ~ (dvd_dvd_int @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])). 39.32/11.36 thf(820,axiom,((zprime @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_p)). 39.32/11.36 thf(3517,plain,((zprime @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 39.32/11.36 thf(149,axiom,((! [A:real,B:real]: ((times_times_real @ A @ B) = (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 39.32/11.36 thf(1609,plain,((! [A:real,B:real]: ((times_times_real @ A @ B) = (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 39.32/11.36 thf(1084,axiom,((! [A:int,B:int,C:int]: ((~ (zcong @ B @ zero_zero_int @ C)) => ((~ (dvd_dvd_int @ C @ A)) <= (zcong @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_Euler_Oaux____1)). 39.32/11.36 thf(4270,plain,((! [A:int,B:int,C:int]: ((~ (zcong @ B @ zero_zero_int @ C)) => (~ (dvd_dvd_int @ C @ A) | ~ (zcong @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084])). 39.32/11.36 thf(525,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))) <= (ord_less_eq_real @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_mult__mono)). 39.32/11.36 thf(2635,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))) | ~ (ord_less_eq_real @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 39.32/11.36 thf(637,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ zero_zero_nat @ A)) = (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_nat__0__less__mult__iff)). 39.32/11.36 thf(2989,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ zero_zero_nat @ A)) = (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 39.32/11.36 thf(1128,axiom,((! [A:int]: ((times_times_int @ pls @ A) = pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_mult__Pls)). 39.32/11.36 thf(4390,plain,((! [A:int]: ((times_times_int @ pls @ A) = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128])). 39.32/11.36 thf(438,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B)) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_le__diff__conv2)). 39.32/11.36 thf(2388,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B)) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 39.32/11.36 thf(726,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_trans__le__add1)). 39.32/11.36 thf(3258,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 39.32/11.36 thf(917,axiom,((zero_zero_int = (number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_zero__is__num__zero)). 39.32/11.36 thf(3788,plain,((zero_zero_int = (number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[917])). 39.32/11.36 thf(932,axiom,((! [A:int,B:int]: ((number_number_of_int @ (times_times_int @ A @ B)) = (times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_number__of__mult)). 39.32/11.36 thf(3840,plain,((! [A:int,B:int]: ((number_number_of_int @ (times_times_int @ A @ B)) = (times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[932])). 39.32/11.36 thf(774,axiom,((! [A:int]: ((ord_less_int @ (number_number_of_int @ A) @ zero_zero_int) = (ord_less_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_less__special_I3_J)). 39.32/11.36 thf(3385,plain,((! [A:int]: ((ord_less_int @ (number_number_of_int @ A) @ zero_zero_int) = (ord_less_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])). 39.32/11.36 thf(800,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (times_times_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 39.32/11.36 thf(3463,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (times_times_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])). 39.32/11.36 thf(66,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_diff__le__mono2)). 39.32/11.36 thf(1379,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 39.32/11.36 thf(444,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_dvd__reduce)). 39.32/11.36 thf(2403,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 39.32/11.36 thf(864,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => (((zcong @ (multInv @ B @ (multInv @ B @ A)) @ A @ B) <= (~ (zcong @ A @ zero_zero_int @ B))) <= (zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_MultInv__prop4)). 39.32/11.36 thf(3638,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zcong @ (multInv @ B @ (multInv @ B @ A)) @ A @ B) | (zcong @ A @ zero_zero_int @ B) | ~ (zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[864])). 39.32/11.36 thf(46,axiom,((! [A:int]: ((ord_less_eq_real @ zero_zero_real @ (number267125858f_real @ A)) = (ord_less_eq_int @ pls @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__special_I1_J)). 39.32/11.36 thf(1319,plain,((! [A:int]: ((ord_less_eq_real @ zero_zero_real @ (number267125858f_real @ A)) = (ord_less_eq_int @ pls @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 39.32/11.36 thf(184,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((ord_less_eq_nat @ zero_zero_nat @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_mult__mono)). 39.32/11.36 thf(1704,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ zero_zero_nat @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 39.32/11.36 thf(256,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))) <= (ord_less_real @ zero_zero_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_real__mult__le__cancel__iff1)). 39.32/11.36 thf(1890,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))) | ~ (ord_less_real @ zero_zero_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 39.32/11.36 thf(432,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (plus_plus_nat @ C @ A)) => (dvd_dvd_nat @ B @ A)) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_divides__add__revr)). 39.32/11.36 thf(2373,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (plus_plus_nat @ C @ A)) => (dvd_dvd_nat @ B @ A)) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 39.32/11.36 thf(135,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_mult__zero__left)). 39.32/11.36 thf(1572,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 39.32/11.36 thf(963,axiom,((! [A:int,B:int,C:int]: (((zprime @ C) => ((((zcong @ B @ A @ C) <= (zcong @ (multInv @ C @ B) @ (multInv @ C @ A) @ C)) <= (~ (zcong @ A @ zero_zero_int @ C))) <= (~ (zcong @ B @ zero_zero_int @ C)))) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_MultInv__prop5)). 39.32/11.36 thf(3919,plain,((! [A:int,B:int,C:int]: (((zprime @ C) => ((zcong @ B @ A @ C) | ~ (zcong @ (multInv @ C @ B) @ (multInv @ C @ A) @ C) | (zcong @ A @ zero_zero_int @ C) | (zcong @ B @ zero_zero_int @ C))) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[963])). 39.32/11.36 thf(200,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_mult__less__cancel__left__neg)). 39.32/11.36 thf(1741,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 39.32/11.36 thf(73,axiom,((ord_less_eq_int @ min @ pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_rel__simps_I23_J)). 39.32/11.36 thf(1398,plain,((ord_less_eq_int @ min @ pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 39.32/11.36 thf(1183,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 39.32/11.36 thf(4551,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183])). 39.32/11.36 thf(956,axiom,(((number_number_of_nat @ (bit1 @ pls)) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_semiring__numeral__1__eq__1)). 39.32/11.36 thf(3902,plain,(((number_number_of_nat @ (bit1 @ pls)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[956])). 39.32/11.36 thf(870,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 39.32/11.36 thf(3657,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[870])). 39.32/11.36 thf(645,axiom,((! [A:real,B:real]: ((((times_times_real @ B @ A) != zero_zero_real) <= (A != zero_zero_real)) <= (B != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_no__zero__divisors)). 39.32/11.36 thf(3014,plain,((! [A:real,B:real]: (~ ((times_times_real @ B @ A) = zero_zero_real) | (A = zero_zero_real) | (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])). 39.32/11.36 thf(484,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) <= (ord_less_eq_int @ A @ zero_zero_int)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_mult__nonneg__nonpos)). 39.32/11.36 thf(2520,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) | ~ (ord_less_eq_int @ A @ zero_zero_int) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 39.32/11.36 thf(307,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_nat__zero__less__power__iff)). 39.32/11.36 thf(2024,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 39.32/11.36 thf(161,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_mult__zero__right)). 39.32/11.36 thf(1641,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 39.32/11.36 thf(888,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__eq__number__of__int__code)). 39.32/11.36 thf(3708,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[888])). 39.32/11.36 thf(405,axiom,((! [A:int]: ((ord_less_eq_int @ A @ (bit1 @ pls)) = (ord_less_eq_real @ (number267125858f_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_le__special_I4_J)). 39.32/11.36 thf(2301,plain,((! [A:int]: ((ord_less_eq_int @ A @ (bit1 @ pls)) = (ord_less_eq_real @ (number267125858f_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 39.32/11.36 thf(108,axiom,((! [A:int,B:(int > $o)]: ((member_int @ A @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mem__def)). 39.32/11.36 thf(1494,plain,((! [A:int,B:(int > $o)]: ((member_int @ A @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 39.32/11.36 thf(836,axiom,((! [A:nat,B:int,C:int,D:int]: ((zprime @ D) => ((~ (dvd_dvd_int @ D @ C)) => ((dvd_dvd_int @ (power_power_int @ D @ A) @ B) <= (dvd_dvd_int @ (power_power_int @ D @ A) @ (times_times_int @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right)). 39.32/11.36 thf(3557,plain,((! [A:nat,B:int,C:int,D:int]: ((zprime @ D) => ((~ (dvd_dvd_int @ D @ C)) => ((dvd_dvd_int @ (power_power_int @ D @ A) @ B) | ~ (dvd_dvd_int @ (power_power_int @ D @ A) @ (times_times_int @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])). 39.32/11.36 thf(250,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) <= (ord_less_real @ one_one_real @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_power__strict__increasing)). 39.32/11.36 thf(1875,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) | ~ (ord_less_real @ one_one_real @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 39.32/11.36 thf(591,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_le__add1)). 39.32/11.36 thf(2852,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 39.32/11.36 thf(716,axiom,((ord_less_int @ min @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_bin__less__0__simps_I2_J)). 39.32/11.36 thf(3231,plain,((ord_less_int @ min @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 39.32/11.36 thf(301,axiom,((! [A:int,B:int]: ((((dvd_dvd_int @ B @ A) => ((dvd_dvd_int @ A @ B) => (B = A))) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_zdvd__antisym__nonneg)). 39.32/11.36 thf(2007,plain,((! [A:int,B:int]: (((dvd_dvd_int @ B @ A) => ((dvd_dvd_int @ A @ B) => (B = A))) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 39.32/11.36 thf(1134,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A @ B)) <= (ord_less_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_power2__less__imp__less)). 39.32/11.36 thf(4411,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A @ B)) | ~ (ord_less_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134])). 39.32/11.36 thf(1130,axiom,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ C @ (times_times_int @ (times_times_int @ A @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 39.32/11.36 thf(4396,plain,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ C @ (times_times_int @ (times_times_int @ A @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130])). 39.32/11.36 thf(169,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_nat @ zero_zero_nat @ B) => (A = C))) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_power__eq__imp__eq__base)). 39.32/11.36 thf(1664,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_nat @ zero_zero_nat @ B) => (A = C))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 39.32/11.36 thf(331,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_mult__strict__right__mono)). 39.32/11.36 thf(2090,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 39.32/11.36 thf(894,axiom,((! [A:int]: ((power_power_real @ (number267125858f_real @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power2__eq__square__number__of)). 39.32/11.36 thf(3724,plain,((! [A:int]: ((power_power_real @ (number267125858f_real @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[894])). 39.32/11.36 thf(674,axiom,((! [A:nat,B:nat,C:real]: (((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) = (ord_less_nat @ A @ B)) <= (ord_less_real @ one_one_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_power__strict__increasing__iff)). 39.32/11.36 thf(3093,plain,((! [A:nat,B:nat,C:real]: (((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) = (ord_less_nat @ A @ B)) | ~ (ord_less_real @ one_one_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 39.32/11.36 thf(106,axiom,((! [A:int]: ((times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (number267125858f_real @ A)) = (number267125858f_real @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0)). 39.32/11.36 thf(1489,plain,((! [A:int]: ((times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (number267125858f_real @ A)) = (number267125858f_real @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 39.32/11.36 thf(380,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ B) => (ord_less_eq_nat @ one_one_nat @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_one__le__power)). 39.32/11.36 thf(2237,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ B) => (ord_less_eq_nat @ one_one_nat @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 39.32/11.36 thf(80,axiom,((! [A:int,B:int]: (((standardRes @ A @ B) = zero_zero_int) = (zcong @ B @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_StandardRes__eq__zcong)). 39.32/11.36 thf(1415,plain,((! [A:int,B:int]: (((standardRes @ A @ B) = zero_zero_int) = (zcong @ B @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 39.32/11.36 thf(823,axiom,(((number267125858f_real @ (bit1 @ pls)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_semiring__numeral__1__eq__1)). 39.32/11.36 thf(3524,plain,(((number267125858f_real @ (bit1 @ pls)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 39.32/11.36 thf(788,axiom,(((number_number_of_nat @ pls) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_nat__number__of__Pls)). 39.32/11.36 thf(3431,plain,(((number_number_of_nat @ pls) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])). 39.32/11.36 thf(949,axiom,((ord_less_nat @ zero_zero_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_pos2)). 39.32/11.36 thf(3887,plain,((ord_less_nat @ zero_zero_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])). 39.32/11.36 thf(414,axiom,((! [A:real,B:nat]: ((dvd_dvd_real @ A @ (power_power_real @ A @ B)) <= ((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_dvd__power)). 39.32/11.36 thf(2324,plain,((! [A:real,B:nat]: ((dvd_dvd_real @ A @ (power_power_real @ A @ B)) | ~ ((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 39.32/11.36 thf(1195,axiom,((! [A:nat]: ((power_power_nat @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_nat @ (times_times_nat @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_power3__eq__cube)). 39.32/11.36 thf(4583,plain,((! [A:nat]: ((power_power_nat @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_nat @ (times_times_nat @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195])). 39.32/11.36 thf(189,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int)) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_mult__pos__neg)). 39.32/11.36 thf(1714,plain,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int)) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 39.32/11.36 thf(308,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_sum__squares__ge__zero)). 39.32/11.36 thf(2027,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 39.32/11.36 thf(667,axiom,((ord_less_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_int__0__less__1)). 39.32/11.36 thf(3075,plain,((ord_less_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 39.32/11.36 thf(225,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_diff__add__inverse)). 39.32/11.36 thf(1811,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 39.32/11.36 thf(264,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ (power_power_real @ A @ B) @ C) = (power_power_real @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 39.32/11.36 thf(1911,plain,((! [A:real,B:nat,C:nat]: ((power_power_real @ (power_power_real @ A @ B) @ C) = (power_power_real @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 39.32/11.36 thf(1200,axiom,((! [A:nat,B:int,C:int,D:int]: ((zcong @ B @ C @ D) => (zcong @ (power_power_int @ B @ A) @ (power_power_int @ C @ A) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_zcong__zpower)). 39.32/11.36 thf(4600,plain,((! [A:nat,B:int,C:int,D:int]: ((zcong @ B @ C @ D) => (zcong @ (power_power_int @ B @ A) @ (power_power_int @ C @ A) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200])). 39.32/11.36 thf(1096,axiom,((! [A:int,B:int]: ((zprime @ B) => ((ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ B) => (((ord_less_int @ A @ B) => ((inv @ B @ (inv @ B @ A)) = A)) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_inv__inv)). 39.32/11.36 thf(4297,plain,((! [A:int,B:int]: ((zprime @ B) => ((ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ B) => (((ord_less_int @ A @ B) => ((inv @ B @ (inv @ B @ A)) = A)) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096])). 39.32/11.36 thf(468,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_dvd__mult)). 39.32/11.36 thf(2469,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 39.32/11.36 thf(81,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ C @ D) => ((ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ D @ B)) <= (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_zadd__zless__mono)). 39.32/11.36 thf(1418,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ C @ D) => ((ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ D @ B)) | ~ (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 39.32/11.36 thf(796,axiom,(((power_power_real @ zero_zero_real @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_zero__power2)). 39.32/11.36 thf(3453,plain,(((power_power_real @ zero_zero_real @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])). 39.32/11.36 thf(52,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_order__le__neq__implies__less)). 39.32/11.36 thf(1334,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 39.32/11.36 thf(886,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ A)) = (ord_less_eq_int @ pls @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__special_I1_J)). 39.32/11.36 thf(3702,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ A)) = (ord_less_eq_int @ pls @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])). 39.32/11.36 thf(791,axiom,((! [A:int,B:int]: ((times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_arith__simps_I32_J)). 39.32/11.36 thf(3438,plain,((! [A:int,B:int]: ((times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 39.32/11.36 thf(1012,axiom,((! [A:int]: ((ord_less_eq_int @ pls @ (bit1 @ A)) = (ord_less_eq_int @ pls @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_rel__simps_I22_J)). 39.32/11.36 thf(4050,plain,((! [A:int]: ((ord_less_eq_int @ pls @ (bit1 @ A)) = (ord_less_eq_int @ pls @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012])). 39.32/11.36 thf(291,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 39.32/11.36 thf(1978,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 39.32/11.36 thf(613,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((! [D:nat]: ((B = (plus_plus_nat @ C @ D)) => (A @ D)) & ((A @ zero_zero_nat) <= (ord_less_nat @ B @ C))) = (A @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_nat__diff__split)). 39.32/11.36 thf(2925,plain,((! [A:(nat > $o),B:nat,C:nat]: ((! [D:nat]: ((B = (plus_plus_nat @ C @ D)) => (A @ D)) & ((A @ zero_zero_nat) | ~ (ord_less_nat @ B @ C))) = (A @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])). 39.32/11.36 thf(982,axiom,((zcong @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ s1 @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096)). 39.32/11.36 thf(3973,plain,((zcong @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ s1 @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])). 39.32/11.36 thf(1038,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) => (A = B)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_power2__eq__imp__eq)). 39.32/11.36 thf(4134,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (A = B)) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038])). 39.32/11.36 thf(764,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ C @ D) => (((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)))) <= (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_mult__mono_H)). 39.32/11.36 thf(3357,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ C @ D) => (((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)))) | ~ (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 39.32/11.36 thf(174,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ B) => ((div_mod_int @ B @ A) = B)) <= (ord_less_eq_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_mod__neg__neg__trivial)). 39.32/11.36 thf(1677,plain,((! [A:int,B:int]: (((ord_less_int @ A @ B) => ((div_mod_int @ B @ A) = B)) | ~ (ord_less_eq_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 39.32/11.36 thf(492,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (div_mod_int @ B @ C)) => ((dvd_dvd_int @ A @ B) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd)). 39.32/11.36 thf(2540,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (div_mod_int @ B @ C)) => ((dvd_dvd_int @ A @ B) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 39.32/11.36 thf(138,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_mult__le__mono1)). 39.32/11.36 thf(1581,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 39.32/11.36 thf(417,axiom,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_dvd__0__left)). 39.32/11.36 thf(2335,plain,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 39.32/11.36 thf(34,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A != B) => (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_order__le__neq__implies__less)). 39.32/11.36 thf(1283,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (A = B)) => (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 39.32/11.36 thf(324,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_dvd__mult2)). 39.32/11.36 thf(2073,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 39.32/11.36 thf(910,axiom,((! [A:int,B:int]: ((plus_plus_int @ (bit0 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__Bit0__Bit1)). 39.32/11.36 thf(3771,plain,((! [A:int,B:int]: ((plus_plus_int @ (bit0 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[910])). 39.32/11.36 thf(936,axiom,(((plus_plus_int @ one_one_int @ one_one_int) = (number_number_of_int @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_one__add__one__is__two)). 39.32/11.36 thf(3851,plain,(((plus_plus_int @ one_one_int @ one_one_int) = (number_number_of_int @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[936])). 39.32/11.36 thf(457,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_comm__mult__strict__left__mono)). 39.32/11.36 thf(2437,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 39.32/11.36 thf(890,axiom,((! [A:int,B:int]: ((minus_minus_int @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_diff__bin__simps_I9_J)). 39.32/11.36 thf(3712,plain,((! [A:int,B:int]: ((minus_minus_int @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])). 39.32/11.36 thf(880,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ (plus_plus_int @ C @ A)) <= (dvd_dvd_int @ B @ A)) <= (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_dvd__add)). 39.32/11.36 thf(3685,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ (plus_plus_int @ C @ A)) | ~ (dvd_dvd_int @ B @ A) | ~ (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[880])). 39.32/11.36 thf(119,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) <= (ord_less_nat @ zero_zero_nat @ A))) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_power__strict__mono)). 39.32/11.36 thf(1526,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A))) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 39.32/11.36 thf(752,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ one_one_int @ C) => ((~ (member_int @ A @ (wset @ (minus_minus_int @ C @ one_one_int) @ B))) => ((member_int @ A @ (wset @ C @ B)) => ((A = C) | (A = (inv @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_wset__mem__imp__or)). 39.32/11.36 thf(3327,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ one_one_int @ C) => ((~ (member_int @ A @ (wset @ (minus_minus_int @ C @ one_one_int) @ B))) => ((member_int @ A @ (wset @ C @ B)) => ((A = C) | (A = (inv @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 39.32/11.36 thf(336,axiom,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 39.32/11.36 thf(2103,plain,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 39.32/11.36 thf(943,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zless__imp__add1__zle)). 39.32/11.36 thf(3870,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])). 39.32/11.36 thf(810,axiom,((! [A:int]: ((bit1 @ A) != pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rel__simps_I46_J)). 39.32/11.36 thf(3492,plain,((! [A:int]: ~ ((bit1 @ A) = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 39.32/11.36 thf(602,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_mult__right__mono)). 39.32/11.36 thf(2884,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])). 39.32/11.36 thf(1022,axiom,((! [A:nat,B:int,C:int]: ((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) <= (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_dvd__power__same)). 39.32/11.36 thf(4082,plain,((! [A:nat,B:int,C:int]: ((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) | ~ (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022])). 39.32/11.36 thf(1005,axiom,((! [A:int]: ((minus_minus_int @ A @ pls) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_diff__bin__simps_I1_J)). 39.32/11.36 thf(4033,plain,((! [A:int]: ((minus_minus_int @ A @ pls) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])). 39.32/11.36 thf(584,axiom,((! [A:int,B:int]: ((~ (zcong @ A @ zero_zero_int @ B)) = ((standardRes @ B @ A) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1190_StandardRes__prop3)). 39.32/11.36 thf(2833,plain,((! [A:int,B:int]: ((~ (zcong @ A @ zero_zero_int @ B)) = (~ ((standardRes @ B @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 39.32/11.36 thf(703,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A))) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_split__mult__neg__le)). 39.32/11.36 thf(3189,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A))) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 39.32/11.36 thf(594,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ B)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_zdvd__imp__le)). 39.32/11.36 thf(2861,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ B)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 39.32/11.36 thf(7,axiom,((! [A:nat,B:nat,C:nat]: ((div_mod_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ B) = (div_mod_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_mod__mult__self3)). 39.32/11.36 thf(1215,plain,((! [A:nat,B:nat,C:nat]: ((div_mod_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ B) = (div_mod_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 39.32/11.36 thf(1024,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_zero__neq__one)). 39.32/11.36 thf(4087,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])). 39.32/11.36 thf(431,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ A) <= (ord_less_eq_int @ C @ A)) <= (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zle__trans)). 39.32/11.36 thf(2371,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ C @ A) | ~ (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 39.32/11.36 thf(1008,axiom,((min != pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_rel__simps_I40_J)). 39.32/11.36 thf(4040,plain,((~ (min = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])). 39.32/11.36 thf(299,axiom,((! [A:int,B:int]: ((~ (member_int @ B @ (d22set @ A))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_d22set__le__swap)). 39.32/11.36 thf(2002,plain,((! [A:int,B:int]: (~ (member_int @ B @ (d22set @ A)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 39.32/11.36 thf(906,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__eq__int__code_I15_J)). 39.32/11.36 thf(3756,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])). 39.32/11.36 thf(721,axiom,((! [A:nat,B:nat]: ((B != A) <= (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_dvd_Oless__imp__not__eq2)). 39.32/11.36 thf(3243,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])). 39.32/11.36 thf(382,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_le__antisym)). 39.32/11.36 thf(2242,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 39.32/11.36 thf(1007,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zcong @ A @ (number_number_of_int @ min) @ B) => (~ (zcong @ A @ one_one_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1)). 39.32/11.36 thf(4038,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zcong @ A @ (number_number_of_int @ min) @ B) => (~ (zcong @ A @ one_one_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])). 39.32/11.36 thf(277,axiom,((! [A:int,B:nat,C:int]: ((zprime @ C) => ((dvd_dvd_int @ C @ (power_power_int @ A @ B)) => (dvd_dvd_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_zprime__zdvd__power)). 39.32/11.36 thf(1943,plain,((! [A:int,B:nat,C:int]: ((zprime @ C) => ((dvd_dvd_int @ C @ (power_power_int @ A @ B)) => (dvd_dvd_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 39.32/11.36 thf(1,conjecture,((? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 39.32/11.36 thf(2,negated_conjecture,((~ (? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),inference(neg_conjecture,[status(cth)],[1])). 39.32/11.36 thf(1201,plain,((~ (? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 39.32/11.36 thf(573,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_diff__0__eq__0)). 39.32/11.36 thf(2804,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])). 39.32/11.36 thf(1175,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) @ zero_zero_int) => (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_even__power__le__0__imp__0)). 39.32/11.36 thf(4519,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) @ zero_zero_int) => (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175])). 39.32/11.36 thf(17,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) <= (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_dvd__mult__right)). 39.32/11.36 thf(1242,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) | ~ (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 39.32/11.36 thf(837,axiom,((! [A:int]: ((plus_plus_int @ A @ A) = (times_times_int @ (plus_plus_int @ one_one_int @ one_one_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 39.32/11.36 thf(3559,plain,((! [A:int]: ((plus_plus_int @ A @ A) = (times_times_int @ (plus_plus_int @ one_one_int @ one_one_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])). 39.32/11.36 thf(853,axiom,((! [A:int,B:int,C:int]: (zcong @ (times_times_int @ A @ B) @ (times_times_int @ C @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_zcong__zmult__self)). 39.32/11.36 thf(3606,plain,((! [A:int,B:int,C:int]: (zcong @ (times_times_int @ A @ B) @ (times_times_int @ C @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])). 39.32/11.36 thf(353,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_less__imp__le__nat)). 39.32/11.36 thf(2154,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 39.32/11.36 thf(958,axiom,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_sum__squares__ge__zero)). 39.32/11.36 thf(3906,plain,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[958])). 39.32/11.36 thf(1197,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ B @ A) @ (plus_plus_int @ C @ A)) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zadd__strict__right__mono)). 39.32/11.36 thf(4588,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ B @ A) @ (plus_plus_int @ C @ A)) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197])). 39.32/11.36 thf(245,axiom,((! [A:real]: ((A = zero_zero_real) = ((plus_plus_real @ A @ A) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_double__eq__0__iff)). 39.32/11.36 thf(1863,plain,((! [A:real]: ((A = zero_zero_real) = ((plus_plus_real @ A @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 39.32/11.36 thf(624,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_comm__semiring__class_Odistrib)). 39.32/11.36 thf(2954,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 39.32/11.36 thf(644,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_986_le__eq__less__or__eq)). 39.32/11.36 thf(3011,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)],[644])). 39.32/11.36 thf(795,axiom,((! [A:int]: ((minus_minus_int @ min @ (bit1 @ A)) = (bit0 @ (minus_minus_int @ min @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_diff__bin__simps_I6_J)). 39.32/11.36 thf(3450,plain,((! [A:int]: ((minus_minus_int @ min @ (bit1 @ A)) = (bit0 @ (minus_minus_int @ min @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])). 39.32/11.36 thf(470,axiom,((! [A:nat]: (dvd_dvd_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_dvd_Oorder__refl)). 39.32/11.36 thf(2473,plain,((! [A:nat]: (dvd_dvd_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 39.32/11.36 thf(840,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 39.32/11.36 thf(3567,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])). 39.32/11.36 thf(702,axiom,((! [A:int]: ((ord_less_eq_real @ one_one_real @ (number267125858f_real @ A)) = (ord_less_eq_int @ (bit1 @ pls) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_le__special_I2_J)). 39.32/11.36 thf(3186,plain,((! [A:int]: ((ord_less_eq_real @ one_one_real @ (number267125858f_real @ A)) = (ord_less_eq_int @ (bit1 @ pls) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 39.32/11.36 thf(1185,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_mult__zero__left)). 39.32/11.36 thf(4557,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185])). 39.32/11.36 thf(748,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C)) = (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_mult__le__cancel1)). 39.32/11.36 thf(3318,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C)) = (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 39.32/11.36 thf(186,axiom,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_one__dvd)). 39.32/11.36 thf(1708,plain,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 39.32/11.36 thf(653,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_dvd__triv__left)). 39.32/11.36 thf(3037,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 39.32/11.36 thf(147,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_comm__mult__left__mono)). 39.32/11.36 thf(1604,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 39.32/11.36 thf(955,axiom,((! [A:int]: ((plus_plus_int @ pls @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__Pls)). 39.32/11.36 thf(3899,plain,((! [A:int]: ((plus_plus_int @ pls @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])). 39.32/11.36 thf(612,axiom,((! [A:int]: ((sr @ A) = (collect_int @ (^ [B:int]: ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_SR__def)). 39.32/11.36 thf(2922,plain,((! [A:int]: ((sr @ A) = (collect_int @ (^ [B:int]: ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 39.32/11.36 thf(987,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (plus_plus_int @ (number_number_of_int @ B) @ C)) = (plus_plus_int @ (number_number_of_int @ (plus_plus_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__number__of__left)). 39.32/11.36 thf(3984,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (plus_plus_int @ (number_number_of_int @ B) @ C)) = (plus_plus_int @ (number_number_of_int @ (plus_plus_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])). 39.32/11.36 thf(529,axiom,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_not__sum__squares__lt__zero)). 39.32/11.36 thf(2646,plain,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 39.32/11.36 thf(826,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zadd__left__mono)). 39.32/11.36 thf(3531,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 39.32/11.36 thf(357,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ zero_zero_nat) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_eq_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_mult__nonpos__nonneg)). 39.32/11.36 thf(2164,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ zero_zero_nat) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 39.32/11.36 thf(214,axiom,((! [A:int,B:int]: ((number267125858f_real @ (minus_minus_int @ A @ B)) = (minus_minus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_number__of__diff)). 39.32/11.36 thf(1783,plain,((! [A:int,B:int]: ((number267125858f_real @ (minus_minus_int @ A @ B)) = (minus_minus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 39.32/11.36 thf(1020,axiom,((! [A:real]: ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_power2__eq__square)). 39.32/11.36 thf(4076,plain,((! [A:real]: ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020])). 39.32/11.36 thf(403,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) <= (ord_less_int @ A @ one_one_int))) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_power__strict__decreasing)). 39.32/11.36 thf(2296,plain,((! [A:int,B:nat,C:nat]: (((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) | ~ (ord_less_int @ A @ one_one_int))) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 39.32/11.36 thf(660,axiom,((~ (ord_less_int @ min @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_rel__simps_I7_J)). 39.32/11.36 thf(3054,plain,((~ (ord_less_int @ min @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])). 39.32/11.36 thf(198,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_divisors__zero)). 39.32/11.36 thf(1736,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 39.32/11.36 thf(477,axiom,((! [A:int,B:int]: ((times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (number267125858f_real @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_arith__simps_I32_J)). 39.32/11.36 thf(2496,plain,((! [A:int,B:int]: ((times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (number267125858f_real @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 39.32/11.36 thf(1101,axiom,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_power2__sum)). 39.32/11.36 thf(4312,plain,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101])). 39.32/11.36 thf(1015,axiom,((! [A:int,B:int,C:int]: ((((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((member_int @ A @ (wset @ B @ C)) => (member_int @ (inv @ C @ A) @ (wset @ B @ C)))) <= (ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ C)) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_wset__mem__inv__mem)). 39.32/11.36 thf(4059,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((member_int @ A @ (wset @ B @ C)) => (member_int @ (inv @ C @ A) @ (wset @ B @ C)))) | ~ (ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ C) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015])). 39.32/11.36 thf(210,axiom,((! [A:nat]: ~ (~ (dvd_dvd_nat @ A @ zero_zero_nat) & (dvd_dvd_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less)). 39.32/11.36 thf(1768,plain,((! [A:nat]: ~ (~ (dvd_dvd_nat @ A @ zero_zero_nat) & (dvd_dvd_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 39.32/11.36 thf(247,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B))) <= (ord_less_eq_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_add__le__mono)). 39.32/11.36 thf(1868,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ D @ B))) | ~ (ord_less_eq_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 39.32/11.36 thf(298,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_power__increasing)). 39.32/11.36 thf(2000,plain,((! [A:real,B:nat,C:nat]: (((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 39.32/11.36 thf(160,axiom,((! [A:nat,B:nat]: ((((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)) <= (A != B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_dvd_Ole__neq__trans)). 39.32/11.36 thf(1636,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)) | (A = B) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 39.32/11.36 thf(10,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ (times_times_real @ C @ A)) <= (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_dvd__mult2)). 39.32/11.36 thf(1223,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ (times_times_real @ C @ A)) | ~ (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 39.32/11.36 thf(1153,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit0 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__eq__int__code_I13_J)). 39.32/11.36 thf(4466,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit0 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153])). 39.32/11.36 thf(942,axiom,((! [A:int]: ((minus_minus_int @ min @ (bit0 @ A)) = (bit1 @ (minus_minus_int @ min @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_diff__bin__simps_I5_J)). 39.32/11.36 thf(3867,plain,((! [A:int]: ((minus_minus_int @ min @ (bit0 @ A)) = (bit1 @ (minus_minus_int @ min @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[942])). 39.32/11.36 thf(345,axiom,((! [A:real,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((times_times_real @ (power_power_real @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_realpow__minus__mult)). 39.32/11.36 thf(2133,plain,((! [A:real,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((times_times_real @ (power_power_real @ A @ (minus_minus_nat @ B @ one_one_nat)) @ A) = (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 39.32/11.36 thf(648,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_zero__neq__one)). 39.32/11.36 thf(3022,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])). 39.32/11.36 thf(1112,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_int @ A @ (plus_plus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zle__add1__eq__le)). 39.32/11.36 thf(4344,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_int @ A @ (plus_plus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112])). 39.32/11.36 thf(514,axiom,((! [A:nat,B:nat]: ((A != B) <= (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_dvd_Oless__imp__not__eq)). 39.32/11.36 thf(2606,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 39.32/11.36 thf(1164,axiom,((! [A:int,B:int]: (zcong @ A @ B @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_zcong__1)). 39.32/11.36 thf(4493,plain,((! [A:int,B:int]: (zcong @ A @ B @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164])). 39.32/11.36 thf(390,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) = ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_less__eq__real__def)). 39.32/11.36 thf(2264,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) = ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 39.32/11.36 thf(446,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 39.32/11.36 thf(2409,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 39.32/11.36 thf(69,axiom,((! [A:int]: (zcong @ A @ zero_zero_int @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_zcong__id)). 39.32/11.36 thf(1387,plain,((! [A:int]: (zcong @ A @ zero_zero_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 39.32/11.36 thf(260,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ C)) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_mult__less__cancel__left__disj)). 39.32/11.36 thf(1900,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ C)) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 39.32/11.36 thf(512,axiom,((~ (ord_less_int @ pls @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_rel__simps_I3_J)). 39.32/11.36 thf(2601,plain,((~ (ord_less_int @ pls @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 39.32/11.36 thf(453,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_add__mult__distrib2)). 39.32/11.36 thf(2428,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 39.32/11.36 thf(889,axiom,((zprime @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zprime__2)). 39.32/11.36 thf(3711,plain,((zprime @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])). 39.32/11.36 thf(55,axiom,((! [A:int,B:int]: (((div_mod_int @ A @ B) = zero_zero_int) = (? [C:int]: (A = (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_zmod__eq__0__iff)). 39.32/11.36 thf(1343,plain,((! [A:int,B:int]: (((div_mod_int @ A @ B) = zero_zero_int) = (? [C:int]: (A = (times_times_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 39.32/11.36 thf(59,axiom,((! [A:int,B:int]: (((div_mod_int @ A @ B) = zero_zero_int) => (? [C:int]: (A = (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_zmod__eq__0D)). 39.32/11.36 thf(1355,plain,((! [A:int,B:int]: (((div_mod_int @ A @ B) = zero_zero_int) => (? [C:int]: (A = (times_times_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 39.32/11.36 thf(395,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_trans__le__add2)). 39.32/11.36 thf(2277,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 39.32/11.36 thf(23,axiom,((! [A:real]: (dvd_dvd_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_dvd__refl)). 39.32/11.36 thf(1255,plain,((! [A:real]: (dvd_dvd_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 39.32/11.36 thf(1123,axiom,((! [A:int,B:int]: (((A != zero_zero_int) => ((times_times_int @ B @ A) != zero_zero_int)) <= (B != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_no__zero__divisors)). 39.32/11.36 thf(4375,plain,((! [A:int,B:int]: (((~ (A = zero_zero_int)) => (~ ((times_times_int @ B @ A) = zero_zero_int))) | (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123])). 39.32/11.36 thf(1143,axiom,((one_one_int = (number_number_of_int @ (bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_semiring__norm_I110_J)). 39.32/11.36 thf(4434,plain,((one_one_int = (number_number_of_int @ (bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143])). 39.32/11.36 thf(989,axiom,((! [A:nat]: ((power_power_real @ (number267125858f_real @ min) @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A)) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_power__m1__even)). 39.32/11.36 thf(3989,plain,((! [A:nat]: ((power_power_real @ (number267125858f_real @ min) @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[989])). 39.32/11.36 thf(1036,axiom,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_real__sum__squared__expand)). 39.32/11.36 thf(4128,plain,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036])). 39.32/11.36 thf(769,axiom,((! [A:int,B:int,C:int,D:int]: (((zcong @ B @ C @ D) => (zcong @ (times_times_int @ A @ (multInv @ D @ B)) @ (times_times_int @ A @ (multInv @ D @ C)) @ D)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_MultInv__zcong__prop1)). 39.32/11.36 thf(3371,plain,((! [A:int,B:int,C:int,D:int]: (((zcong @ B @ C @ D) => (zcong @ (times_times_int @ A @ (multInv @ D @ B)) @ (times_times_int @ A @ (multInv @ D @ C)) @ D)) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])). 39.32/11.36 thf(1060,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (minus_minus_int @ (number_number_of_int @ B) @ C)) = (minus_minus_int @ (number_number_of_int @ (plus_plus_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_add__number__of__diff1)). 39.32/11.36 thf(4204,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (minus_minus_int @ (number_number_of_int @ B) @ C)) = (minus_minus_int @ (number_number_of_int @ (plus_plus_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060])). 39.32/11.36 thf(948,axiom,((! [A:int]: ((plus_plus_int @ A @ pls) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add__Pls__right)). 39.32/11.36 thf(3884,plain,((! [A:int]: ((plus_plus_int @ A @ pls) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])). 39.32/11.36 thf(230,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_int @ B @ A) => ((div_mod_int @ B @ A) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mod__pos__pos__trivial)). 39.32/11.36 thf(1824,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_int @ B @ A) => ((div_mod_int @ B @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 39.32/11.36 thf(1090,axiom,((~ (! [A:int]: ~ (zcong @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_)). 39.32/11.36 thf(4284,plain,((~ (! [A:int]: ~ (zcong @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090])). 39.32/11.36 thf(63,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ A) => (dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A))) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_dvd__diff__nat)). 39.32/11.36 thf(1370,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ A) => (dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A))) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 39.32/11.36 thf(310,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ A) <= (A = (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_dvdI)). 39.32/11.36 thf(2032,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ A) | ~ (A = (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 39.32/11.36 thf(636,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_nat__mult__le__cancel1)). 39.32/11.36 thf(2986,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (ord_less_eq_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])). 39.32/11.36 thf(605,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_eq__imp__le)). 39.32/11.36 thf(2890,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])). 39.32/11.36 thf(448,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_power__add)). 39.32/11.36 thf(2414,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 39.32/11.36 thf(723,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_mult__nonneg__nonpos2)). 39.32/11.36 thf(3250,plain,((! [A:int,B:int]: (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 39.32/11.36 thf(708,axiom,((! [A:int,B:int,C:int]: ((div_mod_int @ (minus_minus_int @ (div_mod_int @ A @ B) @ C) @ B) = (div_mod_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_zdiff__zmod__left)). 39.32/11.36 thf(3207,plain,((! [A:int,B:int,C:int]: ((div_mod_int @ (minus_minus_int @ (div_mod_int @ A @ B) @ C) @ B) = (div_mod_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 39.32/11.36 thf(441,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ A) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_le__trans)). 39.32/11.36 thf(2396,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 39.32/11.36 thf(818,axiom,((ord_less_int @ t @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t__l__p)). 39.32/11.36 thf(3514,plain,((ord_less_int @ t @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 39.32/11.36 thf(879,axiom,((! [A:int,B:int,C:int]: ((div_mod_int @ (times_times_int @ A @ B) @ C) = (div_mod_int @ (times_times_int @ A @ (div_mod_int @ B @ C)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_zmod__zmult1__eq)). 39.32/11.36 thf(3682,plain,((! [A:int,B:int,C:int]: ((div_mod_int @ (times_times_int @ A @ B) @ C) = (div_mod_int @ (times_times_int @ A @ (div_mod_int @ B @ C)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])). 39.32/11.36 thf(757,axiom,((! [A:nat]: ~ ((dvd_dvd_nat @ A @ A) & ~ (dvd_dvd_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_dvd_Oless__irrefl)). 39.32/11.36 thf(3339,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])). 39.32/11.36 thf(304,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 39.32/11.36 thf(2015,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 39.32/11.36 thf(802,axiom,((! [A:int,B:int,C:int]: ((((ord_less_eq_int @ one_one_int @ B) <= (ord_less_int @ A @ C)) <= (C = (plus_plus_int @ A @ (times_times_int @ C @ B)))) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_self__quotient__aux1)). 39.32/11.36 thf(3471,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ one_one_int @ B) | ~ (ord_less_int @ A @ C) | ~ (C = (plus_plus_int @ A @ (times_times_int @ C @ B))) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 39.32/11.36 thf(736,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_gr0I)). 39.32/11.36 thf(3286,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])). 39.32/11.36 thf(131,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (times_times_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 39.32/11.36 thf(1560,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (times_times_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 39.32/11.36 thf(730,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ B) => (ord_less_nat @ one_one_nat @ (times_times_nat @ B @ (power_power_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_power__gt1__lemma)). 39.32/11.36 thf(3271,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ B) => (ord_less_nat @ one_one_nat @ (times_times_nat @ B @ (power_power_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])). 39.32/11.36 thf(599,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_less__irrefl__nat)). 39.32/11.36 thf(2873,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])). 39.32/11.36 thf(1040,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_zero__le__even__power_H)). 39.32/11.36 thf(4140,plain,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040])). 39.32/11.36 thf(268,axiom,((! [A:real]: ((plus_plus_real @ A @ (number267125858f_real @ pls)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__numeral__0__right)). 39.32/11.36 thf(1920,plain,((! [A:real]: ((plus_plus_real @ A @ (number267125858f_real @ pls)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 39.32/11.36 thf(892,axiom,((! [A:int,B:int]: ((div_mod_int @ (number_number_of_int @ (bit0 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_zmod__number__of__Bit0)). 39.32/11.36 thf(3718,plain,((! [A:int,B:int]: ((div_mod_int @ (number_number_of_int @ (bit0 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[892])). 39.32/11.36 thf(96,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => ((ord_less_int @ zero_zero_int @ B) => (((zcong @ C @ B @ A) => (((ord_less_int @ B @ A) => (C = B)) <= (ord_less_int @ C @ A))) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_zcong__less__eq)). 39.32/11.36 thf(1457,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => ((ord_less_int @ zero_zero_int @ B) => (((zcong @ C @ B @ A) => (((ord_less_int @ B @ A) => (C = B)) | ~ (ord_less_int @ C @ A))) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 39.32/11.36 thf(1132,axiom,((! [A:int,B:int]: (((~ (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ B))) => ((div_mod_int @ (number_number_of_int @ (bit1 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (plus_plus_int @ (number_number_of_int @ A) @ one_one_int) @ (number_number_of_int @ B))) @ one_one_int))) & (((div_mod_int @ (number_number_of_int @ (bit1 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))) @ one_one_int)) <= (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_zmod__number__of__Bit1)). 39.32/11.36 thf(4402,plain,((! [A:int,B:int]: (((~ (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ B))) => ((div_mod_int @ (number_number_of_int @ (bit1 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (plus_plus_int @ (number_number_of_int @ A) @ one_one_int) @ (number_number_of_int @ B))) @ one_one_int))) & (((div_mod_int @ (number_number_of_int @ (bit1 @ A)) @ (number_number_of_int @ (bit0 @ B))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))) @ one_one_int)) | ~ (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132])). 39.32/11.36 thf(5,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (div_mod_nat @ B @ C)) = (div_mod_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_mod__mult__distrib2)). 39.32/11.36 thf(1210,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (div_mod_nat @ B @ C)) = (div_mod_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 39.32/11.36 thf(375,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ B @ A))) <= (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_mult__nonneg__nonneg)). 39.32/11.36 thf(2213,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ B @ A))) | ~ (ord_less_eq_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 39.32/11.36 thf(37,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 39.32/11.36 thf(1291,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 39.32/11.36 thf(780,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_dvd__triv__right)). 39.32/11.36 thf(3408,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])). 39.32/11.36 thf(921,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (times_times_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 39.32/11.36 thf(3799,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (times_times_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[921])). 39.32/11.36 thf(61,axiom,((! [A:int,B:real,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (number267125858f_real @ A) @ B) @ (times_times_real @ (number267125858f_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_right__diff__distrib__number__of)). 39.32/11.36 thf(1365,plain,((! [A:int,B:real,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (number267125858f_real @ A) @ B) @ (times_times_real @ (number267125858f_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 39.32/11.36 thf(1056,axiom,((! [A:int]: ((plus_plus_int @ one_one_int @ (number_number_of_int @ A)) = (number_number_of_int @ (plus_plus_int @ (bit1 @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__special_I2_J)). 39.32/11.36 thf(4192,plain,((! [A:int]: ((plus_plus_int @ one_one_int @ (number_number_of_int @ A)) = (number_number_of_int @ (plus_plus_int @ (bit1 @ pls) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056])). 39.32/11.36 thf(925,axiom,((zero_zero_nat = (number_number_of_nat @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_semiring__norm_I113_J)). 39.32/11.36 thf(3810,plain,((zero_zero_nat = (number_number_of_nat @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])). 39.32/11.36 thf(1013,axiom,((! [A:int,B:int]: (((A = B) | (ord_less_int @ A @ B)) = (ord_less_int @ A @ (plus_plus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_zless__add1__eq)). 39.32/11.36 thf(4053,plain,((! [A:int,B:int]: (((A = B) | (ord_less_int @ A @ B)) = (ord_less_int @ A @ (plus_plus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013])). 39.32/11.36 thf(455,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_dvd__imp__le)). 39.32/11.36 thf(2433,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 39.32/11.36 thf(472,axiom,((! [A:nat,B:nat,C:nat]: (((~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A)) => (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A))) <= (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_dvd_Oord__eq__less__trans)). 39.32/11.36 thf(2477,plain,((! [A:nat,B:nat,C:nat]: (((~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A)) => (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A))) | ~ (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 39.32/11.36 thf(673,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ C @ zero_zero_int) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (ord_less_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_mult__less__cancel__left__neg)). 39.32/11.36 thf(3090,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ C @ zero_zero_int) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) = (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])). 39.32/11.36 thf(502,axiom,((! [A:int,B:int]: (zcong @ A @ (div_mod_int @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mod__mod__is__mod)). 39.32/11.36 thf(2565,plain,((! [A:int,B:int]: (zcong @ A @ (div_mod_int @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 39.32/11.36 thf(129,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) <= (ord_less_eq_real @ A @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_mult__nonneg__nonpos)). 39.32/11.36 thf(1555,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) | ~ (ord_less_eq_real @ A @ zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 39.32/11.36 thf(416,axiom,((! [A:(int > $o),B:int,C:int]: ((A @ (div_mod_int @ B @ C)) = (((C = zero_zero_int) => (A @ B)) & ((! [D:int,E:int]: (((ord_less_eq_int @ zero_zero_int @ E) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C)) => (A @ E))) <= (ord_less_int @ zero_zero_int @ C)) & ((! [D:int,E:int]: (((ord_less_int @ C @ E) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_eq_int @ E @ zero_zero_int)) => (A @ E))) <= (ord_less_int @ C @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_split__zmod)). 39.32/11.36 thf(2332,plain,((! [A:(int > $o),B:int,C:int]: ((A @ (div_mod_int @ B @ C)) = (((C = zero_zero_int) => (A @ B)) & (! [D:int,E:int]: (((ord_less_eq_int @ zero_zero_int @ E) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C)) => (A @ E)) | ~ (ord_less_int @ zero_zero_int @ C)) & (! [D:int,E:int]: (((ord_less_int @ C @ E) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_eq_int @ E @ zero_zero_int)) => (A @ E)) | ~ (ord_less_int @ C @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 39.32/11.36 thf(579,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_int @ B @ C) => ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C) @ zero_zero_int) <= (ord_less_eq_int @ C @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_zmult2__lemma__aux2)). 39.32/11.36 thf(2820,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_int @ B @ C) => ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C) @ zero_zero_int) | ~ (ord_less_eq_int @ C @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])). 39.32/11.36 thf(740,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((ord_less_int @ C @ A) => ((ord_less_eq_int @ B @ D) <= (ord_less_int @ E @ A))) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_unique__quotient__lemma)). 39.32/11.36 thf(3297,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ A) => ((ord_less_eq_int @ B @ D) | ~ (ord_less_int @ E @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 39.32/11.36 thf(812,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((A = one_one_int) | (A = zero_zero_int)) <= (ord_less_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_int__pos__lt__two__imp__zero__or__one)). 39.32/11.36 thf(3499,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((A = one_one_int) | (A = zero_zero_int) | ~ (ord_less_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])). 39.32/11.36 thf(663,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_mult__nonneg__nonneg)). 39.32/11.36 thf(3065,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])). 39.32/11.36 thf(761,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ B) = (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_dvd__mult__cancel1)). 39.32/11.36 thf(3349,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ B) = (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])). 39.32/11.36 thf(953,axiom,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_power2__sum)). 39.32/11.36 thf(3894,plain,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[953])). 39.32/11.36 thf(322,axiom,((! [A:int,B:int,C:int,D:int]: (((zcong @ C @ A @ D) => (zcong @ B @ A @ D)) <= (zcong @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_zcong__trans)). 39.32/11.36 thf(2068,plain,((! [A:int,B:int,C:int,D:int]: (((zcong @ C @ A @ D) => (zcong @ B @ A @ D)) | ~ (zcong @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 39.32/11.36 thf(228,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_dvd_Oeq__iff)). 39.32/11.36 thf(1819,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 39.32/11.36 thf(1106,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => ((div_mod_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)) @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)) = (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_pos__zmod__mult__2)). 39.32/11.36 thf(4327,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => ((div_mod_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)) @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)) = (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106])). 39.32/11.36 thf(832,axiom,((! [A:nat,B:nat,C:int]: ((((power_power_int @ (number_number_of_int @ min) @ A) = (power_power_int @ (number_number_of_int @ min) @ B)) <= (zcong @ (power_power_int @ (number_number_of_int @ min) @ A) @ (power_power_int @ (number_number_of_int @ min) @ B) @ C)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_neg__one__power__eq__mod__m)). 39.32/11.36 thf(3546,plain,((! [A:nat,B:nat,C:int]: (((power_power_int @ (number_number_of_int @ min) @ A) = (power_power_int @ (number_number_of_int @ min) @ B)) | ~ (zcong @ (power_power_int @ (number_number_of_int @ min) @ A) @ (power_power_int @ (number_number_of_int @ min) @ B) @ C) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 39.32/11.36 thf(692,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_diff__le__mono)). 39.32/11.36 thf(3144,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 39.32/11.36 thf(650,axiom,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_even__less__0__iff)). 39.32/11.36 thf(3028,plain,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])). 39.32/11.36 thf(421,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (plus_plus_nat @ (C @ A) @ B) @ (C @ (plus_plus_nat @ A @ B))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (C @ D) @ (C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_mono__nat__linear__lb)). 39.32/11.36 thf(2345,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (plus_plus_nat @ (C @ A) @ B) @ (C @ (plus_plus_nat @ A @ B))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (C @ D) @ (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 39.32/11.36 thf(895,axiom,((! [A:int,B:int]: ((quadRes @ A @ B) = (? [C:int]: (zcong @ (power_power_int @ C @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_QuadRes__def)). 39.32/11.36 thf(3727,plain,((! [A:int,B:int]: ((quadRes @ A @ B) = (? [C:int]: (zcong @ (power_power_int @ C @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[895])). 39.32/11.36 thf(33,axiom,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ A) => ((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (ord_less_int @ one_one_int @ (inv @ B @ A)))) <= (zprime @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_inv__g__1)). 39.32/11.36 thf(1281,plain,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ A) => ((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (ord_less_int @ one_one_int @ (inv @ B @ A)))) | ~ (zprime @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 39.32/11.36 thf(556,axiom,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest)). 39.32/11.36 thf(2741,plain,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])). 39.32/11.36 thf(1151,axiom,(((power_power_real @ one_one_real @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_one__power2)). 39.32/11.36 thf(4461,plain,(((power_power_real @ one_one_real @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151])). 39.32/11.36 thf(71,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 39.32/11.37 thf(1392,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 39.32/11.37 thf(377,axiom,((! [A:real,B:real,C:real]: ((C != zero_zero_real) => ((A = B) = ((times_times_real @ C @ A) = (times_times_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_real__mult__left__cancel)). 39.32/11.37 thf(2228,plain,((! [A:real,B:real,C:real]: ((~ (C = zero_zero_real)) => ((A = B) = ((times_times_real @ C @ A) = (times_times_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 39.32/11.37 thf(849,axiom,((! [A:nat]: ((times_times_nat @ A @ A) = (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 39.32/11.37 thf(3595,plain,((! [A:nat]: ((times_times_nat @ A @ A) = (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])). 39.32/11.37 thf(563,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ A @ B))) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_mult__strict__left__mono__neg)). 39.32/11.37 thf(2769,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ A @ B))) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 39.32/11.37 thf(383,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_diff__mult__distrib)). 39.32/11.37 thf(2245,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 39.32/11.37 thf(885,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (times_times_nat @ (plus_plus_nat @ A @ B) @ (minus_minus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_diff__square)). 39.32/11.37 thf(3699,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (times_times_nat @ (plus_plus_nat @ A @ B) @ (minus_minus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[885])). 39.32/11.37 thf(293,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((dvd_dvd_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_nat__mult__dvd__cancel1)). 39.32/11.37 thf(1983,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((dvd_dvd_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) = (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 39.32/11.37 thf(929,axiom,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_combine__common__factor)). 39.32/11.37 thf(3831,plain,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[929])). 39.32/11.37 thf(222,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ C) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_818_comm__mult__strict__left__mono)). 39.32/11.37 thf(1804,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ C) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 39.32/11.37 thf(65,axiom,((! [A:nat,B:nat]: ((A != B) <= (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_dvd_Oless__imp__neq)). 39.32/11.37 thf(1375,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 39.32/11.37 thf(507,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))) <= (ord_less_eq_int @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_mult__mono)). 39.32/11.37 thf(2577,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))) | ~ (ord_less_eq_int @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 39.32/11.37 thf(288,axiom,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_gcd__lcm__complete__lattice__nat_Otop__le)). 39.32/11.37 thf(1970,plain,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 39.32/11.37 thf(545,axiom,((! [A:int,B:int]: (((div_mod_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = zero_zero_int) = (dvd_dvd_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of)). 39.32/11.37 thf(2692,plain,((! [A:int,B:int]: (((div_mod_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = zero_zero_int) = (dvd_dvd_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])). 39.32/11.37 thf(84,axiom,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ A) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_power__commutes)). 39.32/11.37 thf(1425,plain,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ A) = (times_times_real @ A @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 39.32/11.37 thf(172,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_nat__dvd__1__iff__1)). 39.32/11.37 thf(1672,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 39.32/11.37 thf(821,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_power__mult__distrib)). 39.32/11.37 thf(3518,plain,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])). 39.32/11.37 thf(669,axiom,((! [A:nat,B:nat]: ((A = B) => (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_dvd_Oeq__refl)). 39.32/11.37 thf(3078,plain,((! [A:nat,B:nat]: ((A = B) => (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])). 39.32/11.37 thf(998,axiom,((! [A:int,B:int]: (((zprime @ B) => ((~ (zcong @ A @ zero_zero_int @ B)) => (zcong @ (times_times_int @ (multInv @ B @ A) @ A) @ one_one_int @ B))) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_MultInv__prop2a)). 39.32/11.37 thf(4012,plain,((! [A:int,B:int]: (((zprime @ B) => ((~ (zcong @ A @ zero_zero_int @ B)) => (zcong @ (times_times_int @ (multInv @ B @ A) @ A) @ one_one_int @ B))) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])). 39.32/11.37 thf(1032,axiom,((! [A:int,B:nat,C:int]: ((((times_times_nat @ (number_number_of_nat @ C) @ (times_times_nat @ (number_number_of_nat @ A) @ B)) = (times_times_nat @ (number_number_of_nat @ (times_times_int @ C @ A)) @ B)) <= (~ (ord_less_int @ C @ pls))) & (((times_times_nat @ (number_number_of_nat @ C) @ (times_times_nat @ (number_number_of_nat @ A) @ B)) = zero_zero_nat) <= (ord_less_int @ C @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_nat__number__of__mult__left)). 39.32/11.37 thf(4109,plain,((! [A:int,B:nat,C:int]: ((((times_times_nat @ (number_number_of_nat @ C) @ (times_times_nat @ (number_number_of_nat @ A) @ B)) = (times_times_nat @ (number_number_of_nat @ (times_times_int @ C @ A)) @ B)) | (ord_less_int @ C @ pls)) & (((times_times_nat @ (number_number_of_nat @ C) @ (times_times_nat @ (number_number_of_nat @ A) @ B)) = zero_zero_nat) | ~ (ord_less_int @ C @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032])). 39.32/11.37 thf(707,axiom,(((number267125858f_real @ pls) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_number__of__Pls)). 39.32/11.37 thf(3205,plain,(((number267125858f_real @ pls) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])). 39.32/11.37 thf(641,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((E != zero_zero_nat) => (((C = D) & (A != B)) => ((plus_plus_nat @ C @ (times_times_nat @ E @ A)) != (plus_plus_nat @ D @ (times_times_nat @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_add__scale__eq__noteq)). 39.32/11.37 thf(3001,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((~ (E = zero_zero_nat)) => (((C = D) & ~ (A = B)) => (~ ((plus_plus_nat @ C @ (times_times_nat @ E @ A)) = (plus_plus_nat @ D @ (times_times_nat @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])). 39.32/11.37 thf(806,axiom,((! [A:int]: ((ord_less_int @ pls @ A) = (ord_less_int @ zero_zero_int @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_less__special_I1_J)). 39.32/11.37 thf(3482,plain,((! [A:int]: ((ord_less_int @ pls @ A) = (ord_less_int @ zero_zero_int @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 39.32/11.37 thf(208,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) != (plus_plus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A))) = ((C != D) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_crossproduct__noteq)). 39.32/11.37 thf(1762,plain,((! [A:real,B:real,C:real,D:real]: ((~ ((plus_plus_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) = (plus_plus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)))) = (~ (C = D) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 39.32/11.37 thf(335,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_power__mult__distrib)). 39.32/11.37 thf(2100,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 39.32/11.37 thf(28,axiom,((! [A:(int > $o)]: ((collect_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Collect__def)). 39.32/11.37 thf(1270,plain,((! [A:(int > $o)]: ((collect_int @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 39.32/11.37 thf(25,axiom,((! [A:real,B:nat,C:nat]: ((dvd_dvd_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_le__imp__power__dvd)). 39.32/11.37 thf(1259,plain,((! [A:real,B:nat,C:nat]: ((dvd_dvd_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 39.32/11.37 thf(434,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => (((ord_less_eq_int @ zero_zero_int @ A) => (((C = A) <= (zcong @ C @ A @ B)) <= (ord_less_int @ A @ B))) <= (ord_less_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_zcong__zless__imp__eq)). 39.32/11.37 thf(2377,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => (((ord_less_eq_int @ zero_zero_int @ A) => ((C = A) | ~ (zcong @ C @ A @ B) | ~ (ord_less_int @ A @ B))) | ~ (ord_less_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 39.32/11.37 thf(572,axiom,((! [A:int,B:int]: (((A != B) & (ord_less_eq_int @ A @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le)). 39.32/11.37 thf(2801,plain,((! [A:int,B:int]: ((~ (A = B) & (ord_less_eq_int @ A @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])). 39.32/11.37 thf(122,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ B) = (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))) <= (ord_less_real @ zero_zero_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_real__mult__less__iff1)). 39.32/11.37 thf(1534,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ B) = (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))) | ~ (ord_less_real @ zero_zero_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 39.32/11.37 thf(218,axiom,((! [A:int]: ((ord_less_int @ pls @ A) = (ord_less_nat @ zero_zero_nat @ (number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_less__0__number__of)). 39.32/11.37 thf(1794,plain,((! [A:int]: ((ord_less_int @ pls @ A) = (ord_less_nat @ zero_zero_nat @ (number_number_of_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 39.32/11.37 thf(1172,axiom,((! [A:nat]: ((times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_semiring__mult__2)). 39.32/11.37 thf(4512,plain,((! [A:nat]: ((times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172])). 39.32/11.37 thf(712,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((D = B) => ((zcong @ B @ A @ E) => (zcong @ C @ A @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_zcong__eq__trans)). 39.32/11.37 thf(3218,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((D = B) => ((zcong @ B @ A @ E) => (zcong @ C @ A @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])). 39.32/11.37 thf(1181,axiom,((! [A:int,B:int]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rel__simps_I49_J)). 39.32/11.37 thf(4544,plain,((! [A:int,B:int]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181])). 39.32/11.37 thf(593,axiom,((! [A:int,B:int]: ((zprime @ B) => (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => ((inv @ B @ A) != zero_zero_int)) <= (ord_less_int @ one_one_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_inv__not__0)). 39.32/11.37 thf(2858,plain,((! [A:int,B:int]: ((zprime @ B) => (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (~ ((inv @ B @ A) = zero_zero_int))) | ~ (ord_less_int @ one_one_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 39.32/11.37 thf(491,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_le__diff__iff)). 39.32/11.37 thf(2537,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (ord_less_eq_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 39.32/11.37 thf(719,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 39.32/11.37 thf(3237,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])). 39.32/11.37 thf(205,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ one_one_real @ (power_power_real @ B @ A)) <= (ord_less_eq_real @ one_one_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_one__le__power)). 39.32/11.37 thf(1755,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ one_one_real @ (power_power_real @ B @ A)) | ~ (ord_less_eq_real @ one_one_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 39.32/11.37 thf(286,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => (((div_mod_int @ A @ C) = (div_mod_int @ B @ C)) = (zcong @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_zcong__zmod__eq)). 39.32/11.37 thf(1964,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => (((div_mod_int @ A @ C) = (div_mod_int @ B @ C)) = (zcong @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 39.32/11.37 thf(934,axiom,((pls != min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_rel__simps_I37_J)). 39.32/11.37 thf(3846,plain,((~ (pls = min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])). 39.32/11.37 thf(709,axiom,((! [A:int]: ((ord_less_eq_int @ min @ A) = (ord_less_eq_int @ min @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_rel__simps_I26_J)). 39.32/11.37 thf(3210,plain,((! [A:int]: ((ord_less_eq_int @ min @ A) = (ord_less_eq_int @ min @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 39.32/11.37 thf(583,axiom,((! [A:int,B:int,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (times_times_real @ (number267125858f_real @ B) @ C)) = (times_times_real @ (number267125858f_real @ (times_times_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__number__of__left)). 39.32/11.37 thf(2830,plain,((! [A:int,B:int,C:real]: ((times_times_real @ (number267125858f_real @ A) @ (times_times_real @ (number267125858f_real @ B) @ C)) = (times_times_real @ (number267125858f_real @ (times_times_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])). 39.32/11.37 thf(597,axiom,((! [A:int]: ((number267125858f_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ one_one_real @ (number267125858f_real @ A)) @ (number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_number__of__Bit1)). 39.32/11.37 thf(2868,plain,((! [A:int]: ((number267125858f_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ one_one_real @ (number267125858f_real @ A)) @ (number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])). 39.32/11.37 thf(327,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)))) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_power__strict__mono)). 39.32/11.37 thf(2080,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)))) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 39.32/11.37 thf(371,axiom,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)). 39.32/11.37 thf(2196,plain,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 39.32/11.37 thf(275,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_892_linorder__neqE__nat)). 39.32/11.37 thf(1937,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)],[275])). 39.32/11.37 thf(705,axiom,((! [A:nat,B:nat]: (((B = zero_zero_nat) => ((power_power_nat @ A @ B) = one_one_nat)) & (((power_power_nat @ A @ B) = (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat)))) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_power__eq__if)). 39.32/11.37 thf(3194,plain,((! [A:nat,B:nat]: (((B = zero_zero_nat) => ((power_power_nat @ A @ B) = one_one_nat)) & (((power_power_nat @ A @ B) = (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat)))) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])). 39.32/11.37 thf(338,axiom,((! [A:nat,B:nat,C:nat]: ((C != zero_zero_nat) => ((dvd_dvd_nat @ A @ B) <= (dvd_dvd_nat @ (power_power_nat @ A @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_divides__exp2)). 39.32/11.37 thf(2108,plain,((! [A:nat,B:nat,C:nat]: ((~ (C = zero_zero_nat)) => ((dvd_dvd_nat @ A @ B) | ~ (dvd_dvd_nat @ (power_power_nat @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 39.32/11.37 thf(866,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__int__code_I16_J)). 39.32/11.37 thf(3643,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])). 39.32/11.37 thf(162,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ B @ A) <= (dvd_dvd_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_dvd_Oorder__trans)). 39.32/11.37 thf(1644,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ B @ A) | ~ (dvd_dvd_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 39.32/11.37 thf(571,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_diff__cancel2)). 39.32/11.37 thf(2798,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 39.32/11.37 thf(176,axiom,((! [A:int,B:int]: ((plus_plus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (number267125858f_real @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__number__of__eq)). 39.32/11.37 thf(1683,plain,((! [A:int,B:int]: ((plus_plus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (number267125858f_real @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 39.32/11.37 thf(1108,axiom,(((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_zero__power2)). 39.32/11.37 thf(4333,plain,(((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108])). 39.32/11.37 thf(50,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (times_times_nat @ B @ C)) = (power_power_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_power__mult)). 39.32/11.37 thf(1329,plain,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (times_times_nat @ B @ C)) = (power_power_real @ (power_power_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 39.32/11.37 thf(691,axiom,((! [A:int,B:int]: ((ord_less_eq_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (~ (ord_less_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less)). 39.32/11.37 thf(3141,plain,((! [A:int,B:int]: ((ord_less_eq_real @ (number267125858f_real @ A) @ (number267125858f_real @ B)) = (~ (ord_less_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 39.32/11.37 thf(745,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A))) <= (ord_less_eq_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_mult__nonpos__nonpos)). 39.32/11.37 thf(3311,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A))) | ~ (ord_less_eq_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 39.32/11.37 thf(1050,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ A @ B) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_power2__le__imp__le)). 39.32/11.37 thf(4167,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050])). 39.32/11.37 thf(199,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => (((ord_less_eq_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ D) @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C))) <= (ord_less_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_zmult2__lemma__aux1)). 39.32/11.37 thf(1739,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => (((ord_less_eq_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ D) @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C))) | ~ (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 39.32/11.37 thf(1140,axiom,((! [A:int,B:int]: ((B = zero_zero_int) = (A = (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__0__iff)). 39.32/11.37 thf(4425,plain,((! [A:int,B:int]: ((B = zero_zero_int) = (A = (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140])). 39.32/11.37 thf(1138,axiom,((zero_zero_int = (number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_semiring__norm_I112_J)). 39.32/11.37 thf(4421,plain,((zero_zero_int = (number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138])). 39.32/11.37 thf(1102,axiom,((! [A:int]: ((ord_less_int @ (bit1 @ A) @ pls) = (ord_less_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rel__simps_I12_J)). 39.32/11.37 thf(4315,plain,((! [A:int]: ((ord_less_int @ (bit1 @ A) @ pls) = (ord_less_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102])). 39.32/11.37 thf(792,axiom,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 39.32/11.37 thf(3441,plain,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 39.32/11.37 thf(361,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 39.32/11.37 thf(2172,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 39.32/11.37 thf(787,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 39.32/11.37 thf(3428,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 39.32/11.37 thf(497,axiom,((! [A:nat,B:real]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ one_one_real @ (power_power_real @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_one__less__power)). 39.32/11.37 thf(2551,plain,((! [A:nat,B:real]: ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ one_one_real @ (power_power_real @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 39.32/11.37 thf(4,axiom,((! [A:nat,B:nat]: (((div_mod_nat @ A @ B) = zero_zero_nat) = (? [C:nat]: (A = (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_mod__eq__0__iff)). 39.32/11.37 thf(1207,plain,((! [A:nat,B:nat]: (((div_mod_nat @ A @ B) = zero_zero_nat) = (? [C:nat]: (A = (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 39.32/11.37 thf(329,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_le__cube)). 39.32/11.37 thf(2085,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 39.32/11.37 thf(150,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) <= (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_real__add__left__mono)). 39.32/11.37 thf(1612,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) | ~ (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 39.32/11.37 thf(633,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (div_mod_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J)). 39.32/11.37 thf(2978,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (div_mod_int @ B @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])). 39.32/11.37 thf(530,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_zero__le__power)). 39.32/11.37 thf(2649,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 39.32/11.37 thf(739,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 39.32/11.37 thf(3294,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 39.32/11.37 thf(201,axiom,((! [A:int]: ((ord_less_eq_int @ (bit0 @ A) @ min) = (ord_less_eq_int @ A @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_rel__simps_I28_J)). 39.32/11.37 thf(1744,plain,((! [A:int]: ((ord_less_eq_int @ (bit0 @ A) @ min) = (ord_less_eq_int @ A @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 39.32/11.37 thf(629,axiom,((! [A:int]: ((ord_less_int @ (bit0 @ A) @ min) = (ord_less_eq_int @ A @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_rel__simps_I11_J)). 39.32/11.37 thf(2968,plain,((! [A:int]: ((ord_less_int @ (bit0 @ A) @ min) = (ord_less_eq_int @ A @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])). 39.32/11.37 thf(39,axiom,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_power__mono)). 39.32/11.37 thf(1297,plain,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 39.32/11.37 thf(588,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (times_times_nat @ B @ (power_power_nat @ B @ A)) @ (power_power_nat @ B @ A)) <= (ord_less_nat @ B @ one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_power__Suc__less)). 39.32/11.37 thf(2845,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (times_times_nat @ B @ (power_power_nat @ B @ A)) @ (power_power_nat @ B @ A)) | ~ (ord_less_nat @ B @ one_one_nat) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 39.32/11.37 thf(608,axiom,((! [A:nat,B:real]: (((power_power_real @ B @ A) != zero_zero_real) <= (B != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_field__power__not__zero)). 39.32/11.37 thf(2900,plain,((! [A:nat,B:real]: (~ ((power_power_real @ B @ A) = zero_zero_real) | (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])). 39.32/11.37 thf(901,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_dvd__mult__left)). 39.32/11.37 thf(3743,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])). 39.32/11.37 thf(290,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_gr__implies__not0)). 39.32/11.37 thf(1974,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 39.32/11.37 thf(128,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_diff__add__inverse2)). 39.32/11.37 thf(1552,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 39.32/11.37 thf(481,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C)) <= (ord_less_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_zmult2__lemma__aux3)). 39.32/11.37 thf(2505,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ C) => ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ B @ (div_mod_int @ A @ D)) @ C)) | ~ (ord_less_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 39.32/11.37 thf(220,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_le__add2)). 39.32/11.37 thf(1799,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 39.32/11.37 thf(682,axiom,((! [A:real,B:real,C:int]: ((times_times_real @ (plus_plus_real @ A @ B) @ (number267125858f_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (number267125858f_real @ C)) @ (times_times_real @ B @ (number267125858f_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_left__distrib__number__of)). 39.32/11.37 thf(3115,plain,((! [A:real,B:real,C:int]: ((times_times_real @ (plus_plus_real @ A @ B) @ (number267125858f_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (number267125858f_real @ C)) @ (times_times_real @ B @ (number267125858f_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])). 39.32/11.37 thf(754,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_zero__le__square)). 39.32/11.37 thf(3333,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])). 39.32/11.37 thf(1080,axiom,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit1 @ pls)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_mult__numeral__1)). 39.32/11.37 thf(4259,plain,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit1 @ pls)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080])). 39.32/11.37 thf(711,axiom,((! [A:nat,B:nat,C:nat]: ((~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C)) => (((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)) <= (dvd_dvd_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_dvd_Oless__le__trans)). 39.32/11.37 thf(3215,plain,((! [A:nat,B:nat,C:nat]: ((~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C)) => (((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)) | ~ (dvd_dvd_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])). 39.32/11.37 thf(212,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) => ((dvd_dvd_nat @ B @ A) <= (dvd_dvd_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_dvd_Oord__eq__le__trans)). 39.32/11.37 thf(1776,plain,((! [A:nat,B:nat,C:nat]: ((B = C) => ((dvd_dvd_nat @ B @ A) | ~ (dvd_dvd_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 39.32/11.37 thf(27,axiom,((! [A:nat,B:nat]: ((((div_mod_nat @ A @ B) = (div_mod_nat @ (minus_minus_nat @ A @ B) @ B)) <= (~ (ord_less_nat @ A @ B))) & ((ord_less_nat @ A @ B) => ((div_mod_nat @ A @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_mod__if)). 39.32/11.37 thf(1263,plain,((! [A:nat,B:nat]: ((((div_mod_nat @ A @ B) = (div_mod_nat @ (minus_minus_nat @ A @ B) @ B)) | (ord_less_nat @ A @ B)) & ((ord_less_nat @ A @ B) => ((div_mod_nat @ A @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 39.32/11.37 thf(855,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J)). 39.32/11.37 thf(3611,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[855])). 39.32/11.37 thf(808,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ B) & ((ord_less_int @ pls @ B) <= (ord_less_int @ A @ B))) = (ord_less_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_less__nat__number__of)). 39.32/11.37 thf(3486,plain,((! [A:int,B:int]: (((ord_less_int @ A @ B) & ((ord_less_int @ pls @ B) | ~ (ord_less_int @ A @ B))) = (ord_less_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 39.32/11.37 thf(869,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_zadd__left__commute)). 39.32/11.37 thf(3654,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])). 39.32/11.37 thf(141,axiom,((! [A:nat,B:nat]: (((B = one_one_nat) & (A = one_one_nat)) = ((times_times_nat @ A @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_nat__mult__eq__1__iff)). 39.32/11.37 thf(1588,plain,((! [A:nat,B:nat]: (((B = one_one_nat) & (A = one_one_nat)) = ((times_times_nat @ A @ B) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 39.32/11.37 thf(103,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_nat @ A @ B) = (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_power__strict__increasing__iff)). 39.32/11.37 thf(1478,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_nat @ A @ B) = (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 39.32/11.37 thf(1126,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ B) = (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_zadd__commute)). 39.32/11.37 thf(4384,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ B) = (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126])). 39.32/11.37 thf(94,axiom,((! [A:int]: ((ord_less_int @ one_one_int @ A) => (? [B:int]: ((zprime @ B) & (dvd_dvd_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_zprime__factor__exists)). 39.32/11.37 thf(1451,plain,((! [A:int]: ((ord_less_int @ one_one_int @ A) => (? [B:int]: ((zprime @ B) & (dvd_dvd_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 39.32/11.37 thf(406,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_comm__mult__left__mono)). 39.32/11.37 thf(2304,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 39.32/11.37 thf(124,axiom,((! [A:nat]: ((((power_power_real @ zero_zero_real @ A) = zero_zero_real) <= (A != zero_zero_nat)) & (((power_power_real @ zero_zero_real @ A) = one_one_real) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_power__0__left)). 39.32/11.37 thf(1539,plain,((! [A:nat]: ((((power_power_real @ zero_zero_real @ A) = zero_zero_real) | (A = zero_zero_nat)) & (((power_power_real @ zero_zero_real @ A) = one_one_real) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 39.32/11.37 thf(1170,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_sum__power2__ge__zero)). 39.32/11.37 thf(4508,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170])). 39.32/11.37 thf(425,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (div_mod_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_pos__mod__sign)). 39.32/11.37 thf(2355,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (div_mod_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 39.32/11.37 thf(1159,axiom,((! [A:nat,B:int]: (((ord_less_int @ B @ one_one_int) => (ord_less_int @ (times_times_int @ B @ (power_power_int @ B @ A)) @ (power_power_int @ B @ A))) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_power__Suc__less)). 39.32/11.37 thf(4482,plain,((! [A:nat,B:int]: (((ord_less_int @ B @ one_one_int) => (ord_less_int @ (times_times_int @ B @ (power_power_int @ B @ A)) @ (power_power_int @ B @ A))) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159])). 39.32/11.37 thf(273,axiom,((! [A:real,B:nat]: (((power_power_real @ A @ B) = zero_zero_real) = ((B != zero_zero_nat) & (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_power__eq__0__iff)). 39.32/11.37 thf(1932,plain,((! [A:real,B:nat]: (((power_power_real @ A @ B) = zero_zero_real) = (~ (B = zero_zero_nat) & (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 39.32/11.37 thf(1074,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_zdiff__zmult__distrib2)). 39.32/11.37 thf(4244,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074])). 39.32/11.37 thf(713,axiom,((! [A:nat,B:nat]: (((B = A) = (dvd_dvd_nat @ B @ A)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_dvd_Oantisym__conv)). 39.32/11.37 thf(3222,plain,((! [A:nat,B:nat]: (((B = A) = (dvd_dvd_nat @ B @ A)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])). 39.32/11.37 thf(830,axiom,((! [A:int]: ((ord_less_eq_int @ (bit0 @ A) @ pls) = (ord_less_eq_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rel__simps_I27_J)). 39.32/11.37 thf(3540,plain,((! [A:int]: ((ord_less_eq_int @ (bit0 @ A) @ pls) = (ord_less_eq_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])). 39.32/11.37 thf(1113,axiom,((! [A:int]: ((plus_plus_real @ one_one_real @ (number267125858f_real @ A)) = (number267125858f_real @ (plus_plus_int @ (bit1 @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__special_I2_J)). 39.32/11.37 thf(4347,plain,((! [A:int]: ((plus_plus_real @ one_one_real @ (number267125858f_real @ A)) = (number267125858f_real @ (plus_plus_int @ (bit1 @ pls) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113])). 39.32/11.37 thf(241,axiom,((~ (ord_less_int @ pls @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_bin__less__0__simps_I1_J)). 39.32/11.37 thf(1852,plain,((~ (ord_less_int @ pls @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 39.32/11.37 thf(576,axiom,((! [A:int,B:int]: (zcong @ A @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_zcong__refl)). 39.32/11.37 thf(2813,plain,((! [A:int,B:int]: (zcong @ A @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 39.32/11.37 thf(980,axiom,((! [A:int,B:int]: (((A = zero_zero_int) & (B = zero_zero_int)) = ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_sum__power2__eq__zero__iff)). 39.32/11.37 thf(3967,plain,((! [A:int,B:int]: (((A = zero_zero_int) & (B = zero_zero_int)) = ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])). 39.32/11.37 thf(722,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 39.32/11.37 thf(3247,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])). 39.32/11.37 thf(562,axiom,((! [A:real,B:real]: (((A = B) <= (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_real__le__antisym)). 39.32/11.37 thf(2766,plain,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])). 39.32/11.37 thf(145,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_mult__pos__pos)). 39.32/11.37 thf(1599,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 39.32/11.37 thf(547,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (standardRes @ B @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_StandardRes__ubound)). 39.32/11.37 thf(2697,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (standardRes @ B @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 39.32/11.37 thf(19,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_dvd__triv__left)). 39.32/11.37 thf(1246,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 39.32/11.37 thf(680,axiom,((! [A:int]: ((? [B:int,C:int]: ((twoSqu2057625106sum2sq @ (product_Pair_int_int @ B @ C)) = A)) = (twoSqu919416604sum2sq @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_is__sum2sq__def)). 39.32/11.37 thf(3109,plain,((! [A:int]: ((? [B:int,C:int]: ((twoSqu2057625106sum2sq @ (product_Pair_int_int @ B @ C)) = A)) = (twoSqu919416604sum2sq @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])). 39.32/11.37 thf(642,axiom,((! [A:int,B:int]: ((number267125858f_real @ (plus_plus_int @ A @ B)) = (plus_plus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_number__of__add)). 39.32/11.37 thf(3005,plain,((! [A:int,B:int]: ((number267125858f_real @ (plus_plus_int @ A @ B)) = (plus_plus_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])). 39.32/11.37 thf(393,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ A @ B)) <= (ord_less_real @ A @ zero_zero_real)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_mult__strict__left__mono__neg)). 39.32/11.37 thf(2272,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ A @ B)) | ~ (ord_less_real @ A @ zero_zero_real) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 39.32/11.37 thf(1136,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 39.32/11.37 thf(4416,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136])). 39.32/11.37 thf(697,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_power__commutes)). 39.32/11.37 thf(3162,plain,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])). 39.32/11.37 thf(1067,axiom,((! [A:nat,B:int]: ((B != zero_zero_int) => ((power_power_int @ B @ A) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_field__power__not__zero)). 39.32/11.37 thf(4223,plain,((! [A:nat,B:int]: ((~ (B = zero_zero_int)) => (~ ((power_power_int @ B @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067])). 39.32/11.37 thf(1178,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_mult__eq__0__iff)). 39.32/11.37 thf(4535,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178])). 39.32/11.37 thf(930,axiom,((! [A:int,B:int]: ((B = (number_number_of_int @ A)) = ((number_number_of_int @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_number__of__reorient)). 39.32/11.37 thf(3834,plain,((! [A:int,B:int]: ((B = (number_number_of_int @ A)) = ((number_number_of_int @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[930])). 39.32/11.37 thf(922,axiom,((! [A:int,B:int]: ((plus_plus_int @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__Bit1__Bit0)). 39.32/11.37 thf(3802,plain,((! [A:int,B:int]: ((plus_plus_int @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[922])). 39.32/11.37 thf(1115,axiom,((! [A:int]: ((number_number_of_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ one_one_int @ (number_number_of_int @ A)) @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_number__of__Bit1)). 39.32/11.37 thf(4352,plain,((! [A:int]: ((number_number_of_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ one_one_int @ (number_number_of_int @ A)) @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115])). 39.32/11.37 thf(1188,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_int__0__neq__1)). 39.32/11.37 thf(4567,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188])). 39.32/11.37 thf(181,axiom,((! [A:int,B:int]: ((((ord_less_int @ B @ (minus_minus_int @ A @ one_one_int)) <= (B != (minus_minus_int @ A @ one_one_int))) <= (ord_less_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_Euler_Oaux1)). 39.32/11.37 thf(1695,plain,((! [A:int,B:int]: ((ord_less_int @ B @ (minus_minus_int @ A @ one_one_int)) | (B = (minus_minus_int @ A @ one_one_int)) | ~ (ord_less_int @ B @ A) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 39.32/11.37 thf(1157,axiom,((! [A:int]: (((bit0 @ A) = pls) = (A = pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_rel__simps_I44_J)). 39.32/11.37 thf(4476,plain,((! [A:int]: (((bit0 @ A) = pls) = (A = pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157])). 39.32/11.37 thf(132,axiom,((! [A:nat,B:nat]: (((A != zero_zero_nat) => ((times_times_nat @ B @ A) != zero_zero_nat)) <= (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_no__zero__divisors)). 39.32/11.37 thf(1563,plain,((! [A:nat,B:nat]: (((~ (A = zero_zero_nat)) => (~ ((times_times_nat @ B @ A) = zero_zero_nat))) | (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 39.32/11.37 thf(559,axiom,((! [A:$o,B:$o,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (B = A)) => (((A) & (ord_less_eq_int @ zero_zero_int @ C)) = ((B) & (ord_less_eq_int @ zero_zero_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_conj__le__cong)). 39.32/11.37 thf(2748,plain,((! [A:$o,B:$o,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (B = A)) => (((A) & (ord_less_eq_int @ zero_zero_int @ C)) = ((B) & (ord_less_eq_int @ zero_zero_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 39.32/11.37 thf(99,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_add__diff__inverse)). 39.32/11.37 thf(1466,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 39.32/11.37 thf(1148,axiom,((! [A:int]: ((((number_number_of_nat @ A) != zero_zero_nat) => ((power_power_int @ zero_zero_int @ (number_number_of_nat @ A)) = zero_zero_int)) & (((number_number_of_nat @ A) = zero_zero_nat) => ((power_power_int @ zero_zero_int @ (number_number_of_nat @ A)) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_power__0__left__number__of)). 39.32/11.37 thf(4448,plain,((! [A:int]: (((~ ((number_number_of_nat @ A) = zero_zero_nat)) => ((power_power_int @ zero_zero_int @ (number_number_of_nat @ A)) = zero_zero_int)) & (((number_number_of_nat @ A) = zero_zero_nat) => ((power_power_int @ zero_zero_int @ (number_number_of_nat @ A)) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148])). 39.32/11.37 thf(569,axiom,((! [A:real,B:nat,C:real]: (((ord_less_real @ A @ C) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_power__less__imp__less__base)). 39.32/11.37 thf(2793,plain,((! [A:real,B:nat,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])). 39.32/11.37 thf(1006,axiom,((! [A:nat,B:int]: ((ord_less_int @ one_one_int @ B) => (ord_less_int @ one_one_int @ (times_times_int @ B @ (power_power_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_power__gt1__lemma)). 39.32/11.37 thf(4036,plain,((! [A:nat,B:int]: ((ord_less_int @ one_one_int @ B) => (ord_less_int @ one_one_int @ (times_times_int @ B @ (power_power_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006])). 39.32/11.37 thf(518,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ (times_times_nat @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_mult__pos__pos)). 39.32/11.37 thf(2617,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])). 39.32/11.37 thf(535,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((plus_plus_nat @ A @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (plus_plus_nat @ A @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_add__diff__assoc)). 39.32/11.37 thf(2662,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((plus_plus_nat @ A @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (plus_plus_nat @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])). 39.32/11.37 thf(924,axiom,((! [A:int,B:int]: ((times_times_int @ (bit0 @ A) @ B) = (bit0 @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mult__Bit0)). 39.32/11.37 thf(3807,plain,((! [A:int,B:int]: ((times_times_int @ (bit0 @ A) @ B) = (bit0 @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[924])). 39.32/11.37 thf(1043,axiom,((! [A:int]: ((ord_less_int @ pls @ (bit0 @ A)) = (ord_less_int @ pls @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rel__simps_I4_J)). 39.32/11.37 thf(4148,plain,((! [A:int]: ((ord_less_int @ pls @ (bit0 @ A)) = (ord_less_int @ pls @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043])). 39.32/11.37 thf(88,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)). 39.32/11.37 thf(1434,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ B @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 39.32/11.37 thf(243,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 39.32/11.37 thf(1857,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 39.32/11.37 thf(226,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_add__mult__distrib)). 39.32/11.37 thf(1814,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 39.32/11.37 thf(714,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_diff__mult__distrib2)). 39.32/11.37 thf(3225,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 39.32/11.37 thf(1091,axiom,((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_p0)). 39.32/11.37 thf(4288,plain,((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091])). 39.32/11.37 thf(495,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)) = ((A != B) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_dvd_Oless__le)). 39.32/11.37 thf(2546,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)) = (~ (A = B) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 39.32/11.37 thf(560,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_zero__le__power)). 39.32/11.37 thf(2761,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 39.32/11.37 thf(1057,axiom,((! [A:int,B:int]: ((((A = one_one_int) & (B = one_one_int)) | ((B = (number_number_of_int @ min)) & (A = (number_number_of_int @ min)))) = ((times_times_int @ A @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_zmult__eq__1__iff)). 39.32/11.37 thf(4195,plain,((! [A:int,B:int]: ((((A = one_one_int) & (B = one_one_int)) | ((B = (number_number_of_int @ min)) & (A = (number_number_of_int @ min)))) = ((times_times_int @ A @ B) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057])). 39.32/11.37 thf(313,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) <= (((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ B @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_split__mult__neg__le)). 39.32/11.37 thf(2043,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) | ~ (((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ B @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 39.32/11.37 thf(1063,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_real @ (power_power_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__even__eq)). 39.32/11.37 thf(4212,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_real @ (power_power_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063])). 39.32/11.37 thf(701,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_le__iff__add)). 39.32/11.37 thf(3183,plain,((! [A:nat,B:nat]: ((? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 39.32/11.37 thf(318,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C))) <= (ord_less_eq_nat @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_nat__less__add__iff2)). 39.32/11.37 thf(2057,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C))) | ~ (ord_less_eq_nat @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 39.32/11.37 thf(188,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ B))) <= (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_q__pos__lemma)). 39.32/11.37 thf(1712,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 39.32/11.37 thf(848,axiom,((! [A:int,B:int]: ((((times_times_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)) = (number267125858f_real @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ pls @ A)) <= (ord_less_eq_int @ pls @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_semiring__mult__number__of)). 39.32/11.37 thf(3592,plain,((! [A:int,B:int]: (((times_times_real @ (number267125858f_real @ B) @ (number267125858f_real @ A)) = (number267125858f_real @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ pls @ A) | ~ (ord_less_eq_int @ pls @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[848])). 39.32/11.37 thf(238,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_zero__less__mult__pos)). 39.32/11.37 thf(1846,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 39.32/11.37 thf(993,axiom,((one_one_int != zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_one__neq__zero)). 39.32/11.37 thf(3999,plain,((~ (one_one_int = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[993])). 39.32/11.37 thf(627,axiom,((! [A:nat]: ((A = zero_zero_nat) = (dvd_dvd_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique)). 39.32/11.37 thf(2963,plain,((! [A:nat]: ((A = zero_zero_nat) = (dvd_dvd_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])). 39.32/11.37 thf(35,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_dvd_Oless__asym)). 39.32/11.37 thf(1286,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 39.32/11.37 thf(749,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_mult__strict__left__mono)). 39.32/11.37 thf(3321,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 39.32/11.37 thf(430,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ A) <= (~ (ord_less_real @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_linorder__neqE__linordered__idom)). 39.32/11.37 thf(2368,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (ord_less_real @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 39.32/11.37 thf(816,axiom,((! [A:int,B:int]: ((A = B) = ((number_number_of_int @ A) = (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_eq__number__of)). 39.32/11.37 thf(3508,plain,((! [A:int,B:int]: ((A = B) = ((number_number_of_int @ A) = (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 39.32/11.37 thf(258,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_int @ F @ D) => ((((ord_less_eq_int @ B @ E) <= (ord_less_eq_int @ D @ A)) <= (ord_less_int @ zero_zero_int @ D)) <= (ord_less_eq_int @ zero_zero_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_zdiv__mono2__lemma)). 39.32/11.37 thf(1895,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_int @ F @ D) => ((ord_less_eq_int @ B @ E) | ~ (ord_less_eq_int @ D @ A) | ~ (ord_less_int @ zero_zero_int @ D) | ~ (ord_less_eq_int @ zero_zero_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 39.32/11.37 thf(368,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_power__mono)). 39.32/11.37 thf(2189,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 39.32/11.37 thf(152,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_mult__le__mono2)). 39.32/11.37 thf(1616,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 39.32/11.37 thf(639,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__number__of)). 39.32/11.37 thf(2995,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 39.32/11.37 thf(995,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__number__of__int__code)). 39.32/11.37 thf(4004,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])). 39.32/11.37 thf(418,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (div_mod_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_neg__mod__sign)). 39.32/11.37 thf(2338,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (div_mod_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 39.32/11.37 thf(876,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_int @ (power_power_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_power__even__eq)). 39.32/11.37 thf(3675,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_int @ (power_power_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])). 39.32/11.37 thf(451,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) = (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_less__diff__conv)). 39.32/11.37 thf(2423,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) = (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 39.32/11.37 thf(488,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B)) = (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_add__gr__0)). 39.32/11.37 thf(2529,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B)) = (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 39.32/11.37 thf(617,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 39.32/11.37 thf(2936,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 39.32/11.37 thf(871,axiom,((! [A:int]: ~ (ord_less_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_power2__less__0)). 39.32/11.37 thf(3660,plain,((! [A:int]: ~ (ord_less_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])). 39.32/11.37 thf(113,axiom,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_power__one)). 39.32/11.37 thf(1510,plain,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 39.32/11.37 thf(687,axiom,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_power__one)). 39.32/11.37 thf(3130,plain,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])). 39.32/11.37 thf(1037,axiom,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_mult__2)). 39.32/11.37 thf(4131,plain,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037])). 39.32/11.37 thf(540,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 39.32/11.37 thf(2677,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])). 39.32/11.37 thf(401,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_power__le__imp__le__exp)). 39.32/11.37 thf(2292,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 39.32/11.37 thf(351,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ A) <= (ord_less_eq_real @ C @ A)) <= (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_real__le__trans)). 39.32/11.37 thf(2149,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ C @ A) | ~ (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 39.32/11.37 thf(510,axiom,((! [A:$o,B:$o,C:int]: (((B = A) <= (ord_less_eq_int @ zero_zero_int @ C)) => (((B) <= (ord_less_eq_int @ zero_zero_int @ C)) = ((ord_less_eq_int @ zero_zero_int @ C) => (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_imp__le__cong)). 39.32/11.37 thf(2585,plain,((! [A:$o,B:$o,C:int]: (((B = A) | ~ (ord_less_eq_int @ zero_zero_int @ C)) => (((B) | ~ (ord_less_eq_int @ zero_zero_int @ C)) = ((ord_less_eq_int @ zero_zero_int @ C) => (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 39.32/11.37 thf(551,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (standardRes @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_StandardRes__lbound)). 39.32/11.37 thf(2717,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (standardRes @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])). 39.32/11.37 thf(951,axiom,((! [A:int,B:int,C:int,D:int]: (((A = C) | (B = D)) = ((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_crossproduct__eq)). 39.32/11.37 thf(3890,plain,((! [A:int,B:int,C:int,D:int]: (((A = C) | (B = D)) = ((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])). 39.32/11.37 thf(29,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ (times_times_real @ A @ C)) <= (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_dvd__mult)). 39.32/11.37 thf(1273,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ (times_times_real @ A @ C)) | ~ (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 39.32/11.37 thf(1000,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__number__of)). 39.32/11.37 thf(4017,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000])). 39.32/11.37 thf(884,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_int @ one_one_int @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_power__increasing__iff)). 39.32/11.37 thf(3696,plain,((! [A:nat,B:nat,C:int]: ((ord_less_int @ one_one_int @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])). 39.32/11.37 thf(606,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_less__not__refl)). 39.32/11.37 thf(2894,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])). 39.32/11.37 thf(486,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 39.32/11.37 thf(2524,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 39.32/11.37 thf(759,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((B = zero_zero_nat) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1131_divides__le)). 39.32/11.37 thf(3343,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((B = zero_zero_nat) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])). 39.32/11.37 thf(439,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_divides__ge)). 39.32/11.37 thf(2391,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 39.32/11.37 thf(175,axiom,((! [A:int,B:int]: ((zprime @ B) => (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (A != (inv @ B @ A))) <= (ord_less_int @ one_one_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_inv__distinct)). 39.32/11.37 thf(1680,plain,((! [A:int,B:int]: ((zprime @ B) => (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (~ (A = (inv @ B @ A)))) | ~ (ord_less_int @ one_one_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 39.32/11.37 thf(182,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 39.32/11.37 thf(1698,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 39.32/11.37 thf(284,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)) => (ord_less_int @ zero_zero_int @ A)) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_pos__zmult__pos)). 39.32/11.37 thf(1959,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (times_times_int @ B @ A)) => (ord_less_int @ zero_zero_int @ A)) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 39.32/11.37 thf(499,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 39.32/11.37 thf(2556,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 39.32/11.37 thf(1033,axiom,((zcong @ (power_power_int @ s1 @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_s1)). 39.32/11.37 thf(4116,plain,((zcong @ (power_power_int @ s1 @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033])). 39.32/11.37 thf(504,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (times_times_nat @ B @ A)) = (times_times_nat @ (plus_plus_nat @ B @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 39.32/11.37 thf(2570,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (times_times_nat @ B @ A)) = (times_times_nat @ (plus_plus_nat @ B @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 39.32/11.37 thf(202,axiom,((! [A:nat]: ((A = one_one_nat) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot)). 39.32/11.37 thf(1747,plain,((! [A:nat]: ((A = one_one_nat) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 39.32/11.37 thf(126,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)) <= (ord_less_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_mult__neg__pos)). 39.32/11.37 thf(1548,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)) | ~ (ord_less_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 39.32/11.37 thf(271,axiom,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_le__0__eq)). 39.32/11.37 thf(1927,plain,((! [A:nat]: ((A = zero_zero_nat) = (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 39.32/11.37 thf(1129,axiom,(((~ (quadRes @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (number_number_of_int @ min))) => ((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) != one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N)). 39.32/11.37 thf(4393,plain,(((~ (quadRes @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (number_number_of_int @ min))) => (~ ((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129])). 39.32/11.37 thf(737,axiom,((! [A:nat,B:int,C:int]: ((((ord_less_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_power__strict__mono)). 39.32/11.37 thf(3289,plain,((! [A:nat,B:int,C:int]: ((ord_less_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 39.32/11.37 thf(41,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => ((((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_mult__mono_H)). 39.32/11.37 thf(1301,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ C @ D) => (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 39.32/11.37 thf(950,axiom,((one_one_int = (number_number_of_int @ (bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_one__is__num__one)). 39.32/11.37 thf(3888,plain,((one_one_int = (number_number_of_int @ (bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])). 39.32/11.37 thf(1168,axiom,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (minus_minus_int @ (plus_plus_int @ (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ B)) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ A) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))) @ (power_power_int @ B @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_zdiff__power3)). 39.32/11.37 thf(4503,plain,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (minus_minus_int @ (plus_plus_int @ (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ B)) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ A) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))) @ (power_power_int @ B @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168])). 39.32/11.37 thf(1192,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_zero__le__power2)). 39.32/11.37 thf(4577,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192])). 39.32/11.37 thf(828,axiom,(((number_number_of_nat @ pls) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_semiring__numeral__0__eq__0)). 39.32/11.37 thf(3536,plain,(((number_number_of_nat @ pls) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])). 39.32/11.37 thf(814,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_eq_nat @ A @ B) <= (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B))) <= (ord_less_int @ one_one_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_power__le__imp__le__exp)). 39.32/11.37 thf(3504,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) | ~ (ord_less_int @ one_one_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 39.32/11.37 thf(1100,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_sum__power2__le__zero__iff)). 39.32/11.37 thf(4309,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100])). 39.32/11.37 thf(154,axiom,((! [A:int,B:(int > $o)]: ((! [C:int]: ((B @ C) <= ((B @ (minus_minus_int @ C @ one_one_int)) <= (ord_less_int @ one_one_int @ C)))) => (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_d22set__induct__old)). 39.32/11.37 thf(1620,plain,((! [A:int,B:(int > $o)]: ((! [C:int]: ((B @ C) | ~ ((B @ (minus_minus_int @ C @ one_one_int)) | ~ (ord_less_int @ one_one_int @ C)))) => (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 39.32/11.37 thf(798,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_semiring__one__add__one__is__two)). 39.32/11.37 thf(3458,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])). 39.32/11.37 thf(546,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_real__mult__order)). 39.32/11.37 thf(2695,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 39.32/11.37 thf(582,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C)) <= (ord_less_eq_nat @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_nat__le__add__iff1)). 39.32/11.37 thf(2827,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C)) | ~ (ord_less_eq_nat @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])). 39.32/11.37 thf(710,axiom,((! [A:nat,B:real]: ((ord_less_real @ (power_power_real @ B @ A) @ (times_times_real @ B @ (power_power_real @ B @ A))) <= (ord_less_real @ one_one_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_power__less__power__Suc)). 39.32/11.37 thf(3213,plain,((! [A:nat,B:real]: ((ord_less_real @ (power_power_real @ B @ A) @ (times_times_real @ B @ (power_power_real @ B @ A))) | ~ (ord_less_real @ one_one_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])). 39.32/11.37 thf(1111,axiom,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ A @ (times_times_int @ B @ (times_times_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 39.32/11.37 thf(4341,plain,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ A @ (times_times_int @ B @ (times_times_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111])). 39.32/11.37 thf(665,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_plus__nat_Oadd__0)). 39.32/11.37 thf(3070,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 39.32/11.37 thf(909,axiom,((! [A:int]: ((ord_less_eq_int @ A @ pls) = ((number_number_of_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_eq__number__of__0)). 39.32/11.37 thf(3768,plain,((! [A:int]: ((ord_less_eq_int @ A @ pls) = ((number_number_of_nat @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[909])). 39.32/11.37 thf(266,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_mult__right__mono)). 39.32/11.37 thf(1916,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 39.32/11.37 thf(863,axiom,((! [A:int,B:int,C:int]: ((((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((ord_less_int @ one_one_int @ A) => ((ord_less_int @ A @ (minus_minus_int @ C @ one_one_int)) => ((member_int @ A @ (wset @ B @ C)) <= (member_int @ (inv @ C @ A) @ (wset @ B @ C)))))) <= (ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ C)) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_wset__inv__mem__mem)). 39.32/11.37 thf(3636,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => ((ord_less_int @ one_one_int @ A) => ((ord_less_int @ A @ (minus_minus_int @ C @ one_one_int)) => ((member_int @ A @ (wset @ B @ C)) | ~ (member_int @ (inv @ C @ A) @ (wset @ B @ C)))))) | ~ (ord_less_eq_int @ (number_number_of_int @ (bit1 @ (bit0 @ (bit1 @ pls)))) @ C) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[863])). 39.32/11.37 thf(718,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_not__add__less2)). 39.32/11.37 thf(3234,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])). 39.32/11.37 thf(315,axiom,((! [A:int]: ((ord_less_real @ zero_zero_real @ (number267125858f_real @ A)) = (ord_less_int @ pls @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_less__special_I1_J)). 39.32/11.37 thf(2048,plain,((! [A:int]: ((ord_less_real @ zero_zero_real @ (number267125858f_real @ A)) = (ord_less_int @ pls @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 39.32/11.37 thf(1089,axiom,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J)). 39.32/11.37 thf(4283,plain,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089])). 39.32/11.37 thf(70,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ B) = (times_times_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 39.32/11.37 thf(1389,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ B) = (times_times_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 39.32/11.37 thf(725,axiom,((! [A:int,B:int]: ((member_int @ A @ (d22set @ B)) => (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_d22set__g__1)). 39.32/11.37 thf(3255,plain,((! [A:int,B:int]: ((member_int @ A @ (d22set @ B)) => (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])). 39.32/11.37 thf(568,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ C) => ((ord_less_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_mult__strict__right__mono)). 39.32/11.37 thf(2791,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ C) => ((ord_less_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])). 39.32/11.37 thf(720,axiom,((! [A:nat,B:nat]: (((A = B) <= (dvd_dvd_nat @ B @ A)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_dvd_Oantisym)). 39.32/11.37 thf(3240,plain,((! [A:nat,B:nat]: ((A = B) | ~ (dvd_dvd_nat @ B @ A) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])). 39.32/11.37 thf(533,axiom,((! [A:int,B:int,C:int]: ((zprime @ C) => (((ord_less_int @ one_one_int @ A) <= (member_int @ A @ (wset @ B @ C))) <= (ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_wset__g__1)). 39.32/11.37 thf(2657,plain,((! [A:int,B:int,C:int]: ((zprime @ C) => ((ord_less_int @ one_one_int @ A) | ~ (member_int @ A @ (wset @ B @ C)) | ~ (ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 39.32/11.37 thf(590,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) <= (C != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_pow__divides__eq__nat)). 39.32/11.37 thf(2849,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) | (C = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 39.32/11.37 thf(165,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C != D) & (A != B)) = ((plus_plus_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)) != (plus_plus_nat @ (times_times_nat @ C @ B) @ (times_times_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_crossproduct__noteq)). 39.32/11.37 thf(1652,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((~ (C = D) & ~ (A = B)) = (~ ((plus_plus_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)) = (plus_plus_nat @ (times_times_nat @ C @ B) @ (times_times_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 39.32/11.37 thf(898,axiom,((dvd_dvd_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096)). 39.32/11.37 thf(3736,plain,((dvd_dvd_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[898])). 39.32/11.37 thf(972,axiom,((! [A:int,B:int,C:int,D:int]: (((((~ (zcong @ B @ zero_zero_int @ D)) => ((zcong @ C @ (times_times_int @ A @ (multInv @ D @ B)) @ D) <= (zcong @ B @ (times_times_int @ A @ (multInv @ D @ C)) @ D))) <= (~ (zcong @ C @ zero_zero_int @ D))) <= (zprime @ D)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_MultInv__zcong__prop2)). 39.32/11.37 thf(3945,plain,((! [A:int,B:int,C:int,D:int]: (((~ (zcong @ B @ zero_zero_int @ D)) => ((zcong @ C @ (times_times_int @ A @ (multInv @ D @ B)) @ D) | ~ (zcong @ B @ (times_times_int @ A @ (multInv @ D @ C)) @ D))) | (zcong @ C @ zero_zero_int @ D) | ~ (zprime @ D) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])). 39.32/11.37 thf(735,axiom,((! [A:nat,B:nat]: (((B = one_one_nat) & (A = one_one_nat)) = (one_one_nat = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_nat__1__eq__mult__iff)). 39.32/11.37 thf(3283,plain,((! [A:nat,B:nat]: (((B = one_one_nat) & (A = one_one_nat)) = (one_one_nat = (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])). 39.32/11.37 thf(729,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_dvd_Oneq__le__trans)). 39.32/11.37 thf(3266,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A))) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])). 39.32/11.37 thf(539,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_real__le__eq__diff)). 39.32/11.37 thf(2674,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])). 39.32/11.37 thf(183,axiom,((! [A:int]: ((ord_less_eq_int @ A @ min) = (ord_less_eq_int @ (bit1 @ A) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_rel__simps_I30_J)). 39.32/11.37 thf(1701,plain,((! [A:int]: ((ord_less_eq_int @ A @ min) = (ord_less_eq_int @ (bit1 @ A) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 39.32/11.37 thf(442,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_mult__left__mono)). 39.32/11.37 thf(2398,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 39.32/11.37 thf(852,axiom,((! [A:int,B:int,C:int,D:int]: ((zcong @ (plus_plus_int @ B @ A) @ (plus_plus_int @ C @ A) @ D) <= (zcong @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_zcong__shift)). 39.32/11.37 thf(3604,plain,((! [A:int,B:int,C:int,D:int]: ((zcong @ (plus_plus_int @ B @ A) @ (plus_plus_int @ C @ A) @ D) | ~ (zcong @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[852])). 39.32/11.37 thf(1125,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ (times_times_int @ B @ D) @ E) = (zcong @ A @ (times_times_int @ B @ C) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_zcong__zmult__prop2)). 39.32/11.37 thf(4381,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ (times_times_int @ B @ D) @ E) = (zcong @ A @ (times_times_int @ B @ C) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125])). 39.32/11.37 thf(1198,axiom,((! [A:int]: ((plus_plus_int @ A @ (number_number_of_int @ pls)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add__numeral__0__right)). 39.32/11.37 thf(4590,plain,((! [A:int]: ((plus_plus_int @ A @ (number_number_of_int @ pls)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198])). 39.32/11.37 thf(117,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_less__bin__lemma)). 39.32/11.37 thf(1520,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 39.32/11.37 thf(578,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_real__add__mult__distrib)). 39.32/11.37 thf(2817,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 39.32/11.37 thf(1161,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) @ B) | (B = A) | (B = zero_zero_nat)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_divides__cases)). 39.32/11.37 thf(4485,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) @ B) | (B = A) | (B = zero_zero_nat) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161])). 39.32/11.37 thf(659,axiom,((! [A:int,B:real]: (((number267125858f_real @ A) = B) = (B = (number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_number__of__reorient)). 39.32/11.37 thf(3051,plain,((! [A:int,B:real]: (((number267125858f_real @ A) = B) = (B = (number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])). 39.32/11.37 thf(408,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ B) = (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 39.32/11.37 thf(2308,plain,((! [A:nat,B:nat]: ((times_times_nat @ A @ B) = (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 39.32/11.37 thf(867,axiom,((! [A:int]: (((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit0 @ A))) & (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit1 @ A)))) <= (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_number__of1)). 39.32/11.37 thf(3646,plain,((! [A:int]: (((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit0 @ A))) & (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit1 @ A)))) | ~ (ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])). 39.32/11.37 thf(197,axiom,((! [A:int,B:int,C:int]: ((((ord_less_int @ A @ C) & (ord_less_int @ zero_zero_int @ B)) | ((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ C @ A))) = (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_mult__less__cancel__right__disj)). 39.32/11.37 thf(1733,plain,((! [A:int,B:int,C:int]: ((((ord_less_int @ A @ C) & (ord_less_int @ zero_zero_int @ B)) | ((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ C @ A))) = (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 39.32/11.37 thf(1135,axiom,((! [A:real,B:real]: (((A = zero_zero_real) & (B = zero_zero_real)) = (ord_less_eq_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_sum__power2__le__zero__iff)). 39.32/11.37 thf(4413,plain,((! [A:real,B:real]: (((A = zero_zero_real) & (B = zero_zero_real)) = (ord_less_eq_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135])). 39.32/11.37 thf(51,axiom,((! [A:int,B:int,C:int,D:int]: ((zcong @ (times_times_int @ (times_times_int @ (multInv @ D @ A) @ A) @ B) @ (times_times_int @ (multInv @ D @ A) @ C) @ D) <= (zcong @ (times_times_int @ A @ B) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_aux______3)). 39.32/11.37 thf(1332,plain,((! [A:int,B:int,C:int,D:int]: ((zcong @ (times_times_int @ (times_times_int @ (multInv @ D @ A) @ A) @ B) @ (times_times_int @ (multInv @ D @ A) @ C) @ D) | ~ (zcong @ (times_times_int @ A @ B) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 39.32/11.37 thf(915,axiom,((~ (ord_less_int @ pls @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I2_J)). 39.32/11.37 thf(3783,plain,((~ (ord_less_int @ pls @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[915])). 39.32/11.37 thf(464,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ zero_zero_nat @ D) => ((~ (dvd_dvd_nat @ C @ A)) <= (ord_less_nat @ D @ C))) <= (A = (plus_plus_nat @ (times_times_nat @ B @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_divides__div__not)). 39.32/11.37 thf(2457,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ zero_zero_nat @ D) => (~ (dvd_dvd_nat @ C @ A) | ~ (ord_less_nat @ D @ C))) | ~ (A = (plus_plus_nat @ (times_times_nat @ B @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 39.32/11.37 thf(742,axiom,((! [A:real,B:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ B) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 39.32/11.37 thf(3302,plain,((! [A:real,B:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ B) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])). 39.32/11.37 thf(763,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_mult__less__mono2)). 39.32/11.37 thf(3355,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])). 39.32/11.37 thf(173,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_zero__less__power)). 39.32/11.37 thf(1675,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 39.32/11.37 thf(85,axiom,((! [A:int,B:int,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ A @ (power_power_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_zpower__zdvd__prop1)). 39.32/11.37 thf(1428,plain,((! [A:int,B:int,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ A @ (power_power_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 39.32/11.37 thf(356,axiom,((! [A:int]: ((ord_less_int @ A @ min) = (ord_less_int @ (bit1 @ A) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_rel__simps_I13_J)). 39.32/11.37 thf(2161,plain,((! [A:int]: ((ord_less_int @ A @ min) = (ord_less_int @ (bit1 @ A) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 39.32/11.37 thf(1077,axiom,((! [A:int,B:int]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_rel__simps_I51_J)). 39.32/11.37 thf(4251,plain,((! [A:int,B:int]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077])). 39.32/11.37 thf(1177,axiom,((! [A:int,B:int]: ((((((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (plus_plus_int @ B @ A))) <= (~ (ord_less_int @ A @ pls))) & (((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ B)) <= (ord_less_int @ A @ pls))) <= (~ (ord_less_int @ B @ pls))) & ((ord_less_int @ B @ pls) => ((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__nat__number__of)). 39.32/11.37 thf(4526,plain,((! [A:int,B:int]: ((((((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (plus_plus_int @ B @ A))) | (ord_less_int @ A @ pls)) & (((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ B)) | ~ (ord_less_int @ A @ pls))) | (ord_less_int @ B @ pls)) & ((ord_less_int @ B @ pls) => ((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177])). 39.32/11.37 thf(920,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ (times_times_int @ B @ A)) = (times_times_int @ (plus_plus_int @ B @ one_one_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 39.32/11.37 thf(3796,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ (times_times_int @ B @ A)) = (times_times_int @ (plus_plus_int @ B @ one_one_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[920])). 39.32/11.37 thf(215,axiom,((! [A:int,B:nat]: (((A = zero_zero_int) & (B != zero_zero_nat)) = ((power_power_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_power__eq__0__iff)). 39.32/11.37 thf(1786,plain,((! [A:int,B:nat]: (((A = zero_zero_int) & ~ (B = zero_zero_nat)) = ((power_power_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 39.32/11.37 thf(171,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (power_power_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 39.32/11.37 thf(1669,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (power_power_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 39.32/11.37 thf(683,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_mult__less__cancel1)). 39.32/11.37 thf(3118,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])). 39.32/11.37 thf(904,axiom,((! [A:int]: ((plus_plus_int @ (number_number_of_int @ A) @ one_one_int) = (number_number_of_int @ (plus_plus_int @ A @ (bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__special_I3_J)). 39.32/11.37 thf(3751,plain,((! [A:int]: ((plus_plus_int @ (number_number_of_int @ A) @ one_one_int) = (number_number_of_int @ (plus_plus_int @ A @ (bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[904])). 39.32/11.37 thf(309,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 39.32/11.37 thf(2029,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 39.32/11.37 thf(1027,axiom,(((number_number_of_int @ (bit1 @ pls)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_numeral__1__eq__1)). 39.32/11.37 thf(4096,plain,(((number_number_of_int @ (bit1 @ pls)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027])). 39.32/11.37 thf(753,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 39.32/11.37 thf(3330,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])). 39.32/11.37 thf(555,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ (number_number_of_int @ B) @ (number_number_of_int @ A))) = (ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__number__of__eq__not__less)). 39.32/11.37 thf(2738,plain,((! [A:int,B:int]: ((~ (ord_less_int @ (number_number_of_int @ B) @ (number_number_of_int @ A))) = (ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])). 39.32/11.37 thf(1052,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (A = B))) <= ((power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_power2__eq__imp__eq)). 39.32/11.37 thf(4171,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (A = B))) | ~ ((power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052])). 39.32/11.37 thf(872,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ (power_power_int @ A @ B) @ C) = (power_power_int @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 39.32/11.37 thf(3663,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ (power_power_int @ A @ B) @ C) = (power_power_int @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])). 39.32/11.37 thf(758,axiom,((! [A:nat,B:nat]: ((A = (times_times_nat @ A @ B)) => ((B = one_one_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_mult__eq__self__implies__10)). 39.32/11.37 thf(3340,plain,((! [A:nat,B:nat]: ((A = (times_times_nat @ A @ B)) => ((B = one_one_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])). 39.32/11.37 thf(16,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (div_mod_nat @ A @ B) @ C) = (div_mod_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_mod__mult__distrib)). 39.32/11.37 thf(1239,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (div_mod_nat @ A @ B) @ C) = (div_mod_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 39.32/11.37 thf(459,axiom,((! [A:real,B:nat]: (((ord_less_real @ zero_zero_real @ A) => (? [C:real]: (((power_power_real @ C @ B) = A) & (ord_less_real @ zero_zero_real @ C)))) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_realpow__pos__nth)). 39.32/11.37 thf(2442,plain,((! [A:real,B:nat]: (((ord_less_real @ zero_zero_real @ A) => (? [C:real]: (((power_power_real @ C @ B) = A) & (ord_less_real @ zero_zero_real @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 39.32/11.37 thf(790,axiom,(((number_number_of_int @ pls) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_number__of__Pls)). 39.32/11.37 thf(3436,plain,(((number_number_of_int @ pls) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])). 39.32/11.37 thf(358,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (div_mod_int @ A @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_pos__mod__bound)). 39.32/11.37 thf(2166,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (div_mod_int @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 39.32/11.37 thf(209,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) = ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_dvd_Oless__le__not__le)). 39.32/11.37 thf(1765,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) = ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 39.32/11.37 thf(505,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_le__add__diff)). 39.32/11.37 thf(2573,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 39.32/11.37 thf(412,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((plus_plus_nat @ A @ D) = (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B)) <= (ord_less_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_less__add__eq__less)). 39.32/11.37 thf(2319,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((((plus_plus_nat @ A @ D) = (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B)) | ~ (ord_less_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 39.32/11.37 thf(483,axiom,((! [A:int,B:int]: (((zcong @ A @ zero_zero_int @ B) => ((legendre @ A @ B) = zero_zero_int)) & ((~ (zcong @ A @ zero_zero_int @ B)) => ((((legendre @ A @ B) = (number_number_of_int @ min)) <= (~ (quadRes @ B @ A))) & ((quadRes @ B @ A) => ((legendre @ A @ B) = one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_Legendre__def)). 39.32/11.37 thf(2510,plain,((! [A:int,B:int]: (((zcong @ A @ zero_zero_int @ B) => ((legendre @ A @ B) = zero_zero_int)) & ((~ (zcong @ A @ zero_zero_int @ B)) => ((((legendre @ A @ B) = (number_number_of_int @ min)) | (quadRes @ B @ A)) & ((quadRes @ B @ A) => ((legendre @ A @ B) = one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 39.32/11.37 thf(877,axiom,((one_one_nat = (number_number_of_nat @ (bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat)). 39.32/11.37 thf(3678,plain,((one_one_nat = (number_number_of_nat @ (bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])). 39.32/11.37 thf(409,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ B) = (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 39.32/11.37 thf(2311,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ B) = (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 39.32/11.37 thf(677,axiom,((! [A:nat]: ((A != zero_zero_nat) = (~ (dvd_dvd_nat @ zero_zero_nat @ A) & (dvd_dvd_nat @ A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top)). 39.32/11.37 thf(3101,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (~ (dvd_dvd_nat @ zero_zero_nat @ A) & (dvd_dvd_nat @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 39.32/11.37 thf(762,axiom,((! [A:real,B:real,C:real]: ((C != zero_zero_real) => (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_real__mult__right__cancel)). 39.32/11.37 thf(3352,plain,((! [A:real,B:real,C:real]: ((~ (C = zero_zero_real)) => (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])). 39.32/11.37 thf(992,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J)). 39.32/11.37 thf(3996,plain,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])). 39.32/11.37 thf(526,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_exp__eq__1)). 39.32/11.37 thf(2637,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 39.32/11.37 thf(223,axiom,((! [A:int,B:nat,C:int]: ((zprime @ C) => ((dvd_dvd_int @ C @ (power_power_int @ A @ B)) => ((dvd_dvd_int @ C @ A) <= (ord_less_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_zpower__zdvd__prop2)). 39.32/11.37 thf(1806,plain,((! [A:int,B:nat,C:int]: ((zprime @ C) => ((dvd_dvd_int @ C @ (power_power_int @ A @ B)) => ((dvd_dvd_int @ C @ A) | ~ (ord_less_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 39.32/11.37 thf(57,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_nat__mult__1__right)). 39.32/11.37 thf(1349,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 39.32/11.37 thf(398,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__0__iff)). 39.32/11.37 thf(2284,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 39.32/11.37 thf(107,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) => ((ord_less_int @ zero_zero_int @ A) <= (ord_less_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_zero__less__mult__pos2)). 39.32/11.37 thf(1492,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) => ((ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 39.32/11.37 thf(211,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((A = B) | ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_dvd_Ole__imp__less__or__eq)). 39.32/11.37 thf(1771,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((A = B) | ((dvd_dvd_nat @ A @ B) & ~ (dvd_dvd_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 39.32/11.37 thf(1097,axiom,((! [A:int,B:int]: (((A = one_one_int) | (A = (number_number_of_int @ min))) <= ((times_times_int @ A @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma)). 39.32/11.37 thf(4300,plain,((! [A:int,B:int]: ((A = one_one_int) | (A = (number_number_of_int @ min)) | ~ ((times_times_int @ A @ B) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097])). 39.32/11.37 thf(372,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ C @ B) <= (B = C)) => (((A @ C @ B) <= (ord_less_nat @ C @ B)) => (A @ C @ B))) <= ((A @ C @ B) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_nat__less__cases)). 39.32/11.37 thf(2197,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ C @ B) | ~ (B = C)) => (((A @ C @ B) | ~ (ord_less_nat @ C @ B)) => (A @ C @ B))) | ~ ((A @ C @ B) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 39.32/11.37 thf(1166,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ A) @ B) @ (times_times_int @ (number_number_of_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_right__distrib__number__of)). 39.32/11.37 thf(4498,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (number_number_of_int @ A) @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ A) @ B) @ (times_times_int @ (number_number_of_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166])). 39.32/11.37 thf(1121,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int,G:int]: ((plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ (times_times_int @ B @ C)) @ D) @ (times_times_int @ (minus_minus_int @ E @ (times_times_int @ B @ F)) @ G)) = (minus_minus_int @ (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ E @ G)) @ (times_times_int @ B @ (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ F @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_xzgcda__linear__aux1)). 39.32/11.37 thf(4369,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int,G:int]: ((plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ (times_times_int @ B @ C)) @ D) @ (times_times_int @ (minus_minus_int @ E @ (times_times_int @ B @ F)) @ G)) = (minus_minus_int @ (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ E @ G)) @ (times_times_int @ B @ (plus_plus_int @ (times_times_int @ C @ D) @ (times_times_int @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121])). 39.32/11.37 thf(352,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 39.32/11.37 thf(2151,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 39.32/11.37 thf(927,axiom,((! [A:int]: ((times_times_int @ (plus_plus_int @ one_one_int @ one_one_int) @ (number_number_of_int @ A)) = (number_number_of_int @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_double__number__of__Bit0)). 39.32/11.37 thf(3815,plain,((! [A:int]: ((times_times_int @ (plus_plus_int @ one_one_int @ one_one_int) @ (number_number_of_int @ A)) = (number_number_of_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[927])). 39.32/11.37 thf(436,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_power__less__imp__less__base)). 39.32/11.37 thf(2383,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 39.32/11.37 thf(521,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_add__eq__self__zero)). 39.32/11.37 thf(2624,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 39.32/11.37 thf(565,axiom,((! [A:int,B:int,C:int,D:int]: ((zcong @ A @ (times_times_int @ B @ (multInv @ C @ D)) @ C) => (zcong @ (times_times_int @ A @ D) @ (times_times_int @ (times_times_int @ B @ (multInv @ C @ D)) @ D) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_aux______1)). 39.32/11.37 thf(2774,plain,((! [A:int,B:int,C:int,D:int]: ((zcong @ A @ (times_times_int @ B @ (multInv @ C @ D)) @ C) => (zcong @ (times_times_int @ A @ D) @ (times_times_int @ (times_times_int @ B @ (multInv @ C @ D)) @ D) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])). 39.32/11.37 thf(819,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_dvd__mult__right)). 39.32/11.37 thf(3515,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[819])). 39.32/11.37 thf(913,axiom,(((power_power_int @ zero_zero_int @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_zero__power2)). 39.32/11.37 thf(3779,plain,(((power_power_int @ zero_zero_int @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])). 39.32/11.37 thf(610,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((((div_mod_int @ A @ B) = D) <= (B != zero_zero_int)) <= (((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ D) & (ord_less_int @ D @ B))) & (((ord_less_eq_int @ D @ zero_zero_int) & (ord_less_int @ B @ D)) <= (~ (ord_less_int @ zero_zero_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_divmod__int__rel__mod__eq)). 39.32/11.37 thf(2906,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => (((div_mod_int @ A @ B) = D) | (B = zero_zero_int) | ~ (((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ D) & (ord_less_int @ D @ B))) & (((ord_less_eq_int @ D @ zero_zero_int) & (ord_less_int @ B @ D)) | (ord_less_int @ zero_zero_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])). 39.32/11.37 thf(1196,axiom,((! [A:int,B:int,C:int,D:int]: (((zprime @ D) => ((~ (zcong @ C @ zero_zero_int @ D)) => ((zcong @ A @ (times_times_int @ B @ (multInv @ D @ C)) @ D) <= (zcong @ (times_times_int @ (times_times_int @ (multInv @ D @ C) @ C) @ A) @ (times_times_int @ (multInv @ D @ C) @ B) @ D)))) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_aux______4)). 39.32/11.37 thf(4586,plain,((! [A:int,B:int,C:int,D:int]: (((zprime @ D) => ((~ (zcong @ C @ zero_zero_int @ D)) => ((zcong @ A @ (times_times_int @ B @ (multInv @ D @ C)) @ D) | ~ (zcong @ (times_times_int @ (times_times_int @ (multInv @ D @ C) @ C) @ A) @ (times_times_int @ (multInv @ D @ C) @ B) @ D)))) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196])). 39.32/11.37 thf(586,axiom,((! [A:int]: ((div_mod_int @ A @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_zmod__self)). 39.32/11.37 thf(2839,plain,((! [A:int]: ((div_mod_int @ A @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])). 39.32/11.37 thf(1019,axiom,((! [A:int,B:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_zspecial__product)). 39.32/11.37 thf(4073,plain,((! [A:int,B:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019])). 39.32/11.37 thf(221,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((A = B) <= ((times_times_nat @ C @ A) = (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_mult__left__cancel)). 39.32/11.37 thf(1801,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((A = B) | ~ ((times_times_nat @ C @ A) = (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 39.32/11.37 thf(1054,axiom,((! [A:(int > $o),B:int,C:int]: ((((! [D:int]: ((ord_less_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) <= (A @ D)))) => (A @ C)) <= (A @ (plus_plus_int @ B @ one_one_int))) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_int__gr__induct)). 39.32/11.37 thf(4176,plain,((! [A:(int > $o),B:int,C:int]: (((! [D:int]: ((ord_less_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) | ~ (A @ D)))) => (A @ C)) | ~ (A @ (plus_plus_int @ B @ one_one_int)) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054])). 39.32/11.37 thf(690,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: ((((ord_less_int @ C @ A) => ((((ord_less_eq_int @ D @ A) => (ord_less_eq_int @ E @ B)) <= (ord_less_int @ zero_zero_int @ D)) <= (ord_less_eq_int @ zero_zero_int @ F))) <= (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F) @ zero_zero_int)) <= ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_zdiv__mono2__neg__lemma)). 39.32/11.37 thf(3138,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((ord_less_int @ C @ A) => (((ord_less_eq_int @ D @ A) => (ord_less_eq_int @ E @ B)) | ~ (ord_less_int @ zero_zero_int @ D) | ~ (ord_less_eq_int @ zero_zero_int @ F))) | ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F) @ zero_zero_int) | ~ ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])). 39.32/11.37 thf(179,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) => ((B = zero_zero_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_divisors__zero)). 39.32/11.37 thf(1690,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) => ((B = zero_zero_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 39.32/11.37 thf(846,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 39.32/11.37 thf(3586,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[846])). 39.32/11.37 thf(598,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ (plus_plus_int @ C @ B)) <= (ord_less_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_pos__add__strict)). 39.32/11.37 thf(2871,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (plus_plus_int @ C @ B)) | ~ (ord_less_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 39.32/11.37 thf(90,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((C = A) => (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_dvd_Oord__le__eq__trans)). 39.32/11.37 thf(1439,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((C = A) => (dvd_dvd_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 39.32/11.37 thf(1142,axiom,((! [A:int]: (min != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_rel__simps_I42_J)). 39.32/11.37 thf(4430,plain,((! [A:int]: ~ (min = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142])). 39.32/11.37 thf(251,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 39.32/11.37 thf(1877,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 39.32/11.37 thf(1180,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_zadd__zmult__distrib2)). 39.32/11.37 thf(4541,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180])). 39.32/11.37 thf(410,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ B @ A) => (~ (dvd_dvd_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_zdvd__not__zless)). 39.32/11.37 thf(2314,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ B @ A) => (~ (dvd_dvd_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 39.32/11.37 thf(391,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ A @ B) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_real__mult__less__mono2)). 39.32/11.37 thf(2267,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ A @ B) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 39.32/11.37 thf(842,axiom,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 39.32/11.37 thf(3572,plain,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])). 39.32/11.37 thf(460,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) = (A = (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_add__0__iff)). 39.32/11.37 thf(2446,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) = (A = (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 39.32/11.37 thf(698,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_zero__le__mult__iff)). 39.32/11.37 thf(3165,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])). 39.32/11.37 thf(704,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_dvd_Oless__imp__not__less)). 39.32/11.37 thf(3192,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 39.32/11.37 thf(1095,axiom,((dvd_dvd_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (minus_minus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096)). 39.32/11.37 thf(4296,plain,((dvd_dvd_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (minus_minus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095])). 39.32/11.37 thf(845,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 39.32/11.37 thf(3583,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])). 39.32/11.37 thf(498,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_diff__is__0__eq_H)). 39.32/11.37 thf(2553,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 39.32/11.37 thf(178,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zle__refl)). 39.32/11.37 thf(1688,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 39.32/11.37 thf(170,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_mult__strict__left__mono)). 39.32/11.37 thf(1667,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) => ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 39.32/11.37 thf(364,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_nat__add__commute)). 39.32/11.37 thf(2180,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 39.32/11.37 thf(1147,axiom,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (power_power_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_four__x__squared)). 39.32/11.37 thf(4445,plain,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (power_power_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147])). 39.32/11.37 thf(515,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_zero__less__mult__pos)). 39.32/11.37 thf(2610,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 39.32/11.37 thf(688,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_mult__pos__neg2)). 39.32/11.37 thf(3133,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])). 39.32/11.37 thf(997,axiom,(((? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))) <= (t = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06)). 39.32/11.37 thf(4009,plain,((? [A:int,B:int]: ((plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) = (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) | ~ (t = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])). 39.32/11.37 thf(1030,axiom,((! [A:int,B:int]: (((div_mod_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)) @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (plus_plus_int @ A @ one_one_int) @ B)) @ one_one_int)) <= (ord_less_eq_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_neg__zmod__mult__2)). 39.32/11.37 thf(4103,plain,((! [A:int,B:int]: (((div_mod_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)) @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)) = (minus_minus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ (div_mod_int @ (plus_plus_int @ A @ one_one_int) @ B)) @ one_one_int)) | ~ (ord_less_eq_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])). 39.32/11.37 thf(130,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) = ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_dvd_Ole__less)). 39.32/11.37 thf(1557,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) = ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 39.32/11.37 thf(339,axiom,((! [A:int,B:int,C:real]: ((plus_plus_real @ (number267125858f_real @ A) @ (minus_minus_real @ (number267125858f_real @ B) @ C)) = (minus_minus_real @ (number267125858f_real @ (plus_plus_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_add__number__of__diff1)). 39.32/11.37 thf(2111,plain,((! [A:int,B:int,C:real]: ((plus_plus_real @ (number267125858f_real @ A) @ (minus_minus_real @ (number267125858f_real @ B) @ C)) = (minus_minus_real @ (number267125858f_real @ (plus_plus_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 39.32/11.37 thf(666,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (plus_plus_nat @ C @ A)) <= (dvd_dvd_nat @ B @ A)) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_dvd__add)). 39.32/11.37 thf(3073,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (dvd_dvd_nat @ B @ A) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])). 39.32/11.37 thf(295,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_Nat_Odiff__le__self)). 39.32/11.37 thf(1993,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 39.32/11.37 thf(1017,axiom,((~ (! [A:int]: ~ ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_)). 39.32/11.37 thf(4064,plain,((~ (! [A:int]: ~ ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (zcong @ s1 @ A @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017])). 39.32/11.37 thf(158,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ B @ A) => ((minus_minus_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_Nat_Odiff__diff__eq)). 39.32/11.37 thf(1630,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ B @ A) => ((minus_minus_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ A @ B)) = (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 39.32/11.37 thf(389,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 39.32/11.37 thf(2261,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (times_times_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 39.32/11.37 thf(196,axiom,((! [A:real,B:real,C:real,D:real]: (((((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_mult__mono_H)). 39.32/11.37 thf(1731,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 39.32/11.37 thf(1082,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J)). 39.32/11.37 thf(4264,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082])). 39.32/11.37 thf(652,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 39.32/11.37 thf(3034,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])). 39.32/11.37 thf(48,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ A @ B)) <= (ord_less_eq_real @ A @ zero_zero_real)) <= (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_mult__left__mono__neg)). 39.32/11.37 thf(1325,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ A @ B)) | ~ (ord_less_eq_real @ A @ zero_zero_real) | ~ (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 39.32/11.37 thf(856,axiom,((! [A:int]: ((zero_zero_nat = (number_number_of_nat @ A)) = (ord_less_eq_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_eq__0__number__of)). 39.32/11.37 thf(3614,plain,((! [A:int]: ((zero_zero_nat = (number_number_of_nat @ A)) = (ord_less_eq_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[856])). 39.32/11.37 thf(493,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ B @ A) => (dvd_dvd_int @ B @ (minus_minus_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_dvd__diff)). 39.32/11.37 thf(2542,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ B @ A) => (dvd_dvd_int @ B @ (minus_minus_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 39.32/11.37 thf(97,axiom,((! [A:int]: (((div_mod_int @ (number_number_of_int @ min) @ A) = (minus_minus_int @ A @ one_one_int)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_zmod__minus1)). 39.32/11.37 thf(1460,plain,((! [A:int]: (((div_mod_int @ (number_number_of_int @ min) @ A) = (minus_minus_int @ A @ one_one_int)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 39.32/11.37 thf(400,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ B) = (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_nat__mult__commute)). 39.32/11.37 thf(2289,plain,((! [A:nat,B:nat]: ((times_times_nat @ A @ B) = (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 39.32/11.37 thf(386,axiom,((! [A:int,B:nat,C:int]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) => ((dvd_dvd_int @ A @ C) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_pow__divides__pow__int)). 39.32/11.37 thf(2252,plain,((! [A:int,B:nat,C:int]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) => ((dvd_dvd_int @ A @ C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 39.32/11.37 thf(940,axiom,(((bit1 @ min) = min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_Bit1__Min)). 39.32/11.37 thf(3861,plain,(((bit1 @ min) = min)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])). 39.32/11.37 thf(614,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) = (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_mult__le__0__iff)). 39.32/11.37 thf(2928,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) = (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 39.32/11.37 thf(67,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_le__neq__implies__less)). 39.32/11.37 thf(1381,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 39.32/11.37 thf(465,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_mult__pos__neg)). 39.32/11.37 thf(2461,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 39.32/11.37 thf(631,axiom,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least)). 39.32/11.37 thf(2974,plain,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 39.32/11.37 thf(415,axiom,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)) | ((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A))) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_split__mult__neg__le)). 39.32/11.37 thf(2329,plain,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)) | ((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A))) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 39.32/11.37 thf(587,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_Nat_Oadd__0__right)). 39.32/11.37 thf(2842,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 39.32/11.37 thf(281,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ B) <= (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) <= (ord_less_nat @ zero_zero_nat @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_nat__power__less__imp__less)). 39.32/11.37 thf(1952,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 39.32/11.37 thf(952,axiom,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)). 39.32/11.37 thf(3893,plain,((ord_less_eq_int @ zero_zero_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])). 39.32/11.37 thf(1184,axiom,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (minus_minus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_power2__diff)). 39.32/11.37 thf(4554,plain,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (minus_minus_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_real @ (times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184])). 39.32/11.37 thf(325,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_divides__mul__r)). 39.32/11.37 thf(2075,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 39.32/11.37 thf(554,axiom,((! [A:nat,B:(nat > $o)]: (((B @ A) => (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (plus_plus_nat @ C @ one_one_nat)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (B @ D)))))) <= (~ (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_ex__least__nat__less)). 39.32/11.37 thf(2725,plain,((! [A:nat,B:(nat > $o)]: (((B @ A) => (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (plus_plus_nat @ C @ one_one_nat)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (B @ D)))))) | (B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 39.32/11.37 thf(360,axiom,((ord_less_eq_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 39.32/11.37 thf(2171,plain,((ord_less_eq_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 39.32/11.37 thf(696,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((((C != zero_zero_nat) => (! [D:nat,E:nat]: (((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ E)) <= (ord_less_nat @ E @ C)))) & ((C = zero_zero_nat) => (A @ B))) = (A @ (div_mod_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_split__mod)). 39.32/11.37 thf(3159,plain,((! [A:(nat > $o),B:nat,C:nat]: ((((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: (((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ E)) | ~ (ord_less_nat @ E @ C)))) & ((C = zero_zero_nat) => (A @ B))) = (A @ (div_mod_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 39.32/11.37 thf(615,axiom,((! [A:int]: ((div_mod_int @ A @ (number_number_of_int @ min)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_zmod__minus1__right)). 39.32/11.37 thf(2931,plain,((! [A:int]: ((div_mod_int @ A @ (number_number_of_int @ min)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])). 39.32/11.37 thf(975,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_zmult__1)). 39.32/11.37 thf(3953,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[975])). 39.32/11.37 thf(524,axiom,((! [A:int,B:int,C:int]: ((zprime @ C) => (((~ (zcong @ A @ zero_zero_int @ C)) => (~ (zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C))) <= (~ (zcong @ B @ zero_zero_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_zcong__zmult__prop3)). 39.32/11.37 thf(2633,plain,((! [A:int,B:int,C:int]: ((zprime @ C) => (((~ (zcong @ A @ zero_zero_int @ C)) => (~ (zcong @ (times_times_int @ B @ A) @ zero_zero_int @ C))) | (zcong @ B @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 39.32/11.37 thf(751,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) <= (dvd_dvd_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_divides__exp)). 39.32/11.37 thf(3325,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) | ~ (dvd_dvd_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])). 39.32/11.37 thf(1098,axiom,((! [A:int,B:int]: ((((zcong @ (times_times_int @ (times_times_int @ A @ (multInv @ B @ A)) @ (multInv @ B @ (multInv @ B @ A))) @ A @ B) <= (~ (zcong @ A @ zero_zero_int @ B))) <= (zprime @ B)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_Int2_Oaux____2)). 39.32/11.37 thf(4304,plain,((! [A:int,B:int]: ((zcong @ (times_times_int @ (times_times_int @ A @ (multInv @ B @ A)) @ (multInv @ B @ (multInv @ B @ A))) @ A @ B) | (zcong @ A @ zero_zero_int @ B) | ~ (zprime @ B) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098])). 39.32/11.37 thf(354,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_diff__commute)). 39.32/11.37 thf(2156,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 39.32/11.37 thf(373,axiom,((! [A:real]: ((plus_plus_real @ (number267125858f_real @ pls) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__numeral__0)). 39.32/11.37 thf(2207,plain,((! [A:real]: ((plus_plus_real @ (number267125858f_real @ pls) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 39.32/11.37 thf(959,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((zcong @ (times_times_int @ C @ A) @ (times_times_int @ D @ B) @ E) <= (zcong @ A @ B @ E)) <= (zcong @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_zcong__zmult)). 39.32/11.37 thf(3908,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ (times_times_int @ C @ A) @ (times_times_int @ D @ B) @ E) | ~ (zcong @ A @ B @ E) | ~ (zcong @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[959])). 39.32/11.37 thf(1023,axiom,((! [A:int]: ((power_power_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__eq__square__number__of)). 39.32/11.37 thf(4084,plain,((! [A:int]: ((power_power_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023])). 39.32/11.37 thf(236,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_Nat_Odiff__cancel)). 39.32/11.37 thf(1841,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 39.32/11.37 thf(458,axiom,((! [A:int,B:int,C:real]: ((plus_plus_real @ (number267125858f_real @ A) @ (plus_plus_real @ (number267125858f_real @ B) @ C)) = (plus_plus_real @ (number267125858f_real @ (plus_plus_int @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__number__of__left)). 39.32/11.37 thf(2439,plain,((! [A:int,B:int,C:real]: ((plus_plus_real @ (number267125858f_real @ A) @ (plus_plus_real @ (number267125858f_real @ B) @ C)) = (plus_plus_real @ (number267125858f_real @ (plus_plus_int @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 39.32/11.37 thf(1070,axiom,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 39.32/11.37 thf(4232,plain,((! [A:int,B:int,C:int,D:int]: ((times_times_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (times_times_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070])). 39.32/11.37 thf(423,axiom,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_mult__zero__right)). 39.32/11.37 thf(2350,plain,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 39.32/11.37 thf(6,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_dvd__triv__right)). 39.32/11.37 thf(1213,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 39.32/11.37 thf(907,axiom,((! [A:int]: (((bit1 @ A) = min) = (A = min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_rel__simps_I47_J)). 39.32/11.37 thf(3759,plain,((! [A:int]: (((bit1 @ A) = min) = (A = min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])). 39.32/11.37 thf(316,axiom,((one_one_real != zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_one__neq__zero)). 39.32/11.37 thf(2051,plain,((~ (one_one_real = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 39.32/11.37 thf(785,axiom,((! [A:int,B:int]: ((ord_less_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_int @ A @ B) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_power2__less__imp__less)). 39.32/11.37 thf(3423,plain,((! [A:int,B:int]: ((ord_less_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_int @ A @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 39.32/11.37 thf(92,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_zero__neq__one)). 39.32/11.37 thf(1445,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 39.32/11.37 thf(120,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ B @ A) => (((minus_minus_nat @ C @ B) = (minus_minus_nat @ A @ B)) = (C = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_eq__diff__iff)). 39.32/11.37 thf(1528,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ B @ A) => (((minus_minus_nat @ C @ B) = (minus_minus_nat @ A @ B)) = (C = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 39.32/11.37 thf(347,axiom,((! [A:nat]: (dvd_dvd_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_dvd__refl)). 39.32/11.37 thf(2139,plain,((! [A:nat]: (dvd_dvd_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 39.32/11.37 thf(881,axiom,((! [A:int]: (((d22set @ (minus_minus_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))) = (wset @ (minus_minus_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) @ A)) <= (zprime @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_d22set__eq__wset)). 39.32/11.37 thf(3687,plain,((! [A:int]: (((d22set @ (minus_minus_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls))))) = (wset @ (minus_minus_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) @ A)) | ~ (zprime @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])). 39.32/11.37 thf(194,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_combine__common__factor)). 39.32/11.37 thf(1726,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 39.32/11.37 thf(21,axiom,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ B @ (minus_minus_real @ C @ A)) <= (dvd_dvd_real @ B @ A)) <= (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_dvd__diff)). 39.32/11.37 thf(1250,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ (minus_minus_real @ C @ A)) | ~ (dvd_dvd_real @ B @ A) | ~ (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 39.32/11.37 thf(1062,axiom,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_semiring__mult__2)). 39.32/11.37 thf(4209,plain,((! [A:int]: ((times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062])). 39.32/11.37 thf(289,axiom,((ord_less_int @ min @ pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_rel__simps_I6_J)). 39.32/11.37 thf(1973,plain,((ord_less_int @ min @ pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 39.32/11.37 thf(1047,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 39.32/11.37 thf(4158,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047])). 39.32/11.37 thf(947,axiom,((! [A:real,B:real]: (((B != zero_zero_real) | (A != zero_zero_real)) = (ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_sum__power2__gt__zero__iff)). 39.32/11.37 thf(3881,plain,((! [A:real,B:real]: ((~ (B = zero_zero_real) | ~ (A = zero_zero_real)) = (ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])). 39.32/11.37 thf(156,axiom,((~ (ord_less_eq_int @ pls @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_rel__simps_I20_J)). 39.32/11.37 thf(1626,plain,((~ (ord_less_eq_int @ pls @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 39.32/11.37 thf(517,axiom,((! [A:int,B:nat,C:nat]: ((times_times_nat @ (number_number_of_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (number_number_of_nat @ A) @ B) @ (times_times_nat @ (number_number_of_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_right__distrib__number__of)). 39.32/11.37 thf(2614,plain,((! [A:int,B:nat,C:nat]: ((times_times_nat @ (number_number_of_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (number_number_of_nat @ A) @ B) @ (times_times_nat @ (number_number_of_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 39.32/11.37 thf(249,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) <= (ord_less_eq_real @ A @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_mult__nonneg__nonpos2)). 39.32/11.37 thf(1873,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) | ~ (ord_less_eq_real @ A @ zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 39.32/11.37 thf(969,axiom,(((number_number_of_int @ pls) != (number_number_of_int @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_eq__number__of__Pls__Min)). 39.32/11.37 thf(3936,plain,((~ ((number_number_of_int @ pls) = (number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])). 39.32/11.37 thf(777,axiom,((! [A:int,B:int]: (((power_power_int @ A @ (number_number_of_nat @ B)) = zero_zero_int) = ((A = zero_zero_int) & ((number_number_of_nat @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_power__eq__0__iff__number__of)). 39.32/11.37 thf(3395,plain,((! [A:int,B:int]: (((power_power_int @ A @ (number_number_of_nat @ B)) = zero_zero_int) = ((A = zero_zero_int) & ~ ((number_number_of_nat @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 39.32/11.37 thf(469,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_dvd__mult__right)). 39.32/11.37 thf(2471,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 39.32/11.37 thf(311,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_nat__add__assoc)). 39.32/11.37 thf(2037,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 39.32/11.37 thf(693,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((power_power_nat @ zero_zero_nat @ A) = one_one_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_power__0__left)). 39.32/11.37 thf(3146,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((power_power_nat @ zero_zero_nat @ A) = one_one_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 39.32/11.37 thf(461,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_nat__less__add__iff1)). 39.32/11.37 thf(2449,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ E @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 39.32/11.37 thf(984,axiom,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_not__sum__power2__lt__zero)). 39.32/11.37 thf(3975,plain,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[984])). 39.32/11.37 thf(1116,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat__1__add__1)). 39.32/11.37 thf(4355,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (number_number_of_nat @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116])). 39.32/11.37 thf(509,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (plus_plus_int @ B @ A) @ zero_zero_int) => ((div_mod_int @ B @ A) = (plus_plus_int @ B @ A))) <= (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_mod__pos__neg__trivial)). 39.32/11.37 thf(2582,plain,((! [A:int,B:int]: (((ord_less_eq_int @ (plus_plus_int @ B @ A) @ zero_zero_int) => ((div_mod_int @ B @ A) = (plus_plus_int @ B @ A))) | ~ (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 39.32/11.37 thf(935,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_zero__le__even__power_H)). 39.32/11.37 thf(3849,plain,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[935])). 39.32/11.37 thf(317,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C)) = (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_mult__le__cancel2)). 39.32/11.37 thf(2054,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C)) = (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 39.32/11.37 thf(1061,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zprime @ B) => ((zcong @ (times_times_int @ A @ (multInv @ B @ A)) @ one_one_int @ B) <= (~ (zcong @ A @ zero_zero_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_MultInv__prop2)). 39.32/11.37 thf(4207,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zprime @ B) => ((zcong @ (times_times_int @ A @ (multInv @ B @ A)) @ one_one_int @ B) | (zcong @ A @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061])). 39.32/11.37 thf(279,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ zero_zero_int) => ((ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int) <= (ord_less_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_mult__neg__pos)). 39.32/11.37 thf(1948,plain,((! [A:int,B:int]: ((ord_less_int @ B @ zero_zero_int) => ((ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int) | ~ (ord_less_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 39.32/11.37 thf(793,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__int__code_I14_J)). 39.32/11.37 thf(3444,plain,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])). 39.32/11.37 thf(381,axiom,((! [A:nat,B:nat]: (((A = one_one_nat) & (B = one_one_nat)) = ((times_times_nat @ A @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_nat__mult__eq__one)). 39.32/11.37 thf(2239,plain,((! [A:nat,B:nat]: (((A = one_one_nat) & (B = one_one_nat)) = ((times_times_nat @ A @ B) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 39.32/11.37 thf(651,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 39.32/11.37 thf(3031,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])). 39.32/11.37 thf(139,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ B @ zero_zero_int) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_mult__nonpos__nonneg)). 39.32/11.37 thf(1583,plain,((! [A:int,B:int]: ((ord_less_eq_int @ B @ zero_zero_int) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 39.32/11.37 thf(1150,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))) = ((B != zero_zero_int) | (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_sum__squares__gt__zero__iff)). 39.32/11.37 thf(4458,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))) = (~ (B = zero_zero_int) | ~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150])). 39.32/11.37 thf(536,axiom,((! [A:int,B:int]: ((((B = zero_zero_int) <= (zcong @ B @ zero_zero_int @ A)) <= (ord_less_int @ B @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_zcong__zless__0)). 39.32/11.37 thf(2665,plain,((! [A:int,B:int]: ((B = zero_zero_int) | ~ (zcong @ B @ zero_zero_int @ A) | ~ (ord_less_int @ B @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])). 39.32/11.37 thf(875,axiom,((! [A:int,B:int]: ((times_times_int @ A @ B) = (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zmult__commute)). 39.32/11.37 thf(3672,plain,((! [A:int,B:int]: ((times_times_int @ A @ B) = (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[875])). 39.32/11.37 thf(262,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((dvd_dvd_nat @ B @ C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj)). 39.32/11.37 thf(1905,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((dvd_dvd_nat @ B @ C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 39.32/11.37 thf(82,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ A @ B)) <= (ord_less_eq_int @ A @ zero_zero_int)) <= (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_mult__left__mono__neg)). 39.32/11.37 thf(1420,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ A @ B)) | ~ (ord_less_eq_int @ A @ zero_zero_int) | ~ (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 39.32/11.37 thf(986,axiom,((! [A:int,B:int]: ((plus_plus_int @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__Bit0__Bit0)). 39.32/11.37 thf(3981,plain,((! [A:int,B:int]: ((plus_plus_int @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[986])). 39.32/11.37 thf(480,axiom,((! [A:nat,B:int,C:int]: (((ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_power__mono)). 39.32/11.37 thf(2503,plain,((! [A:nat,B:int,C:int]: ((ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 39.32/11.37 thf(31,axiom,((! [A:nat,B:real,C:real]: ((dvd_dvd_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) <= (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_dvd__power__same)). 39.32/11.37 thf(1277,plain,((! [A:nat,B:real,C:real]: ((dvd_dvd_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) | ~ (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 39.32/11.37 thf(344,axiom,((! [A:int,B:(int > $o),C:int]: ((((! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ (times_times_int @ A @ C))))) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ C))))) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_decr__mult__lemma)). 39.32/11.37 thf(2124,plain,((! [A:int,B:(int > $o),C:int]: (! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ (times_times_int @ A @ C)))) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ C)))) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 39.32/11.37 thf(379,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_zle__diff1__eq)). 39.32/11.37 thf(2234,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 39.32/11.37 thf(964,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((plus_plus_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = (number_number_of_int @ (plus_plus_int @ B @ A))) <= (ord_less_eq_int @ pls @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_semiring__add__number__of)). 39.32/11.37 thf(3921,plain,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((plus_plus_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = (number_number_of_int @ (plus_plus_int @ B @ A))) | ~ (ord_less_eq_int @ pls @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])). 39.32/11.37 thf(54,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) = ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_nat__add__left__cancel)). 39.32/11.37 thf(1340,plain,((! [A:nat,B:nat,C:nat]: ((B = C) = ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 39.32/11.37 thf(797,axiom,((! [A:int]: (((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ A) @ one_one_int)) = one_one_int) <= (zprime @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_Legendre__1mod4)). 39.32/11.37 thf(3455,plain,((! [A:int]: (((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ A) @ one_one_int)) = one_one_int) | ~ (zprime @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 39.32/11.37 thf(101,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) <= ((minus_minus_nat @ B @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_diffs0__imp__equal)). 39.32/11.37 thf(1472,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) | ~ ((minus_minus_nat @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 39.32/11.37 thf(733,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_nat__le__add__iff2)). 39.32/11.37 thf(3278,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])). 39.32/11.37 thf(1194,axiom,((! [A:nat,B:int]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_int @ one_one_int @ (power_power_int @ B @ A))) <= (ord_less_int @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_one__less__power)). 39.32/11.37 thf(4581,plain,((! [A:nat,B:int]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_int @ one_one_int @ (power_power_int @ B @ A))) | ~ (ord_less_int @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194])). 39.32/11.37 thf(503,axiom,((! [A:int,B:int]: ((A = B) | (ord_less_int @ B @ A) | (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zless__linear)). 39.32/11.37 thf(2567,plain,((! [A:int,B:int]: ((A = B) | (ord_less_int @ B @ A) | (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 39.32/11.37 thf(550,axiom,((! [A:real,B:nat,C:nat]: ((((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_power__strict__decreasing)). 39.32/11.37 thf(2715,plain,((! [A:real,B:nat,C:nat]: (((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 39.32/11.37 thf(285,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_diff__self__eq__0)). 39.32/11.37 thf(1961,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 39.32/11.37 thf(1118,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) = (dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_zdvd__reduce)). 39.32/11.37 thf(4360,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) = (dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118])). 39.32/11.37 thf(681,axiom,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 39.32/11.37 thf(3112,plain,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 39.32/11.37 thf(433,axiom,((! [A:int,B:int]: (zcong @ A @ (standardRes @ B @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_StandardRes__prop1)). 39.32/11.37 thf(2375,plain,((! [A:int,B:int]: (zcong @ A @ (standardRes @ B @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 39.32/11.37 thf(670,axiom,((! [A:real]: ((~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ A))) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_not__real__square__gt__zero)). 39.32/11.37 thf(3082,plain,((! [A:real]: ((~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ A))) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])). 39.32/11.37 thf(22,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((div_mod_nat @ A @ B) = (div_mod_nat @ (minus_minus_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_mod__geq)). 39.32/11.37 thf(1252,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((div_mod_nat @ A @ B) = (div_mod_nat @ (minus_minus_nat @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 39.32/11.37 thf(204,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_trans__less__add2)). 39.32/11.37 thf(1753,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 39.32/11.37 thf(944,axiom,((! [A:nat]: (((power_power_int @ (number_number_of_int @ min) @ A) = (number_number_of_int @ min)) | ((power_power_int @ (number_number_of_int @ min) @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_neg__one__power)). 39.32/11.37 thf(3872,plain,((! [A:nat]: (((power_power_int @ (number_number_of_int @ min) @ A) = (number_number_of_int @ min)) | ((power_power_int @ (number_number_of_int @ min) @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[944])). 39.32/11.37 thf(544,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of)). 39.32/11.37 thf(2689,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])). 39.32/11.37 thf(1010,axiom,(((power_power_nat @ one_one_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__power2)). 39.32/11.37 thf(4045,plain,(((power_power_nat @ one_one_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])). 39.32/11.37 thf(619,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_mult__nonpos__nonpos)). 39.32/11.37 thf(2942,plain,((! [A:int,B:int]: (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])). 39.32/11.37 thf(404,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 39.32/11.37 thf(2298,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 39.32/11.37 thf(776,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) @ zero_zero_real) => (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_even__power__le__0__imp__0)). 39.32/11.37 thf(3391,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) @ zero_zero_real) => (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])). 39.32/11.37 thf(899,axiom,((! [A:int,B:int]: ((times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_times__numeral__code_I5_J)). 39.32/11.37 thf(3737,plain,((! [A:int,B:int]: ((times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[899])). 39.32/11.37 thf(771,axiom,((! [A:nat]: ((power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_power2__eq__square)). 39.32/11.37 thf(3376,plain,((! [A:nat]: ((power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 39.32/11.37 thf(865,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ (power_power_int @ A @ B) @ C) = (power_power_int @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zpower__zpower)). 39.32/11.37 thf(3640,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ (power_power_int @ A @ B) @ C) = (power_power_int @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[865])). 39.32/11.37 thf(115,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_mult__pos__neg2)). 39.32/11.37 thf(1516,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 39.32/11.37 thf(595,axiom,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_mult__zero__left)). 39.32/11.37 thf(2863,plain,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])). 39.32/11.37 thf(11,axiom,((! [A:real]: ((A = zero_zero_real) <= (dvd_dvd_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_dvd__0__left)). 39.32/11.37 thf(1225,plain,((! [A:real]: ((A = zero_zero_real) | ~ (dvd_dvd_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 39.32/11.37 thf(1120,axiom,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B)) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zadd__power2)). 39.32/11.37 thf(4366,plain,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B)) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120])). 39.32/11.37 thf(319,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) = ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_real__less__def)). 39.32/11.37 thf(2060,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) = ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 39.32/11.37 thf(1085,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_rel__simps_I32_J)). 39.32/11.37 thf(4272,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085])). 39.32/11.37 thf(133,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_power__increasing__iff)). 39.32/11.37 thf(1566,plain,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 39.32/11.37 thf(349,axiom,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) | (B = C)) = ((times_times_nat @ A @ B) = (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_nat__mult__eq__cancel__disj)). 39.32/11.37 thf(2143,plain,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) | (B = C)) = ((times_times_nat @ A @ B) = (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 39.32/11.37 thf(303,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A)) <= (((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ B @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_split__mult__pos__le)). 39.32/11.37 thf(2012,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A)) | ~ (((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ B @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 39.32/11.37 thf(957,axiom,(((plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int) = (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_t)). 39.32/11.37 thf(3904,plain,(((plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int) = (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[957])). 39.32/11.37 thf(727,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ B) = (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_mult__less__cancel__left__pos)). 39.32/11.37 thf(3260,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ B) = (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])). 39.32/11.37 thf(905,axiom,(((number_number_of_nat @ (bit1 @ pls)) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1)). 39.32/11.37 thf(3754,plain,(((number_number_of_nat @ (bit1 @ pls)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])). 39.32/11.37 thf(62,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_mult__left__mono)). 39.32/11.37 thf(1368,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 39.32/11.37 thf(715,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) & (A = zero_zero_nat)) = ((power_power_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_power__eq__0__iff)). 39.32/11.37 thf(3228,plain,((! [A:nat,B:nat]: ((~ (B = zero_zero_nat) & (A = zero_zero_nat)) = ((power_power_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])). 39.32/11.37 thf(1154,axiom,((! [A:int]: ((A = zero_zero_int) = ((plus_plus_int @ A @ A) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_double__eq__0__iff)). 39.32/11.37 thf(4469,plain,((! [A:int]: ((A = zero_zero_int) = ((plus_plus_int @ A @ A) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154])). 39.32/11.37 thf(213,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_le__add__diff__inverse2)). 39.32/11.37 thf(1780,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 39.32/11.37 thf(121,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => (((power_power_real @ C @ A) = (power_power_real @ C @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_power__inject__exp)). 39.32/11.37 thf(1531,plain,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => (((power_power_real @ C @ A) = (power_power_real @ C @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 39.32/11.37 thf(1105,axiom,((! [A:int]: ((ord_less_eq_int @ pls @ A) = (ord_less_int @ pls @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rel__simps_I5_J)). 39.32/11.37 thf(4324,plain,((! [A:int]: ((ord_less_eq_int @ pls @ A) = (ord_less_int @ pls @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105])). 39.32/11.37 thf(854,axiom,((! [A:int]: ((bit1 @ A) = (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Bit1__def)). 39.32/11.37 thf(3608,plain,((! [A:int]: ((bit1 @ A) = (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])). 39.32/11.37 thf(13,axiom,((! [A:real,B:real,C:real]: ((A = (times_times_real @ B @ C)) => (dvd_dvd_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_dvdI)). 39.32/11.37 thf(1230,plain,((! [A:real,B:real,C:real]: ((A = (times_times_real @ B @ C)) => (dvd_dvd_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 39.32/11.37 thf(1199,axiom,((! [A:int,B:int]: ((((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (times_times_int @ B @ A))) <= (~ (ord_less_int @ B @ pls))) & ((ord_less_int @ B @ pls) => ((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_mult__nat__number__of)). 39.32/11.37 thf(4593,plain,((! [A:int,B:int]: ((((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (times_times_int @ B @ A))) | (ord_less_int @ B @ pls)) & ((ord_less_int @ B @ pls) => ((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199])). 39.32/11.37 thf(604,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) <= (ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_norR__mem__unique__aux)). 39.32/11.37 thf(2888,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) | ~ (ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])). 39.32/11.37 thf(647,axiom,((! [A:int,B:int,C:int]: ((zcong @ B @ A @ C) = (zcong @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_zcong__sym)). 39.32/11.37 thf(3019,plain,((! [A:int,B:int,C:int]: ((zcong @ B @ A @ C) = (zcong @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])). 39.32/11.37 thf(1133,axiom,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_one__dvd)). 39.32/11.37 thf(4409,plain,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133])). 39.32/11.37 thf(332,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_less__nat__zero__code)). 39.32/11.37 thf(2092,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 39.32/11.37 thf(731,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 39.32/11.37 thf(3273,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 39.32/11.37 thf(1001,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I33_J)). 39.32/11.37 thf(4020,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_eq_int @ (bit1 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001])). 39.32/11.37 thf(835,axiom,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit1 @ pls))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_mult__numeral__1__right)). 39.32/11.37 thf(3554,plain,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit1 @ pls))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[835])). 39.32/11.37 thf(706,axiom,((! [A:nat,B:nat,C:nat]: (((A = C) | (B = zero_zero_nat)) = ((times_times_nat @ A @ B) = (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_mult__cancel2)). 39.32/11.37 thf(3202,plain,((! [A:nat,B:nat,C:nat]: (((A = C) | (B = zero_zero_nat)) = ((times_times_nat @ A @ B) = (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])). 39.32/11.37 thf(14,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (div_mod_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_mod__less__eq__dividend)). 39.32/11.37 thf(1235,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (div_mod_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 39.32/11.37 thf(1042,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => (A = B))) <= ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_power2__eq__imp__eq)). 39.32/11.37 thf(4145,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => (A = B))) | ~ ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042])). 39.32/11.37 thf(859,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => ((C = (plus_plus_int @ A @ (times_times_int @ C @ B))) => ((ord_less_eq_int @ B @ one_one_int) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_self__quotient__aux2)). 39.32/11.37 thf(3623,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => ((C = (plus_plus_int @ A @ (times_times_int @ C @ B))) => ((ord_less_eq_int @ B @ one_one_int) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])). 39.32/11.37 thf(765,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_nat__add__right__cancel)). 39.32/11.37 thf(3359,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])). 39.32/11.37 thf(1034,axiom,(((ord_less_eq_int @ zero_zero_int @ s) & (zcong @ s1 @ s @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (ord_less_int @ s @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_s0p)). 39.32/11.37 thf(4117,plain,(((ord_less_eq_int @ zero_zero_int @ s) & (zcong @ s1 @ s @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) & (ord_less_int @ s @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034])). 39.32/11.37 thf(190,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ C @ D) => ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_mult__dvd__mono)). 39.32/11.37 thf(1716,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ C @ D) => ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 39.32/11.37 thf(463,axiom,((! [A:nat,B:nat]: ((A = B) = ((dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_divides__antisym)). 39.32/11.37 thf(2454,plain,((! [A:nat,B:nat]: ((A = B) = ((dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 39.32/11.37 thf(743,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_power__mult__distrib)). 39.32/11.37 thf(3305,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])). 39.32/11.37 thf(87,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_dvd__pos__nat)). 39.32/11.37 thf(1432,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ A)) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 39.32/11.37 thf(928,axiom,((! [A:(int > $o),B:int,C:int]: ((((A @ C) <= (! [D:int]: ((ord_less_eq_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) <= (A @ D))))) <= (A @ B)) <= (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_int__ge__induct)). 39.32/11.37 thf(3818,plain,((! [A:(int > $o),B:int,C:int]: ((A @ C) | ~ (! [D:int]: ((ord_less_eq_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) | ~ (A @ D)))) | ~ (A @ B) | ~ (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])). 39.32/11.37 thf(911,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_nat @ (power_power_nat @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__even__eq)). 39.32/11.37 thf(3774,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ B)) = (power_power_nat @ (power_power_nat @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[911])). 39.32/11.37 thf(232,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_le__imp__power__dvd)). 39.32/11.37 thf(1830,plain,((! [A:int,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 39.32/11.37 thf(686,axiom,((! [A:nat,B:int]: (((A = zero_zero_nat) & ((number_number_of_nat @ B) != zero_zero_nat)) = ((power_power_nat @ A @ (number_number_of_nat @ B)) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_power__eq__0__iff__number__of)). 39.32/11.37 thf(3127,plain,((! [A:nat,B:int]: (((A = zero_zero_nat) & ~ ((number_number_of_nat @ B) = zero_zero_nat)) = ((power_power_nat @ A @ (number_number_of_nat @ B)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])). 39.32/11.37 thf(167,axiom,((! [A:int,B:int,C:int]: (((div_mod_int @ A @ B) = (div_mod_int @ C @ B)) = (dvd_dvd_int @ B @ (minus_minus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zmod__eq__dvd__iff)). 39.32/11.37 thf(1658,plain,((! [A:int,B:int,C:int]: (((div_mod_int @ A @ B) = (div_mod_int @ C @ B)) = (dvd_dvd_int @ B @ (minus_minus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 39.32/11.37 thf(413,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ A)) <= (ord_less_real @ A @ zero_zero_real)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_mult__strict__right__mono__neg)). 39.32/11.37 thf(2322,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ A)) | ~ (ord_less_real @ A @ zero_zero_real) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 39.32/11.37 thf(474,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_dvd_Oless__not__sym)). 39.32/11.37 thf(2486,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (~ ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 39.32/11.37 thf(1073,axiom,((! [A:int,B:nat,C:nat]: ((times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (power_power_int @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 39.32/11.37 thf(4241,plain,((! [A:int,B:nat,C:nat]: ((times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (power_power_int @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073])). 39.32/11.37 thf(609,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_mult__less__cancel__left__pos)). 39.32/11.37 thf(2903,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[609])). 39.32/11.37 thf(8,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((div_mod_nat @ B @ A) = (div_mod_nat @ (minus_minus_nat @ B @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_le__mod__geq)). 39.32/11.37 thf(1218,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((div_mod_nat @ B @ A) = (div_mod_nat @ (minus_minus_nat @ B @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 39.32/11.37 thf(655,axiom,((! [A:int]: ((zprime @ A) = ((ord_less_int @ one_one_int @ A) & ! [B:int]: (((dvd_dvd_int @ B @ A) & (ord_less_eq_int @ zero_zero_int @ B)) => ((B = A) | (B = one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_zprime__def)). 39.32/11.37 thf(3041,plain,((! [A:int]: ((zprime @ A) = ((ord_less_int @ one_one_int @ A) & ! [B:int]: (((dvd_dvd_int @ B @ A) & (ord_less_eq_int @ zero_zero_int @ B)) => ((B = A) | (B = one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])). 39.32/11.37 thf(937,axiom,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_sum__power2__ge__zero)). 39.32/11.37 thf(3853,plain,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])). 39.32/11.37 thf(1049,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ (number_number_of_int @ C)) = (minus_minus_int @ (times_times_int @ A @ (number_number_of_int @ C)) @ (times_times_int @ B @ (number_number_of_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_left__diff__distrib__number__of)). 39.32/11.37 thf(4164,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ (number_number_of_int @ C)) = (minus_minus_int @ (times_times_int @ A @ (number_number_of_int @ C)) @ (times_times_int @ B @ (number_number_of_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049])). 39.32/11.37 thf(891,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_zadd__zmult__distrib)). 39.32/11.37 thf(3715,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[891])). 39.32/11.37 thf(679,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)) <= (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_mult__pos__neg)). 39.32/11.37 thf(3107,plain,((! [A:real,B:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)) | ~ (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])). 39.32/11.37 thf(981,axiom,((! [A:int]: ((pls = A) = (pls = (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_rel__simps_I38_J)). 39.32/11.37 thf(3970,plain,((! [A:int]: ((pls = A) = (pls = (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])). 39.32/11.37 thf(1144,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 39.32/11.37 thf(4436,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144])). 39.32/11.37 thf(1031,axiom,((! [A:nat,B:nat,C:int]: ((((power_power_int @ C @ A) = (power_power_int @ C @ B)) = (A = B)) <= (ord_less_int @ one_one_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_power__inject__exp)). 39.32/11.37 thf(4106,plain,((! [A:nat,B:nat,C:int]: ((((power_power_int @ C @ A) = (power_power_int @ C @ B)) = (A = B)) | ~ (ord_less_int @ one_one_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])). 39.32/11.37 thf(508,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_nat__mult__1)). 39.32/11.37 thf(2579,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 39.32/11.37 thf(1179,axiom,((! [A:int]: ((power_power_int @ (number_number_of_int @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of)). 39.32/11.37 thf(4538,plain,((! [A:int]: ((power_power_int @ (number_number_of_int @ A) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_int @ (number_number_of_int @ A) @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179])). 39.32/11.37 thf(219,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_trans__less__add1)). 39.32/11.37 thf(1797,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 39.32/11.37 thf(1083,axiom,((! [A:int]: ((ord_less_int @ A @ pls) = (ord_less_int @ (bit0 @ A) @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rel__simps_I10_J)). 39.32/11.37 thf(4267,plain,((! [A:int]: ((ord_less_int @ A @ pls) = (ord_less_int @ (bit0 @ A) @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083])). 39.32/11.37 thf(618,axiom,((! [A:int]: ((ord_less_eq_int @ A @ pls) = (ord_less_eq_real @ (number267125858f_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_le__special_I3_J)). 39.32/11.37 thf(2939,plain,((! [A:int]: ((ord_less_eq_int @ A @ pls) = (ord_less_eq_real @ (number267125858f_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 39.32/11.37 thf(64,axiom,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 39.32/11.37 thf(1372,plain,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 39.32/11.37 thf(1174,axiom,((! [A:int,B:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_add__number__of__eq)). 39.32/11.37 thf(4516,plain,((! [A:int,B:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174])). 39.32/11.37 thf(1065,axiom,((! [A:int,B:int]: ((zcong @ A @ (minus_minus_int @ B @ one_one_int) @ B) = (zcong @ (times_times_int @ A @ (minus_minus_int @ B @ one_one_int)) @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_inv__not__p__minus__1__aux)). 39.32/11.37 thf(4217,plain,((! [A:int,B:int]: ((zcong @ A @ (minus_minus_int @ B @ one_one_int) @ B) = (zcong @ (times_times_int @ A @ (minus_minus_int @ B @ one_one_int)) @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065])). 39.32/11.37 thf(76,axiom,((! [A:int]: ((zprime @ A) => (zcong @ (zfact @ (minus_minus_int @ A @ one_one_int)) @ (number_number_of_int @ min) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_Wilson__Russ)). 39.32/11.37 thf(1404,plain,((! [A:int]: ((zprime @ A) => (zcong @ (zfact @ (minus_minus_int @ A @ one_one_int)) @ (number_number_of_int @ min) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 39.32/11.37 thf(60,axiom,((! [A:int]: ((((number_number_of_nat @ A) = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ A)) = one_one_nat)) & (((number_number_of_nat @ A) != zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ A)) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_power__0__left__number__of)). 39.32/11.37 thf(1358,plain,((! [A:int]: ((((number_number_of_nat @ A) = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ A)) = one_one_nat)) & ((~ ((number_number_of_nat @ A) = zero_zero_nat)) => ((power_power_nat @ zero_zero_nat @ (number_number_of_nat @ A)) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 39.32/11.37 thf(259,axiom,((! [A:nat,B:real]: ((ord_less_real @ zero_zero_real @ (power_power_real @ B @ A)) <= (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_zero__less__power)). 39.32/11.37 thf(1898,plain,((! [A:nat,B:real]: ((ord_less_real @ zero_zero_real @ (power_power_real @ B @ A)) | ~ (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 39.32/11.37 thf(24,axiom,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ B @ A) <= (dvd_dvd_real @ C @ A)) <= (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_dvd__trans)). 39.32/11.37 thf(1257,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ A) | ~ (dvd_dvd_real @ C @ A) | ~ (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 39.32/11.37 thf(685,axiom,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ C @ (times_times_real @ (times_times_real @ A @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 39.32/11.37 thf(3124,plain,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ C @ (times_times_real @ (times_times_real @ A @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 39.32/11.37 thf(452,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => ((ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_power__le__imp__le__exp)). 39.32/11.37 thf(2426,plain,((! [A:nat,B:nat,C:real]: ((ord_less_real @ one_one_real @ C) => ((ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 39.32/11.37 thf(638,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ C @ B) @ A) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_add__diff__assoc2)). 39.32/11.37 thf(2992,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ C @ B) @ A) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 39.32/11.37 thf(292,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_le__imp__0__less)). 39.32/11.37 thf(1981,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 39.32/11.37 thf(9,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) => ((dvd_dvd_real @ B @ (plus_plus_real @ C @ A)) <= (dvd_dvd_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_dvd__add)). 39.32/11.37 thf(1221,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) => ((dvd_dvd_real @ B @ (plus_plus_real @ C @ A)) | ~ (dvd_dvd_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 39.32/11.37 thf(1162,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_zpower__zadd__distrib)). 39.32/11.37 thf(4488,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162])). 39.32/11.37 thf(396,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_zero__less__power__nat__eq)). 39.32/11.37 thf(2279,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 39.32/11.37 thf(1171,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => (((~ (zcong @ (multInv @ B @ A) @ zero_zero_int @ B)) <= (~ (zcong @ A @ zero_zero_int @ B))) <= (zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_MultInv__prop3)). 39.32/11.37 thf(4510,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => (~ (zcong @ (multInv @ B @ A) @ zero_zero_int @ B) | (zcong @ A @ zero_zero_int @ B) | ~ (zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171])). 39.32/11.37 thf(426,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_real__mult__1)). 39.32/11.37 thf(2357,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 39.32/11.37 thf(775,axiom,((! [A:int,B:int,C:nat]: ((div_mod_int @ (power_power_int @ (div_mod_int @ A @ B) @ C) @ B) = (div_mod_int @ (power_power_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_zpower__zmod)). 39.32/11.37 thf(3388,plain,((! [A:int,B:int,C:nat]: ((div_mod_int @ (power_power_int @ (div_mod_int @ A @ B) @ C) @ B) = (div_mod_int @ (power_power_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])). 39.32/11.37 thf(111,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_real__zero__not__eq__one)). 39.32/11.37 thf(1504,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 39.32/11.37 thf(1071,axiom,((! [A:int,B:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_plus__numeral__code_I9_J)). 39.32/11.37 thf(4235,plain,((! [A:int,B:int]: ((plus_plus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (number_number_of_int @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071])). 39.32/11.37 thf(140,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_mult__0__right)). 39.32/11.37 thf(1585,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 39.32/11.37 thf(1026,axiom,((! [A:int,B:int,C:int]: ((? [D:int]: (B = (plus_plus_int @ A @ (times_times_int @ C @ D)))) = (zcong @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_zcong__iff__lin)). 39.32/11.37 thf(4093,plain,((! [A:int,B:int,C:int]: ((? [D:int]: (B = (plus_plus_int @ A @ (times_times_int @ C @ D)))) = (zcong @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])). 39.32/11.37 thf(622,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_mult__left__mono)). 39.32/11.37 thf(2949,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])). 39.32/11.37 thf(553,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 39.32/11.37 thf(2722,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])). 39.32/11.37 thf(574,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_less__not__refl2)). 39.32/11.37 thf(2807,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])). 39.32/11.37 thf(695,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((minus_minus_nat @ (plus_plus_nat @ C @ A) @ B) = (plus_plus_nat @ (minus_minus_nat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_diff__add__assoc2)). 39.32/11.37 thf(3156,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((minus_minus_nat @ (plus_plus_nat @ C @ A) @ B) = (plus_plus_nat @ (minus_minus_nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 39.32/11.37 thf(1079,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ (times_times_int @ C @ A)) <= (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_dvd__mult2)). 39.32/11.37 thf(4257,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ (times_times_int @ C @ A)) | ~ (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079])). 39.32/11.37 thf(778,axiom,((! [A:real]: ((A = zero_zero_real) = ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_zero__eq__power2)). 39.32/11.37 thf(3398,plain,((! [A:real]: ((A = zero_zero_real) = ((power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])). 39.32/11.37 thf(456,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_mult__nonneg__nonpos2)). 39.32/11.37 thf(2435,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 39.32/11.37 thf(847,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ pls @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_semiring__mult__number__of)). 39.32/11.37 thf(3589,plain,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((times_times_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ pls @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])). 39.32/11.37 thf(664,axiom,((! [A:nat,B:nat,C:nat]: (((C = (plus_plus_nat @ A @ B)) = ((minus_minus_nat @ C @ B) = A)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_le__imp__diff__is__add)). 39.32/11.37 thf(3067,plain,((! [A:nat,B:nat,C:nat]: (((C = (plus_plus_nat @ A @ B)) = ((minus_minus_nat @ C @ B) = A)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])). 39.32/11.37 thf(1137,axiom,(((bit0 @ pls) = pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Bit0__Pls)). 39.32/11.37 thf(4419,plain,(((bit0 @ pls) = pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137])). 39.32/11.37 thf(237,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ C @ A) => (dvd_dvd_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_dvd__trans)). 39.32/11.37 thf(1844,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ C @ A) => (dvd_dvd_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 39.32/11.37 thf(370,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ D @ B))) <= (dvd_dvd_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_dvd__power__le)). 39.32/11.37 thf(2194,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ D @ B))) | ~ (dvd_dvd_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 39.32/11.37 thf(79,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_comm__semiring__class_Odistrib)). 39.32/11.37 thf(1412,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 39.32/11.37 thf(376,axiom,((! [A:(int > $o),B:int,C:int]: ((ord_less_int @ B @ C) => ((A @ (minus_minus_int @ C @ one_one_int)) => ((A @ B) <= (! [D:int]: (((A @ (minus_minus_int @ D @ one_one_int)) <= (A @ D)) <= (ord_less_int @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_int__less__induct)). 39.32/11.37 thf(2215,plain,((! [A:(int > $o),B:int,C:int]: ((ord_less_int @ B @ C) => ((A @ (minus_minus_int @ C @ one_one_int)) => ((A @ B) | ~ (! [D:int]: ((A @ (minus_minus_int @ D @ one_one_int)) | ~ (A @ D) | ~ (ord_less_int @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 39.32/11.37 thf(246,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_add__leD1)). 39.32/11.37 thf(1866,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 39.32/11.37 thf(1016,axiom,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_mult__2__right)). 39.32/11.37 thf(4061,plain,((! [A:int]: ((times_times_int @ A @ (number_number_of_int @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])). 39.32/11.37 thf(654,axiom,((! [A:nat,B:real]: (((ord_less_real @ B @ one_one_real) => (ord_less_real @ (times_times_real @ B @ (power_power_real @ B @ A)) @ (power_power_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_power__Suc__less)). 39.32/11.37 thf(3039,plain,((! [A:nat,B:real]: (((ord_less_real @ B @ one_one_real) => (ord_less_real @ (times_times_real @ B @ (power_power_real @ B @ A)) @ (power_power_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])). 39.32/11.37 thf(699,axiom,((! [A:(int > $o),B:int,C:int]: ((ord_less_eq_int @ B @ C) => (((A @ B) <= (! [D:int]: (((A @ (minus_minus_int @ D @ one_one_int)) <= (A @ D)) <= (ord_less_eq_int @ D @ C)))) <= (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_int__le__induct)). 39.32/11.37 thf(3168,plain,((! [A:(int > $o),B:int,C:int]: ((ord_less_eq_int @ B @ C) => ((A @ B) | ~ (! [D:int]: ((A @ (minus_minus_int @ D @ one_one_int)) | ~ (A @ D) | ~ (ord_less_eq_int @ D @ C))) | ~ (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 39.32/11.37 thf(276,axiom,((! [A:real,B:int]: (((power_power_real @ A @ (number_number_of_nat @ B)) = zero_zero_real) = ((A = zero_zero_real) & ((number_number_of_nat @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_power__eq__0__iff__number__of)). 39.32/11.37 thf(1940,plain,((! [A:real,B:int]: (((power_power_real @ A @ (number_number_of_nat @ B)) = zero_zero_real) = ((A = zero_zero_real) & ~ ((number_number_of_nat @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 39.32/11.37 thf(789,axiom,((! [A:int]: ((minus_minus_int @ pls @ (bit0 @ A)) = (bit0 @ (minus_minus_int @ pls @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_diff__bin__simps_I3_J)). 39.32/11.37 thf(3433,plain,((! [A:int]: ((minus_minus_int @ pls @ (bit0 @ A)) = (bit0 @ (minus_minus_int @ pls @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 39.32/11.37 thf(1182,axiom,((! [A:int]: ((minus_minus_int @ pls @ (bit1 @ A)) = (bit1 @ (minus_minus_int @ min @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_diff__bin__simps_I4_J)). 39.32/11.37 thf(4548,plain,((! [A:int]: ((minus_minus_int @ pls @ (bit1 @ A)) = (bit1 @ (minus_minus_int @ min @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182])). 39.32/11.37 thf(1092,axiom,((ord_less_eq_int @ pls @ pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I19_J)). 39.32/11.37 thf(4289,plain,((ord_less_eq_int @ pls @ pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092])). 39.32/11.37 thf(1087,axiom,((! [A:real]: ((A != zero_zero_real) = (ord_less_real @ zero_zero_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_zero__less__power2)). 39.32/11.37 thf(4278,plain,((! [A:real]: ((~ (A = zero_zero_real)) = (ord_less_real @ zero_zero_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087])). 39.32/11.37 thf(235,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ A) => (~ (dvd_dvd_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_nat__dvd__not__less)). 39.32/11.37 thf(1839,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ B @ A) => (~ (dvd_dvd_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 39.32/11.37 thf(858,axiom,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_semiring__mult__2__right)). 39.32/11.37 thf(3620,plain,((! [A:real]: ((times_times_real @ A @ (number267125858f_real @ (bit0 @ (bit1 @ pls)))) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[858])). 39.32/11.37 thf(267,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((ord_less_eq_int @ B @ zero_zero_int) | (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_zdvd__bounds)). 39.32/11.37 thf(1918,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((ord_less_eq_int @ B @ zero_zero_int) | (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 39.32/11.37 thf(45,axiom,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ A @ (times_times_real @ B @ (times_times_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 39.32/11.37 thf(1316,plain,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ A @ (times_times_real @ B @ (times_times_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 39.32/11.37 thf(164,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A)) => (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_dvd_Ole__less__trans)). 39.32/11.37 thf(1649,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => ((~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A)) => (~ (dvd_dvd_nat @ A @ B) & (dvd_dvd_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 39.32/11.37 thf(839,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (number267125858f_real @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_semiring__one__add__one__is__two)). 39.32/11.37 thf(3565,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (number267125858f_real @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[839])). 39.32/11.37 thf(779,axiom,((! [A:int]: (((ord_less_eq_int @ A @ zero_zero_int) => ((zfact @ A) = one_one_int)) & (((zfact @ A) = (times_times_int @ A @ (zfact @ (minus_minus_int @ A @ one_one_int)))) <= (~ (ord_less_eq_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_zfact_Osimps)). 39.32/11.37 thf(3401,plain,((! [A:int]: (((ord_less_eq_int @ A @ zero_zero_int) => ((zfact @ A) = one_one_int)) & (((zfact @ A) = (times_times_int @ A @ (zfact @ (minus_minus_int @ A @ one_one_int)))) | (ord_less_eq_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 39.32/11.37 thf(227,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_le__refl)). 39.32/11.37 thf(1817,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 39.32/11.37 thf(626,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((B = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = ((plus_plus_nat @ (times_times_nat @ D @ A) @ B) = (plus_plus_nat @ (times_times_nat @ E @ A) @ C))) <= (ord_less_eq_nat @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_nat__eq__add__iff2)). 39.32/11.37 thf(2960,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((B = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)) = ((plus_plus_nat @ (times_times_nat @ D @ A) @ B) = (plus_plus_nat @ (times_times_nat @ E @ A) @ C))) | ~ (ord_less_eq_nat @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])). 39.32/11.37 thf(827,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rel__simps_I16_J)). 39.32/11.37 thf(3533,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 39.32/11.37 thf(794,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_zdiff__zmult__distrib)). 39.32/11.37 thf(3447,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])). 39.32/11.37 thf(557,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_le__diff__conv)). 39.32/11.37 thf(2743,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])). 39.32/11.37 thf(93,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 39.32/11.37 thf(1448,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 39.32/11.37 thf(476,axiom,((! [A:$o,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) & ~ (dvd_dvd_nat @ C @ B)) => ((A) <= ((dvd_dvd_nat @ C @ B) & ~ (dvd_dvd_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_dvd_Oless__imp__triv)). 39.32/11.37 thf(2490,plain,((! [A:$o,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) & ~ (dvd_dvd_nat @ C @ B)) => ((A) | ~ ((dvd_dvd_nat @ C @ B) & ~ (dvd_dvd_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 39.32/11.37 thf(367,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ B)) <= (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_dvd__diffD)). 39.32/11.37 thf(2187,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ B)) | ~ (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 39.32/11.37 thf(760,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((B = D) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_crossproduct__eq)). 39.32/11.37 thf(3346,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((B = D) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 39.32/11.37 thf(611,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 39.32/11.37 thf(2919,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])). 39.32/11.37 thf(420,axiom,((one_one_nat != zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_one__neq__zero)). 39.32/11.37 thf(2342,plain,((~ (one_one_nat = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 39.32/11.37 thf(136,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 39.32/11.37 thf(1575,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 39.32/11.37 thf(1152,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ E) => (((((plus_plus_int @ B @ A) = one_one_int) => (ord_less_int @ (plus_plus_int @ (times_times_int @ B @ D) @ (times_times_int @ A @ C)) @ E)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ B))) <= (ord_less_int @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_convex__bound__lt)). 39.32/11.37 thf(4463,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ E) => ((((plus_plus_int @ B @ A) = one_one_int) => (ord_less_int @ (plus_plus_int @ (times_times_int @ B @ D) @ (times_times_int @ A @ C)) @ E)) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ zero_zero_int @ B))) | ~ (ord_less_int @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152])). 39.32/11.37 thf(661,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (? [C:int]: ((ord_less_eq_int @ zero_zero_int @ C) & ! [D:int]: (((ord_less_eq_int @ zero_zero_int @ D) & (ord_less_int @ D @ B) & (zcong @ A @ D @ B)) => (D = C)) & (zcong @ A @ C @ B) & (ord_less_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_zcong__zless__unique)). 39.32/11.37 thf(3056,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) => (? [C:int]: ((ord_less_eq_int @ zero_zero_int @ C) & ! [D:int]: (((ord_less_eq_int @ zero_zero_int @ D) & (ord_less_int @ D @ B) & (zcong @ A @ D @ B)) => (D = C)) & (zcong @ A @ C @ B) & (ord_less_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])). 39.32/11.37 thf(528,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_real__mult__le__cancel__iff2)). 39.32/11.37 thf(2643,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 39.32/11.37 thf(297,axiom,((! [A:nat,B:real]: ((ord_less_real @ one_one_real @ (times_times_real @ B @ (power_power_real @ B @ A))) <= (ord_less_real @ one_one_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_power__gt1__lemma)). 39.32/11.37 thf(1998,plain,((! [A:nat,B:real]: ((ord_less_real @ one_one_real @ (times_times_real @ B @ (power_power_real @ B @ A))) | ~ (ord_less_real @ one_one_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 39.32/11.37 thf(1191,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_comm__semiring__class_Odistrib)). 39.32/11.37 thf(4574,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191])). 39.32/11.37 thf(163,axiom,((! [A:int,B:int]: ((number267125858f_real @ (times_times_int @ A @ B)) = (times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_number__of__mult)). 39.32/11.37 thf(1646,plain,((! [A:int,B:int]: ((number267125858f_real @ (times_times_int @ A @ B)) = (times_times_real @ (number267125858f_real @ A) @ (number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 39.32/11.37 thf(1035,axiom,((! [A:nat]: ((((power_power_int @ zero_zero_int @ A) = zero_zero_int) <= (A != zero_zero_nat)) & (((power_power_int @ zero_zero_int @ A) = one_one_int) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_power__0__left)). 39.32/11.37 thf(4121,plain,((! [A:nat]: ((((power_power_int @ zero_zero_int @ A) = zero_zero_int) | (A = zero_zero_nat)) & (((power_power_int @ zero_zero_int @ A) = one_one_int) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035])). 39.32/11.37 thf(362,axiom,((! [A:int,B:int]: ((zcong @ A @ B @ zero_zero_int) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_IntPrimes_Ozcong__zero)). 39.32/11.37 thf(2174,plain,((! [A:int,B:int]: ((zcong @ A @ B @ zero_zero_int) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 39.32/11.37 thf(334,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_mult__nonpos__nonneg)). 39.32/11.37 thf(2098,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 39.32/11.37 thf(489,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_938_nat__le__linear)). 39.32/11.37 thf(2532,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)],[489])). 39.32/11.37 thf(104,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_989_less__or__eq__imp__le)). 39.32/11.37 thf(1481,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)],[104])). 39.32/11.37 thf(903,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 39.32/11.37 thf(3748,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[903])). 39.32/11.37 thf(630,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (power_power_nat @ A @ B) @ C) = (power_power_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 39.32/11.37 thf(2971,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (power_power_nat @ A @ B) @ C) = (power_power_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 39.32/11.37 thf(454,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ one_one_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_power__increasing)). 39.32/11.37 thf(2431,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ one_one_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 39.32/11.37 thf(768,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ (times_times_int @ D @ B) @ E) = (zcong @ A @ (times_times_int @ C @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_zcong__zmult__prop1)). 39.32/11.37 thf(3368,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ (times_times_int @ D @ B) @ E) = (zcong @ A @ (times_times_int @ C @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 39.32/11.37 thf(724,axiom,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 39.32/11.37 thf(3252,plain,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (times_times_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 39.32/11.37 thf(616,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_mult__right__mono__neg)). 39.32/11.37 thf(2934,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) => ((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])). 39.32/11.37 thf(511,axiom,((! [A:int]: ((((power_power_real @ zero_zero_real @ (number_number_of_nat @ A)) = one_one_real) <= ((number_number_of_nat @ A) = zero_zero_nat)) & (((number_number_of_nat @ A) != zero_zero_nat) => ((power_power_real @ zero_zero_real @ (number_number_of_nat @ A)) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_power__0__left__number__of)). 39.32/11.37 thf(2594,plain,((! [A:int]: ((((power_power_real @ zero_zero_real @ (number_number_of_nat @ A)) = one_one_real) | ~ ((number_number_of_nat @ A) = zero_zero_nat)) & ((~ ((number_number_of_nat @ A) = zero_zero_nat)) => ((power_power_real @ zero_zero_real @ (number_number_of_nat @ A)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])). 39.32/11.37 thf(192,axiom,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_power__0)). 39.32/11.37 thf(1721,plain,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 39.32/11.37 thf(261,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_le0)). 39.32/11.37 thf(1903,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 39.32/11.37 thf(445,axiom,((! [A:int,B:int]: ((~ (ord_less_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A))) = (ord_less_eq_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__number__of__eq__not__less)). 39.32/11.37 thf(2406,plain,((! [A:int,B:int]: ((~ (ord_less_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A))) = (ord_less_eq_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 39.32/11.37 thf(575,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_add__lessD1)). 39.32/11.37 thf(2811,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 39.32/11.37 thf(678,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 39.32/11.37 thf(3104,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])). 39.32/11.37 thf(300,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_nat__mult__assoc)). 39.32/11.37 thf(2004,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 39.32/11.37 thf(242,axiom,((! [A:int,B:int,C:nat]: (((dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (dvd_dvd_int @ A @ B)) <= (C != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_pow__divides__eq__int)). 39.32/11.37 thf(1854,plain,((! [A:int,B:int,C:nat]: (((dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (dvd_dvd_int @ A @ B)) | (C = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 39.32/11.37 thf(1110,axiom,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_power__one__right)). 39.32/11.37 thf(4338,plain,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110])). 39.32/11.37 thf(18,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_dvd__mult__left)). 39.32/11.37 thf(1244,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 39.32/11.37 thf(229,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (div_mod_nat @ A @ D)) @ B) @ (times_times_nat @ C @ D)) <= (ord_less_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_mod__lemma)). 39.32/11.37 thf(1822,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (div_mod_nat @ A @ D)) @ B) @ (times_times_nat @ C @ D)) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 39.32/11.37 thf(1165,axiom,((! [A:int]: ((ord_less_int @ (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_odd__less__0)). 39.32/11.37 thf(4495,plain,((! [A:int]: ((ord_less_int @ (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165])). 39.32/11.37 thf(118,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 39.32/11.37 thf(1523,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 39.32/11.37 thf(440,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_zero__less__mult__pos2)). 39.32/11.37 thf(2394,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 39.32/11.37 thf(671,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_998_nat__add__left__cancel__le)). 39.32/11.37 thf(3085,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) = (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 39.32/11.37 thf(620,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (((plus_plus_nat @ (times_times_nat @ E @ A) @ B) = (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_nat__eq__add__iff1)). 39.32/11.37 thf(2944,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (((plus_plus_nat @ (times_times_nat @ E @ A) @ B) = (plus_plus_nat @ (times_times_nat @ D @ A) @ C)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ B) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 39.32/11.37 thf(985,axiom,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B)) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_zdiff__power2)). 39.32/11.37 thf(3978,plain,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_int @ (minus_minus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B)) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[985])). 39.32/11.37 thf(1094,axiom,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 39.32/11.37 thf(4293,plain,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094])). 39.32/11.37 thf(1104,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit0 @ A) @ (bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I31_J)). 39.32/11.37 thf(4321,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ (bit0 @ A) @ (bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104])). 39.32/11.37 thf(1045,axiom,((! [A:int]: ((ord_less_eq_int @ pls @ A) = (ord_less_eq_int @ pls @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_rel__simps_I21_J)). 39.32/11.37 thf(4153,plain,((! [A:int]: ((ord_less_eq_int @ pls @ A) = (ord_less_eq_int @ pls @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045])). 39.32/11.37 thf(185,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) | (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zle__linear)). 39.32/11.37 thf(1706,plain,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) | (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 39.32/11.37 thf(114,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_diff__add__0)). 39.32/11.37 thf(1513,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 39.32/11.37 thf(168,axiom,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_sum__squares__eq__zero__iff)). 39.32/11.37 thf(1661,plain,((! [A:real,B:real]: (((B = zero_zero_real) & (A = zero_zero_real)) = ((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 39.32/11.37 thf(342,axiom,((! [A:int]: ((ord_less_real @ one_one_real @ (number267125858f_real @ A)) = (ord_less_int @ (bit1 @ pls) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_less__special_I2_J)). 39.32/11.37 thf(2120,plain,((! [A:int]: ((ord_less_real @ one_one_real @ (number267125858f_real @ A)) = (ord_less_int @ (bit1 @ pls) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 39.32/11.37 thf(333,axiom,((! [A:real,B:real]: ((times_times_real @ A @ B) = (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_real__mult__commute)). 39.32/11.37 thf(2095,plain,((! [A:real,B:real]: ((times_times_real @ A @ B) = (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 39.32/11.37 thf(1122,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => ((ord_less_eq_int @ pls @ A) => ((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (plus_plus_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_semiring__add__number__of)). 39.32/11.37 thf(4372,plain,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => ((ord_less_eq_int @ pls @ A) => ((plus_plus_nat @ (number_number_of_nat @ B) @ (number_number_of_nat @ A)) = (number_number_of_nat @ (plus_plus_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122])). 39.32/11.37 thf(700,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_le__imp__power__dvd)). 39.32/11.37 thf(3181,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])). 39.32/11.37 thf(471,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_eq_nat @ A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_mult__nonneg__nonpos)). 39.32/11.37 thf(2475,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 39.32/11.37 thf(850,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zmult__assoc)). 39.32/11.37 thf(3598,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])). 39.32/11.37 thf(38,axiom,((! [A:nat,B:nat]: (((A != B) & (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_nat__less__le)). 39.32/11.37 thf(1294,plain,((! [A:nat,B:nat]: ((~ (A = B) & (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 39.32/11.37 thf(1127,axiom,((! [A:int]: ((A = zero_zero_int) = ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_zero__eq__power2)). 39.32/11.37 thf(4387,plain,((! [A:int]: ((A = zero_zero_int) = ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127])). 39.32/11.37 thf(321,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ A @ B)) <= (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_diff__less__mono2)). 39.32/11.37 thf(2066,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ A @ B)) | ~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 39.32/11.37 thf(919,axiom,((! [A:int,B:int,C:int]: ((div_mod_int @ (times_times_int @ A @ (div_mod_int @ B @ C)) @ C) = (div_mod_int @ (times_times_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_zmod__simps_I3_J)). 39.32/11.37 thf(3793,plain,((! [A:int,B:int,C:int]: ((div_mod_int @ (times_times_int @ A @ (div_mod_int @ B @ C)) @ C) = (div_mod_int @ (times_times_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[919])). 39.32/11.37 thf(541,axiom,((! [A:int]: ((number267125858f_real @ (bit0 @ A)) = (plus_plus_real @ (plus_plus_real @ zero_zero_real @ (number267125858f_real @ A)) @ (number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_number__of__Bit0)). 39.32/11.37 thf(2680,plain,((! [A:int]: ((number267125858f_real @ (bit0 @ A)) = (plus_plus_real @ (plus_plus_real @ zero_zero_real @ (number267125858f_real @ A)) @ (number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 39.32/11.37 thf(365,axiom,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_dvd__0__right)). 39.32/11.37 thf(2183,plain,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 39.32/11.37 thf(257,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_dvd__power__same)). 39.32/11.37 thf(1893,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 39.32/11.37 thf(402,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_mult__nonneg__nonneg)). 39.32/11.37 thf(2294,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 39.32/11.37 thf(1028,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_power__add)). 39.32/11.37 thf(4098,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028])). 39.32/11.37 thf(1189,axiom,((quadRes @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (number_number_of_int @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096)). 39.32/11.37 thf(4570,plain,((quadRes @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ (number_number_of_int @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189])). 39.32/11.37 thf(1099,axiom,((! [A:int]: ((min = (bit1 @ A)) = (min = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_rel__simps_I43_J)). 39.32/11.37 thf(4306,plain,((! [A:int]: ((min = (bit1 @ A)) = (min = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099])). 39.32/11.37 thf(834,axiom,((! [A:nat,B:int,C:int,D:int]: ((zprime @ D) => (((dvd_dvd_int @ (power_power_int @ D @ A) @ (times_times_int @ C @ B)) => (dvd_dvd_int @ (power_power_int @ D @ A) @ B)) <= (~ (dvd_dvd_int @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left)). 39.32/11.37 thf(3552,plain,((! [A:nat,B:int,C:int,D:int]: ((zprime @ D) => (((dvd_dvd_int @ (power_power_int @ D @ A) @ (times_times_int @ C @ B)) => (dvd_dvd_int @ (power_power_int @ D @ A) @ B)) | (dvd_dvd_int @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 39.32/11.37 thf(784,axiom,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_semiring__mult__2)). 39.32/11.37 thf(3420,plain,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 39.32/11.37 thf(151,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ (power_power_nat @ B @ C) @ D) => ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ D) <= (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_power__le__dvd)). 39.32/11.37 thf(1614,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ (power_power_nat @ B @ C) @ D) => ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ D) | ~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 39.32/11.37 thf(399,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ one_one_nat @ (power_power_nat @ B @ A))) <= (ord_less_nat @ one_one_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_one__less__power)). 39.32/11.37 thf(2287,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ one_one_nat @ (power_power_nat @ B @ A))) | ~ (ord_less_nat @ one_one_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 39.32/11.37 thf(542,axiom,((! [A:real]: ((plus_plus_real @ A @ A) = (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 39.32/11.37 thf(2683,plain,((! [A:real]: ((plus_plus_real @ A @ A) = (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])). 39.32/11.37 thf(887,axiom,((! [A:int]: ((ord_less_int @ (bit1 @ pls) @ A) = (ord_less_int @ one_one_int @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_less__special_I2_J)). 39.32/11.37 thf(3705,plain,((! [A:int]: ((ord_less_int @ (bit1 @ pls) @ A) = (ord_less_int @ one_one_int @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])). 39.32/11.37 thf(738,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_real__mult__assoc)). 39.32/11.37 thf(3291,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])). 39.32/11.37 thf(851,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 39.32/11.37 thf(3601,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[851])). 39.32/11.37 thf(125,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_real__le__linear)). 39.32/11.37 thf(1546,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 39.32/11.37 thf(485,axiom,((! [A:int,B:int,C:int]: ((((dvd_dvd_int @ C @ B) | (dvd_dvd_int @ C @ A)) <= (dvd_dvd_int @ C @ (times_times_int @ A @ B))) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_zprime__zdvd__zmult__better)). 39.32/11.37 thf(2522,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ C @ B) | (dvd_dvd_int @ C @ A) | ~ (dvd_dvd_int @ C @ (times_times_int @ A @ B)) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 39.32/11.37 thf(822,axiom,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (minus_minus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_power2__diff)). 39.32/11.37 thf(3521,plain,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (minus_minus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])). 39.32/11.37 thf(20,axiom,((! [A:real,B:real,C:real,D:real]: ((dvd_dvd_real @ C @ D) => ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_mult__dvd__mono)). 39.32/11.37 thf(1248,plain,((! [A:real,B:real,C:real,D:real]: ((dvd_dvd_real @ C @ D) => ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ (times_times_real @ C @ A) @ (times_times_real @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 39.32/11.37 thf(772,axiom,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_not__sum__squares__lt__zero)). 39.32/11.37 thf(3379,plain,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])). 39.32/11.37 thf(990,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D) => (((~ (zcong @ C @ zero_zero_int @ D)) => ((((zcong @ A @ B @ D) <= (zcong @ (times_times_int @ C @ (multInv @ D @ A)) @ (times_times_int @ C @ (multInv @ D @ B)) @ D)) <= (~ (zcong @ A @ zero_zero_int @ D))) <= (~ (zcong @ B @ zero_zero_int @ D)))) <= (zprime @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_MultInv__zcong__prop3)). 39.32/11.37 thf(3992,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ D) => (((~ (zcong @ C @ zero_zero_int @ D)) => ((zcong @ A @ B @ D) | ~ (zcong @ (times_times_int @ C @ (multInv @ D @ A)) @ (times_times_int @ C @ (multInv @ D @ B)) @ D) | (zcong @ A @ zero_zero_int @ D) | (zcong @ B @ zero_zero_int @ D))) | ~ (zprime @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])). 39.32/11.37 thf(263,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (times_times_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 39.32/11.37 thf(1908,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (times_times_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 39.32/11.37 thf(343,axiom,((ord_less_eq_int @ min @ min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_rel__simps_I24_J)). 39.32/11.37 thf(2123,plain,((ord_less_eq_int @ min @ min)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 39.32/11.37 thf(388,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = ((A != zero_zero_real) | (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_sum__squares__gt__zero__iff)). 39.32/11.37 thf(2258,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = (~ (A = zero_zero_real) | ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 39.32/11.37 thf(999,axiom,((! [A:int,B:int]: ((ord_less_eq_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B)) = ((ord_less_eq_int @ A @ pls) <= (~ (ord_less_eq_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_le__nat__number__of)). 39.32/11.37 thf(4014,plain,((! [A:int,B:int]: ((ord_less_eq_nat @ (number_number_of_nat @ A) @ (number_number_of_nat @ B)) = ((ord_less_eq_int @ A @ pls) | (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])). 39.32/11.37 thf(137,axiom,((! [A:int,B:nat,C:int]: (((((ord_less_nat @ zero_zero_nat @ B) => (A = C)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_power__eq__imp__eq__base)). 39.32/11.37 thf(1578,plain,((! [A:int,B:nat,C:int]: (((ord_less_nat @ zero_zero_nat @ B) => (A = C)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 39.32/11.37 thf(1155,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) => (ord_less_nat @ A @ B)) <= (ord_less_int @ one_one_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_power__less__imp__less__exp)). 39.32/11.37 thf(4472,plain,((! [A:nat,B:nat,C:int]: (((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) => (ord_less_nat @ A @ B)) | ~ (ord_less_int @ one_one_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155])). 39.32/11.37 thf(1131,axiom,((! [A:int]: ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_power2__eq__square)). 39.32/11.37 thf(4399,plain,((! [A:int]: ((power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131])). 39.32/11.37 thf(437,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_diff__diff__left)). 39.32/11.37 thf(2385,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 39.32/11.37 thf(916,axiom,((! [A:int]: ((plus_plus_real @ (number267125858f_real @ A) @ one_one_real) = (number267125858f_real @ (plus_plus_int @ A @ (bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__special_I3_J)). 39.32/11.37 thf(3785,plain,((! [A:int]: ((plus_plus_real @ (number267125858f_real @ A) @ one_one_real) = (number267125858f_real @ (plus_plus_int @ A @ (bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])). 39.32/11.37 thf(817,axiom,((! [A:int,B:int]: ((number_number_of_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_number__of__diff)). 39.32/11.37 thf(3511,plain,((! [A:int,B:int]: ((number_number_of_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (number_number_of_int @ A) @ (number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 39.32/11.37 thf(1124,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ (times_times_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 39.32/11.37 thf(4378,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ (times_times_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124])). 39.32/11.37 thf(717,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ one_one_int @ C) => ((member_int @ A @ (wset @ C @ B)) <= (member_int @ A @ (wset @ (minus_minus_int @ C @ one_one_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_wset__subset)). 39.32/11.37 thf(3232,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ one_one_int @ C) => ((member_int @ A @ (wset @ C @ B)) | ~ (member_int @ A @ (wset @ (minus_minus_int @ C @ one_one_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 39.32/11.37 thf(490,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_nat__add__left__cancel__less)). 39.32/11.37 thf(2534,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 39.32/11.37 thf(387,axiom,((! [A:int,B:int]: ((zprime @ B) => ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => (((A = (minus_minus_int @ B @ one_one_int)) | (A = one_one_int)) <= (zcong @ (times_times_int @ A @ A) @ one_one_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_zcong__square__zless)). 39.32/11.37 thf(2255,plain,((! [A:int,B:int]: ((zprime @ B) => ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => ((A = (minus_minus_int @ B @ one_one_int)) | (A = one_one_int) | ~ (zcong @ (times_times_int @ A @ A) @ one_one_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 39.32/11.37 thf(635,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 39.32/11.37 thf(2983,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 39.32/11.37 thf(552,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((A = B) = ((times_times_nat @ C @ A) = (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_nat__mult__eq__cancel1)). 39.32/11.37 thf(2719,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((A = B) = ((times_times_nat @ C @ A) = (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 39.32/11.37 thf(1078,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add1__zle__eq)). 39.32/11.37 thf(4254,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078])). 39.32/11.37 thf(897,axiom,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_power__commutes)). 39.32/11.37 thf(3733,plain,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])). 39.32/11.37 thf(72,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_sum__squares__le__zero__iff)). 39.32/11.37 thf(1395,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 39.32/11.37 thf(988,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_zero__le__power2)). 39.32/11.37 thf(3987,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])). 39.32/11.37 thf(770,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ B) = (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 39.32/11.37 thf(3373,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ B) = (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 39.32/11.37 thf(143,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_add__is__0)). 39.32/11.37 thf(1593,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 39.32/11.37 thf(931,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((dvd_dvd_int @ D @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ D @ (plus_plus_int @ (plus_plus_int @ B @ (times_times_int @ A @ E)) @ C))) <= (dvd_dvd_int @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_zdvd__period)). 39.32/11.37 thf(3837,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((dvd_dvd_int @ D @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ D @ (plus_plus_int @ (plus_plus_int @ B @ (times_times_int @ A @ E)) @ C))) | ~ (dvd_dvd_int @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[931])). 39.32/11.37 thf(623,axiom,((! [A:int,B:int]: (((number267125858f_real @ A) = (number267125858f_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_eq__number__of)). 39.32/11.37 thf(2951,plain,((! [A:int,B:int]: (((number267125858f_real @ A) = (number267125858f_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 39.32/11.37 thf(1176,axiom,((! [A:int,B:int]: (((A = zero_zero_int) & (B = zero_zero_int)) = (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_sum__squares__le__zero__iff)). 39.32/11.37 thf(4523,plain,((! [A:int,B:int]: (((A = zero_zero_int) & (B = zero_zero_int)) = (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176])). 39.32/11.37 thf(577,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ B @ E) => (zcong @ (minus_minus_int @ C @ A) @ (minus_minus_int @ D @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_zcong__zdiff)). 39.32/11.37 thf(2815,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((zcong @ C @ D @ E) => ((zcong @ A @ B @ E) => (zcong @ (minus_minus_int @ C @ A) @ (minus_minus_int @ D @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])). 39.32/11.37 thf(42,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) => ((times_times_nat @ B @ A) = (plus_plus_nat @ A @ (times_times_nat @ (minus_minus_nat @ B @ one_one_nat) @ A)))) & ((B = zero_zero_nat) => ((times_times_nat @ B @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_mult__eq__if)). 39.32/11.37 thf(1303,plain,((! [A:nat,B:nat]: (((~ (B = zero_zero_nat)) => ((times_times_nat @ B @ A) = (plus_plus_nat @ A @ (times_times_nat @ (minus_minus_nat @ B @ one_one_nat) @ A)))) & ((B = zero_zero_nat) => ((times_times_nat @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 39.32/11.37 thf(294,axiom,((! [A:nat,B:nat,C:nat]: ((~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C)) => ((C = A) => ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_dvd_Oord__less__eq__trans)). 39.32/11.37 thf(1986,plain,((! [A:nat,B:nat,C:nat]: ((~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C)) => ((C = A) => ((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 39.32/11.37 thf(918,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) = (ord_less_nat @ A @ B)) <= (ord_less_int @ one_one_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_power__strict__increasing__iff)). 39.32/11.37 thf(3790,plain,((! [A:nat,B:nat,C:int]: (((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) = (ord_less_nat @ A @ B)) | ~ (ord_less_int @ one_one_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])). 39.32/11.37 thf(756,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => (((ord_less_eq_int @ A @ B) => (member_int @ A @ (wset @ B @ C))) <= (ord_less_int @ one_one_int @ A))) <= (zprime @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_wset__mem)). 39.32/11.37 thf(3337,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (minus_minus_int @ C @ one_one_int)) => (((ord_less_eq_int @ A @ B) => (member_int @ A @ (wset @ B @ C))) | ~ (ord_less_int @ one_one_int @ A))) | ~ (zprime @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])). 39.32/11.37 thf(1117,axiom,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_add__diff__add)). 39.32/11.37 thf(4357,plain,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117])). 39.32/11.37 thf(811,axiom,((! [A:int,B:int]: ((times_times_int @ (bit1 @ A) @ B) = (plus_plus_int @ (bit0 @ (times_times_int @ A @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_mult__Bit1)). 39.32/11.37 thf(3496,plain,((! [A:int,B:int]: ((times_times_int @ (bit1 @ A) @ B) = (plus_plus_int @ (bit0 @ (times_times_int @ A @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])). 39.32/11.37 thf(1163,axiom,((! [A:int,B:int,C:int,D:int]: ((zcong @ B @ C @ D) => (zcong @ (times_times_int @ A @ B) @ (times_times_int @ A @ C) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_zcong__scalar2)). 39.32/11.37 thf(4491,plain,((! [A:int,B:int,C:int,D:int]: ((zcong @ B @ C @ D) => (zcong @ (times_times_int @ A @ B) @ (times_times_int @ A @ C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163])). 39.32/11.37 thf(206,axiom,((! [A:int]: ((ord_less_real @ (number267125858f_real @ A) @ one_one_real) = (ord_less_int @ A @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_less__special_I4_J)). 39.32/11.37 thf(1757,plain,((! [A:int]: ((ord_less_real @ (number267125858f_real @ A) @ one_one_real) = (ord_less_int @ A @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 39.32/11.37 thf(1193,axiom,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zprime @ B) => ((zcong @ (multInv @ B @ (multInv @ B @ A)) @ (times_times_int @ (times_times_int @ A @ (multInv @ B @ A)) @ (multInv @ B @ (multInv @ B @ A))) @ B) <= (~ (zcong @ A @ zero_zero_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_Int2_Oaux____1)). 39.32/11.37 thf(4579,plain,((! [A:int,B:int]: ((ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ B) => ((zprime @ B) => ((zcong @ (multInv @ B @ (multInv @ B @ A)) @ (times_times_int @ (times_times_int @ A @ (multInv @ B @ A)) @ (multInv @ B @ (multInv @ B @ A))) @ B) | (zcong @ A @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193])). 39.32/11.37 thf(882,axiom,((! [A:int]: ((times_times_int @ A @ A) = (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 39.32/11.37 thf(3690,plain,((! [A:int]: ((times_times_int @ A @ A) = (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[882])). 39.32/11.37 thf(1149,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__int__code_I15_J)). 39.32/11.37 thf(4455,plain,((! [A:int,B:int]: ((ord_less_int @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149])). 39.32/11.37 thf(662,axiom,((! [A:int,B:int]: (((A = B) <= (ord_less_eq_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zle__antisym)). 39.32/11.37 thf(3062,plain,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 39.32/11.37 thf(89,axiom,((! [A:nat,B:nat,C:nat]: ((((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)) <= (~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A))) <= (~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_dvd_Oless__trans)). 39.32/11.37 thf(1436,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ A) & ~ (dvd_dvd_nat @ A @ B)) | ~ (~ (dvd_dvd_nat @ A @ C) & (dvd_dvd_nat @ C @ A)) | ~ (~ (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 39.32/11.37 thf(976,axiom,((! [A:nat]: ((times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__mult__2)). 39.32/11.37 thf(3956,plain,((! [A:nat]: ((times_times_nat @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))) @ A) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[976])). 39.32/11.37 thf(1004,axiom,((! [A:int]: ((bit0 @ A) != min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_rel__simps_I45_J)). 39.32/11.37 thf(4029,plain,((! [A:int]: ~ ((bit0 @ A) = min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])). 39.32/11.37 thf(954,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B)) <= (ord_less_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_power2__less__imp__less)). 39.32/11.37 thf(3897,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B)) | ~ (ord_less_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[954])). 39.32/11.37 thf(1114,axiom,((! [A:int,B:int,C:int]: ((zcong @ (times_times_int @ (standardRes @ C @ A) @ (standardRes @ C @ B)) @ (times_times_int @ A @ B) @ C) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_StandardRes__prop4)). 39.32/11.37 thf(4350,plain,((! [A:int,B:int,C:int]: ((zcong @ (times_times_int @ (standardRes @ C @ A) @ (standardRes @ C @ B)) @ (times_times_int @ A @ B) @ C) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114])). 39.32/11.37 thf(1088,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_power2__le__imp__le)). 39.32/11.37 thf(4281,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_nat @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088])). 39.32/11.37 thf(216,axiom,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 39.32/11.37 thf(1789,plain,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 39.32/11.37 thf(429,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_power__decreasing)). 39.32/11.37 thf(2366,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 39.32/11.37 thf(750,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_mult__strict__right__mono)). 39.32/11.37 thf(3323,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])). 39.32/11.37 thf(1146,axiom,((! [A:int]: ((ord_less_eq_int @ (number_number_of_int @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_le__special_I3_J)). 39.32/11.37 thf(4442,plain,((! [A:int]: ((ord_less_eq_int @ (number_number_of_int @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146])). 39.32/11.37 thf(519,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_mult__eq__0__iff)). 39.32/11.37 thf(2619,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 39.32/11.37 thf(312,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_power__add)). 39.32/11.37 thf(2040,plain,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 39.32/11.37 thf(945,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) => ((A = zero_zero_int) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_divisors__zero)). 39.32/11.37 thf(3875,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) => ((A = zero_zero_int) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[945])). 39.32/11.37 thf(1156,axiom,(((twoSqu2057625106sum2sq @ (product_Pair_int_int @ s @ one_one_int)) = (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096)). 39.32/11.37 thf(4474,plain,(((twoSqu2057625106sum2sq @ (product_Pair_int_int @ s @ one_one_int)) = (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156])). 39.32/11.37 thf(996,axiom,((! [A:nat,B:int]: ((ord_less_int @ (power_power_int @ B @ A) @ (times_times_int @ B @ (power_power_int @ B @ A))) <= (ord_less_int @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_power__less__power__Suc)). 39.32/11.37 thf(4007,plain,((! [A:nat,B:int]: ((ord_less_int @ (power_power_int @ B @ A) @ (times_times_int @ B @ (power_power_int @ B @ A))) | ~ (ord_less_int @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])). 39.32/11.37 thf(558,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))) <= (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_comm__mult__left__mono)). 39.32/11.37 thf(2746,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))) | ~ (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])). 39.32/11.37 thf(180,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_less__imp__diff__less)). 39.32/11.37 thf(1693,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 39.32/11.37 thf(323,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 39.32/11.37 thf(2070,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 39.32/11.37 thf(805,axiom,((! [A:int,B:int]: (((B != zero_zero_int) | (A != zero_zero_int)) = (ord_less_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_sum__power2__gt__zero__iff)). 39.32/11.37 thf(3479,plain,((! [A:int,B:int]: ((~ (B = zero_zero_int) | ~ (A = zero_zero_int)) = (ord_less_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 39.32/11.37 thf(449,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ B @ A) = (zcong @ A @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_zcong__eq__zdvd__prop)). 39.32/11.37 thf(2417,plain,((! [A:int,B:int]: ((dvd_dvd_int @ B @ A) = (zcong @ A @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 39.32/11.37 thf(36,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ C @ E) => (((((plus_plus_real @ B @ A) = one_one_real) => (ord_less_real @ (plus_plus_real @ (times_times_real @ B @ D) @ (times_times_real @ A @ C)) @ E)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ zero_zero_real @ B))) <= (ord_less_real @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_convex__bound__lt)). 39.32/11.37 thf(1288,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ C @ E) => ((((plus_plus_real @ B @ A) = one_one_real) => (ord_less_real @ (plus_plus_real @ (times_times_real @ B @ D) @ (times_times_real @ A @ C)) @ E)) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ zero_zero_real @ B))) | ~ (ord_less_real @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 39.32/11.37 thf(187,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_pos__add__strict)). 39.32/11.37 thf(1710,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 39.32/11.37 thf(570,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B)) = (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_nat__neq__iff)). 39.32/11.37 thf(2795,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B)) = (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 39.32/11.37 thf(862,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_zadd__0__right)). 39.32/11.37 thf(3633,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[862])). 39.32/11.37 thf(419,axiom,((! [A:int,B:int,C:int]: ((((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ C) => (~ (zcong @ C @ A @ B)))) <= (ord_less_int @ C @ B)) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_zcong__not)). 39.32/11.37 thf(2340,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ C) => (~ (zcong @ C @ A @ B)))) | ~ (ord_less_int @ C @ B) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 39.32/11.37 thf(537,axiom,((! [A:nat]: ((plus_plus_nat @ A @ A) = (times_times_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 39.32/11.37 thf(2668,plain,((! [A:nat]: ((plus_plus_nat @ A @ A) = (times_times_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])). 39.32/11.37 thf(815,axiom,(((plus_plus_int @ one_one_int @ one_one_int) = (number_number_of_int @ (bit0 @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_semiring__one__add__one__is__two)). 39.32/11.37 thf(3506,plain,(((plus_plus_int @ one_one_int @ one_one_int) = (number_number_of_int @ (bit0 @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 39.32/11.37 thf(933,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 39.32/11.37 thf(3843,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[933])). 39.32/11.37 thf(306,axiom,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 39.32/11.37 thf(2021,plain,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 39.32/11.37 thf(56,axiom,((! [A:int,B:int,C:int]: ((div_mod_int @ (minus_minus_int @ A @ (div_mod_int @ B @ C)) @ C) = (div_mod_int @ (minus_minus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_zdiff__zmod__right)). 39.32/11.37 thf(1346,plain,((! [A:int,B:int,C:int]: ((div_mod_int @ (minus_minus_int @ A @ (div_mod_int @ B @ C)) @ C) = (div_mod_int @ (minus_minus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 39.32/11.37 thf(320,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_diff__diff__cancel)). 39.32/11.37 thf(2063,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 39.32/11.37 thf(923,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ (times_times_int @ A @ C)) <= (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_dvd__mult)). 39.32/11.37 thf(3805,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ (times_times_int @ A @ C)) | ~ (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[923])). 39.32/11.37 thf(531,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (plus_plus_nat @ A @ B) @ C)) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_diff__diff__right)). 39.32/11.37 thf(2651,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (plus_plus_nat @ A @ B) @ C)) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 39.32/11.37 thf(1103,axiom,((! [A:int]: ((ord_less_int @ (number_number_of_int @ A) @ one_one_int) = (ord_less_int @ A @ (bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_less__special_I4_J)). 39.32/11.37 thf(4318,plain,((! [A:int]: ((ord_less_int @ (number_number_of_int @ A) @ one_one_int) = (ord_less_int @ A @ (bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103])). 39.32/11.37 thf(496,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) => (ord_less_nat @ A @ B)) <= (ord_less_nat @ one_one_nat @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_power__less__imp__less__exp)). 39.32/11.37 thf(2549,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) => (ord_less_nat @ A @ B)) | ~ (ord_less_nat @ one_one_nat @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 39.32/11.37 thf(589,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (minus_minus_nat @ A @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_diff__less)). 39.32/11.37 thf(2847,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (minus_minus_nat @ A @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 39.32/11.37 thf(127,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_comm__mult__strict__left__mono)). 39.32/11.37 thf(1550,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 39.32/11.37 thf(1169,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ one_one_int @ (power_power_int @ B @ A)) <= (ord_less_eq_int @ one_one_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_one__le__power)). 39.32/11.37 thf(4506,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ one_one_int @ (power_power_int @ B @ A)) | ~ (ord_less_eq_int @ one_one_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169])). 39.32/11.37 thf(482,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((minus_minus_nat @ (plus_plus_nat @ A @ C) @ B) = (plus_plus_nat @ A @ (minus_minus_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_diff__add__assoc)). 39.32/11.37 thf(2507,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((minus_minus_nat @ (plus_plus_nat @ A @ C) @ B) = (plus_plus_nat @ A @ (minus_minus_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 39.32/11.37 thf(1069,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 39.32/11.37 thf(4229,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069])). 39.32/11.37 thf(40,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ B @ A) => (dvd_dvd_int @ B @ (div_mod_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_zdvd__zmod)). 39.32/11.37 thf(1299,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ C) => ((dvd_dvd_int @ B @ A) => (dvd_dvd_int @ B @ (div_mod_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 39.32/11.37 thf(668,axiom,((! [A:int]: (dvd_dvd_int @ A @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_dvd__0__right)). 39.32/11.37 thf(3076,plain,((! [A:int]: (dvd_dvd_int @ A @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 39.32/11.37 thf(1167,axiom,((pls = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_Pls__def)). 39.32/11.37 thf(4501,plain,((pls = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167])). 39.32/11.37 thf(74,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_mult__pos__pos)). 39.32/11.37 thf(1399,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 39.32/11.37 thf(1119,axiom,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_not__sum__power2__lt__zero)). 39.32/11.37 thf(4363,plain,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119])). 39.32/11.37 thf(272,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_zero__le__square)). 39.32/11.37 thf(1930,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 39.32/11.37 thf(424,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 39.32/11.37 thf(2353,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 39.32/11.37 thf(355,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_divides__mul__l)). 39.32/11.37 thf(2159,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 39.32/11.37 thf(766,axiom,((! [A:real]: ~ (ord_less_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_power2__less__0)). 39.32/11.37 thf(3362,plain,((! [A:real]: ~ (ord_less_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])). 39.32/11.37 thf(58,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_dvd__antisym)). 39.32/11.37 thf(1352,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 39.32/11.37 thf(983,axiom,((zcong @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_s)). 39.32/11.37 thf(3974,plain,((zcong @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[983])). 39.32/11.37 thf(649,axiom,((! [A:nat]: (((dvd_dvd_nat @ one_one_nat @ A) & ~ (dvd_dvd_nat @ A @ one_one_nat)) = (A != one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_gcd__lcm__complete__lattice__nat_Obot__less)). 39.32/11.37 thf(3025,plain,((! [A:nat]: (((dvd_dvd_nat @ one_one_nat @ A) & ~ (dvd_dvd_nat @ A @ one_one_nat)) = (~ (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])). 39.32/11.37 thf(231,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 39.32/11.37 thf(1827,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 39.32/11.37 thf(26,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (div_mod_nat @ A @ B) @ B) <= (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_mod__less__divisor)). 39.32/11.37 thf(1261,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (div_mod_nat @ A @ B) @ B) | ~ (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 39.32/11.37 thf(628,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E)) => ((ord_less_eq_int @ E @ zero_zero_int) => (((ord_less_int @ A @ C) => (ord_less_eq_int @ D @ B)) <= (ord_less_int @ A @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_unique__quotient__lemma__neg)). 39.32/11.37 thf(2966,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E)) => ((ord_less_eq_int @ E @ zero_zero_int) => (((ord_less_int @ A @ C) => (ord_less_eq_int @ D @ B)) | ~ (ord_less_int @ A @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])). 39.32/11.37 thf(831,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 39.32/11.37 thf(3543,plain,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 39.32/11.37 thf(841,axiom,(((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096)). 39.32/11.37 thf(3570,plain,(((legendre @ (number_number_of_int @ min) @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])). 39.32/11.37 thf(68,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real))) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_split__mult__pos__le)). 39.32/11.37 thf(1384,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real))) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 39.32/11.37 thf(123,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_mult__less__mono1)). 39.32/11.37 thf(1537,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 39.32/11.37 thf(1160,axiom,((ord_less_eq_int @ one_one_int @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tpos)). 39.32/11.37 thf(4484,plain,((ord_less_eq_int @ one_one_int @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160])). 39.32/11.37 thf(809,axiom,((! [A:int]: ((bit0 @ A) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Bit0__def)). 39.32/11.37 thf(3489,plain,((! [A:int]: ((bit0 @ A) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])). 39.32/11.37 thf(110,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_less__not__refl3)). 39.32/11.37 thf(1500,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 39.32/11.37 thf(979,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_eq_int @ one_one_int @ A) => (ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))) <= (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_power__increasing)). 39.32/11.37 thf(3965,plain,((! [A:int,B:nat,C:nat]: (((ord_less_eq_int @ one_one_int @ A) => (ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))) | ~ (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[979])). 39.32/11.37 thf(269,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_le__square)). 39.32/11.37 thf(1923,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 39.32/11.37 thf(829,axiom,((! [A:int,B:int,C:int]: (((zcong @ A @ B @ C) => (zcong @ (multInv @ C @ A) @ (multInv @ C @ B) @ C)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_MultInv__prop1)). 39.32/11.37 thf(3538,plain,((! [A:int,B:int,C:int]: (((zcong @ A @ B @ C) => (zcong @ (multInv @ C @ A) @ (multInv @ C @ B) @ C)) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])). 39.32/11.37 thf(270,axiom,((! [A:int,B:int]: ((((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (ord_less_int @ (inv @ B @ A) @ (minus_minus_int @ B @ one_one_int))) <= (ord_less_int @ one_one_int @ A)) <= (zprime @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_inv__less__p__minus__1)). 39.32/11.37 thf(1925,plain,((! [A:int,B:int]: (((ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)) => (ord_less_int @ (inv @ B @ A) @ (minus_minus_int @ B @ one_one_int))) | ~ (ord_less_int @ one_one_int @ A) | ~ (zprime @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 39.32/11.37 thf(1107,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__number__of)). 39.32/11.37 thf(4330,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (number_number_of_int @ A) @ (number_number_of_int @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107])). 39.32/11.37 thf(970,axiom,((! [A:int]: ((A != zero_zero_int) = (ord_less_int @ zero_zero_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_zero__less__power2)). 39.32/11.37 thf(3939,plain,((! [A:int]: ((~ (A = zero_zero_int)) = (ord_less_int @ zero_zero_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])). 39.32/11.37 thf(900,axiom,((! [A:int,B:int]: ((minus_minus_int @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_diff__bin__simps_I7_J)). 39.32/11.37 thf(3740,plain,((! [A:int,B:int]: ((minus_minus_int @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[900])). 39.32/11.37 thf(252,axiom,(((number267125858f_real @ pls) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_semiring__numeral__0__eq__0)). 39.32/11.37 thf(1880,plain,(((number267125858f_real @ pls) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 39.32/11.37 thf(473,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A))) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_diff__less__mono)). 39.32/11.37 thf(2484,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A))) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 39.32/11.37 thf(254,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => ((((dvd_dvd_int @ B @ C) | (dvd_dvd_int @ B @ A)) <= (dvd_dvd_int @ B @ (times_times_int @ C @ A))) <= (zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_zprime__zdvd__zmult)). 39.32/11.37 thf(1885,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => ((dvd_dvd_int @ B @ C) | (dvd_dvd_int @ B @ A) | ~ (dvd_dvd_int @ B @ (times_times_int @ C @ A)) | ~ (zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 39.32/11.37 thf(548,axiom,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ C) => ((! [D:int]: ((B @ D) => (B @ (plus_plus_int @ D @ C)))) => ((ord_less_eq_int @ zero_zero_int @ A) => (! [D:int]: ((B @ D) => (B @ (plus_plus_int @ D @ (times_times_int @ A @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_incr__mult__lemma)). 39.32/11.37 thf(2699,plain,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ C) => ((! [D:int]: ((B @ D) => (B @ (plus_plus_int @ D @ C)))) => ((ord_less_eq_int @ zero_zero_int @ A) => (! [D:int]: ((B @ D) => (B @ (plus_plus_int @ D @ (times_times_int @ A @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 39.32/11.37 thf(926,axiom,((! [A:int]: ((number_number_of_int @ (bit0 @ A)) = (plus_plus_int @ (plus_plus_int @ zero_zero_int @ (number_number_of_int @ A)) @ (number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_number__of__Bit0)). 39.32/11.37 thf(3812,plain,((! [A:int]: ((number_number_of_int @ (bit0 @ A)) = (plus_plus_int @ (plus_plus_int @ zero_zero_int @ (number_number_of_int @ A)) @ (number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[926])). 39.32/11.37 thf(824,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_power2__le__imp__le)). 39.32/11.37 thf(3526,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (power_power_real @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 39.32/11.37 thf(974,axiom,((! [A:real]: ((power_power_real @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_real @ (times_times_real @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_power3__eq__cube)). 39.32/11.37 thf(3950,plain,((! [A:real]: ((power_power_real @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (times_times_real @ (times_times_real @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[974])). 39.32/11.37 thf(844,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_zadd__assoc)). 39.32/11.37 thf(3580,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])). 39.32/11.37 thf(675,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_left__add__mult__distrib)). 39.32/11.37 thf(3096,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])). 39.32/11.37 thf(239,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_dvd_Oless__imp__le)). 39.32/11.37 thf(1848,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ B @ A) & (dvd_dvd_nat @ A @ B)) => (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 39.32/11.37 thf(1139,axiom,((! [A:int]: ((~ (zcong @ one_one_int @ (number_number_of_int @ min) @ A)) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_one__not__neg__one__mod__m)). 39.32/11.37 thf(4423,plain,((! [A:int]: (~ (zcong @ one_one_int @ (number_number_of_int @ min) @ A) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139])). 39.32/11.37 thf(1014,axiom,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit1 @ pls)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_mult__numeral__1)). 39.32/11.37 thf(4056,plain,((! [A:real]: ((times_times_real @ (number267125858f_real @ (bit1 @ pls)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])). 39.32/11.37 thf(657,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) <= (ord_less_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_power__strict__decreasing)). 39.32/11.37 thf(3047,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])). 39.32/11.37 thf(148,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => (((div_mod_int @ (div_mod_int @ A @ B) @ C) = (div_mod_int @ A @ C)) <= (dvd_dvd_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_zmod__zdvd__zmod)). 39.32/11.37 thf(1606,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ C) => (((div_mod_int @ (div_mod_int @ A @ B) @ C) = (div_mod_int @ A @ C)) | ~ (dvd_dvd_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 39.32/11.37 thf(803,axiom,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ B)) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ A) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))) @ (power_power_int @ B @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zadd__power3)). 39.32/11.37 thf(3474,plain,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) = (plus_plus_int @ (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls))))) @ B)) @ (times_times_int @ (times_times_int @ (number_number_of_int @ (bit1 @ (bit1 @ pls))) @ A) @ (power_power_int @ B @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))))) @ (power_power_int @ B @ (number_number_of_nat @ (bit1 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])). 39.32/11.37 thf(825,axiom,((! [A:int]: ((power_power_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit0 @ (bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_quartic__square__square)). 39.32/11.37 thf(3528,plain,((! [A:int]: ((power_power_int @ (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (power_power_int @ A @ (number_number_of_nat @ (bit0 @ (bit0 @ (bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 39.32/11.37 thf(1109,axiom,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ B) = (times_times_int @ (plus_plus_int @ A @ one_one_int) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 39.32/11.37 thf(4335,plain,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ B) = (times_times_int @ (plus_plus_int @ A @ one_one_int) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109])). 39.32/11.37 thf(601,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (power_power_nat @ A @ B)) <= ((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_dvd__power)). 39.32/11.37 thf(2879,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (power_power_nat @ A @ B)) | ~ ((ord_less_nat @ zero_zero_nat @ B) | (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 39.32/11.37 thf(527,axiom,((! [A:int,B:int,C:int]: (((zcong @ A @ B @ C) = ((standardRes @ C @ A) = (standardRes @ C @ B))) <= (ord_less_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_StandardRes__prop2)). 39.32/11.37 thf(2640,plain,((! [A:int,B:int,C:int]: (((zcong @ A @ B @ C) = ((standardRes @ C @ A) = (standardRes @ C @ B))) | ~ (ord_less_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])). 39.32/11.37 thf(965,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_rel__simps_I15_J)). 39.32/11.37 thf(3924,plain,((! [A:int,B:int]: ((ord_less_int @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[965])). 39.32/11.37 thf(860,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((times_times_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = (number_number_of_int @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ pls @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_semiring__mult__number__of)). 39.32/11.37 thf(3626,plain,((! [A:int,B:int]: ((ord_less_eq_int @ pls @ B) => (((times_times_int @ (number_number_of_int @ B) @ (number_number_of_int @ A)) = (number_number_of_int @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ pls @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[860])). 39.32/11.37 thf(278,axiom,((! [A:int]: ((ord_less_eq_int @ one_one_int @ A) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_int__one__le__iff__zero__less)). 39.32/11.37 thf(1945,plain,((! [A:int]: ((ord_less_eq_int @ one_one_int @ A) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 39.32/11.37 thf(741,axiom,((! [A:int,B:int]: ((member_int @ A @ (sr @ B)) => ((standardRes @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_StandardRes__SR__prop)). 39.32/11.37 thf(3299,plain,((! [A:int,B:int]: ((member_int @ A @ (sr @ B)) => ((standardRes @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 39.32/11.37 thf(98,axiom,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_eq_int @ min @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_rel__simps_I25_J)). 39.32/11.37 thf(1463,plain,((! [A:int]: ((ord_less_int @ min @ A) = (ord_less_eq_int @ min @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 39.32/11.37 thf(640,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_power__increasing__iff)). 39.32/11.37 thf(2998,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ C) => ((ord_less_eq_nat @ A @ B) = (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])). 39.32/11.37 thf(305,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ A @ C) & (ord_less_real @ zero_zero_real @ B)) | ((ord_less_real @ C @ A) & (ord_less_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_mult__less__cancel__right__disj)). 39.32/11.37 thf(2018,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ A @ C) & (ord_less_real @ zero_zero_real @ B)) | ((ord_less_real @ C @ A) & (ord_less_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 39.32/11.37 thf(596,axiom,((! [A:int,B:int]: ((zprime @ B) => (((zcong @ (times_times_int @ A @ (inv @ B @ A)) @ one_one_int @ B) <= (ord_less_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_inv__is__inv)). 39.32/11.37 thf(2866,plain,((! [A:int,B:int]: ((zprime @ B) => ((zcong @ (times_times_int @ A @ (inv @ B @ A)) @ one_one_int @ B) | ~ (ord_less_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 39.32/11.37 thf(1048,axiom,((! [A:nat]: ((times_times_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__mult__2__right)). 39.32/11.37 thf(4161,plain,((! [A:nat]: ((times_times_nat @ A @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048])). 39.32/11.37 thf(747,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_real__le__refl)). 39.32/11.37 thf(3316,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 39.32/11.37 thf(1055,axiom,((! [A:int,B:int]: ((minus_minus_int @ (bit1 @ A) @ (bit1 @ B)) = (bit0 @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_diff__bin__simps_I10_J)). 39.32/11.37 thf(4189,plain,((! [A:int,B:int]: ((minus_minus_int @ (bit1 @ A) @ (bit1 @ B)) = (bit0 @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055])). 39.32/11.37 thf(369,axiom,((! [A:int]: ((A = zero_zero_int) <= (dvd_dvd_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_dvd__0__left)). 39.32/11.37 thf(2191,plain,((! [A:int]: ((A = zero_zero_int) | ~ (dvd_dvd_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 39.32/11.37 thf(3,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((div_mod_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1187_mod__less)). 39.32/11.37 thf(1204,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((div_mod_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 39.32/11.37 thf(337,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ zero_zero_int) => (((ord_less_eq_int @ B @ zero_zero_int) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_q__neg__lemma)). 39.32/11.37 thf(2106,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ zero_zero_int) => ((ord_less_eq_int @ B @ zero_zero_int) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 39.32/11.37 thf(330,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C)) = (minus_minus_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_nat__diff__add__eq2)). 39.32/11.37 thf(2087,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ D @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ E @ A) @ C)) = (minus_minus_nat @ B @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ E @ D) @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 39.32/11.37 thf(968,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)) != (plus_plus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A))) = ((C != D) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_crossproduct__noteq)). 39.32/11.37 thf(3933,plain,((! [A:int,B:int,C:int,D:int]: ((~ ((plus_plus_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)) = (plus_plus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A)))) = (~ (C = D) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[968])). 39.32/11.37 thf(893,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__zero__right)). 39.32/11.37 thf(3721,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[893])). 39.32/11.37 thf(1053,axiom,((! [A:int,B:int,C:int]: ((zprime @ C) => ((((~ (zcong @ A @ zero_zero_int @ C)) => ((~ (zcong @ A @ (times_times_int @ B @ (multInv @ C @ A)) @ C)) <= (~ (quadRes @ C @ B)))) <= (~ (zcong @ B @ zero_zero_int @ C))) <= (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_MultInvPair__distinct)). 39.32/11.37 thf(4174,plain,((! [A:int,B:int,C:int]: ((zprime @ C) => (((~ (zcong @ A @ zero_zero_int @ C)) => (~ (zcong @ A @ (times_times_int @ B @ (multInv @ C @ A)) @ C) | (quadRes @ C @ B))) | (zcong @ B @ zero_zero_int @ C) | ~ (ord_less_int @ (number_number_of_int @ (bit0 @ (bit1 @ pls))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053])). 39.32/11.37 thf(634,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (times_times_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 39.32/11.37 thf(2980,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (times_times_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])). 39.32/11.37 thf(843,axiom,((~ (! [A:int]: ((plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int) != (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_)). 39.32/11.37 thf(3575,plain,((~ (! [A:int]: ~ ((plus_plus_int @ (power_power_int @ s @ (number_number_of_nat @ (bit0 @ (bit1 @ pls)))) @ one_one_int) = (times_times_int @ (plus_plus_int @ (times_times_int @ (number_number_of_int @ (bit0 @ (bit0 @ (bit1 @ pls)))) @ m) @ one_one_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[843])). 39.32/11.37 thf(363,axiom,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ A) => (((inv @ B @ A) != one_one_int) <= (ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)))) <= (zprime @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_inv__not__1)). 39.32/11.37 thf(2177,plain,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ A) => (~ ((inv @ B @ A) = one_one_int) | ~ (ord_less_int @ A @ (minus_minus_int @ B @ one_one_int)))) | ~ (zprime @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 39.32/11.37 thf(994,axiom,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ C @ D) => ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_mult__dvd__mono)). 39.32/11.37 thf(4002,plain,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ C @ D) => ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ (times_times_int @ C @ A) @ (times_times_int @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])). 39.32/11.37 thf(248,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) = (ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_zero__less__diff)). 39.32/11.37 thf(1870,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) = (ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 39.32/11.37 thf(874,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rel__simps_I17_J)). 39.32/11.37 thf(3669,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) = (ord_less_int @ (bit1 @ A) @ (bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])). 39.32/11.37 thf(564,axiom,((! [A:nat,B:nat,C:nat]: (((B = zero_zero_nat) | (dvd_dvd_nat @ A @ C)) = (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H)). 39.32/11.37 thf(2771,plain,((! [A:nat,B:nat,C:nat]: (((B = zero_zero_nat) | (dvd_dvd_nat @ A @ C)) = (dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 39.32/11.37 thf(4730,plain,($false),inference(cvc4,[status(thm)],[1322,4262,2463,2559,2544,3927,2822,2630,4201,2452,4560,3962,1337,1718,2612,1469,2306,4571,4101,3008,1454,1633,2778,1995,3930,4169,3666,1729,2412,2876,1237,4290,3477,3863,1850,2499,1956,1950,1686,2250,1750,2976,2210,4226,1882,3549,1618,1401,3912,2854,1486,2363,3680,2077,4043,2117,1596,1406,2231,2622,3858,3762,4515,1443,2776,1808,2659,3417,2527,3153,3460,1422,2947,1569,3959,2248,2671,3910,2282,1591,2114,2837,4215,2380,3382,4479,2686,1310,3365,4220,2316,3781,3313,1954,2146,1497,3017,4090,1655,3049,3745,3135,3942,3649,4026,3044,1275,2141,1327,3693,2627,2168,3414,3121,4247,3562,1507,2360,3276,2575,1835,3629,2348,3502,4079,3730,2886,4156,2957,3335,4047,4142,2046,3994,1914,2763,3915,3088,3777,3308,2010,1935,3947,1601,3281,3466,4198,2082,4137,1724,1475,2400,2825,1967,3878,2136,1518,1228,1623,4249,1887,2603,4563,1760,2269,2708,2501,2466,2654,1628,1409,4238,3263,4439,3425,1792,1430,4070,4151,3617,1860,2274,3485,1313,1279,4275,3410,2185,2562,4023,2488,1832,2897,4428,3855,2420,3099,3517,1609,4270,2635,2989,4390,2388,3258,3788,3840,3385,3463,1379,2403,3638,1319,1704,1890,2373,1572,3919,1741,1398,4551,3902,3657,3014,2520,2024,1641,3708,2301,1494,3557,1875,2852,3231,2007,4411,4396,1664,2090,3724,3093,1489,2237,1415,3524,3431,3887,2324,4583,1714,2027,3075,1811,1911,4600,4297,2469,1418,3453,1334,3702,3438,4050,1978,2925,3973,4134,3357,1677,2540,1581,2335,1283,2073,3771,3851,2437,3712,3685,1526,3327,2103,3870,3492,2884,4082,4033,2833,3189,2861,1215,4087,2371,4040,2002,3756,3243,2242,4038,1943,1201,2804,4519,1242,3559,3606,2154,3906,4588,1863,2954,3011,3450,2473,3567,3186,4557,3318,1708,3037,1604,3899,2922,3984,2646,3531,2164,1783,4076,2296,3054,1736,2496,4312,4059,1768,1868,2000,1636,1223,4466,3867,2133,3022,4344,2606,4493,2264,2409,1387,1900,2601,2428,3711,1343,1355,2277,1255,4375,4434,3989,4128,3371,4204,3884,1824,4284,1370,2032,2986,2890,2414,3250,3207,2396,3514,3682,3339,2015,3471,3286,1560,3271,2873,4140,1920,3718,1457,4402,1210,2213,1291,3408,3799,1365,4192,3810,4053,2433,2477,3090,2565,1555,2332,2820,3297,3499,3065,3349,3894,2068,1819,4327,3546,3144,3028,2345,3727,1281,2741,4461,1392,2228,3595,2769,2245,3699,1983,3831,1804,1375,2577,1970,2692,1425,1672,3518,3078,4012,4109,3205,3001,3482,1762,2100,1270,1259,2377,2801,1534,1794,4512,3218,4544,2858,2537,3237,1755,1964,3846,3210,2830,2868,2080,2196,1937,3194,2108,3643,1644,2798,1683,4333,1329,3141,3311,4167,1739,4425,4421,4315,3441,2172,3428,2551,1207,2085,1612,2978,2649,3294,1744,2968,1297,2845,2900,3743,1974,1552,2505,1799,3115,3333,4259,3215,1776,1263,3611,3486,3654,1588,1478,4384,1451,2304,1539,4508,2355,4482,1932,4244,3222,3540,4347,1852,2813,3967,3247,2766,1599,2697,1246,3109,3005,2272,4416,3162,4223,4535,3834,3802,4352,4567,1695,4476,1563,2748,1466,4448,2793,4036,2617,2662,3807,4148,1434,1857,1814,3225,4288,2546,2761,4195,2043,4212,3183,2057,1712,3592,1846,3999,2963,1286,3321,2368,3508,1895,2189,1616,2995,4004,2338,3675,2423,2529,2936,3660,1510,3130,4131,2677,2292,2149,2585,2717,3890,1273,4017,3696,2894,2524,3343,2391,1680,1698,1959,2556,4116,2570,1747,1548,1927,4393,3289,1301,3888,4503,4577,3536,3504,4309,1620,3458,2695,2827,3213,4341,3070,3768,1916,3636,3234,2048,4283,1389,3255,2791,3240,2657,2849,1652,3736,3945,3283,3266,2674,1701,2398,3604,4381,4590,1520,2817,4485,3051,2308,3646,1733,4413,1332,3783,2457,3302,3355,1675,1428,2161,4251,4526,3796,1786,1669,3118,3751,2029,4096,3330,2738,4171,3663,3340,1239,2442,3436,2166,1765,2573,2319,2510,3678,2311,3101,3352,3996,2637,1806,1349,2284,1492,1771,4300,2197,4498,4369,2151,3815,2383,2624,2774,3515,3779,2906,4586,2839,4073,1801,4176,3138,1690,3586,2871,1439,4430,1877,4541,2314,2267,3572,2446,3165,3192,4296,3583,2553,1688,1667,2180,4445,2610,3133,4009,4103,1557,2111,3073,1993,4064,1630,2261,1731,4264,3034,1325,3614,2542,1460,2289,2252,3861,2928,1381,2461,2974,2329,2842,1952,3893,4554,2075,2725,2171,3159,2931,3953,2633,3325,4304,2156,2207,3908,4084,1841,2439,4232,2350,1213,3759,2051,3423,1445,1528,2139,3687,1726,1250,4209,1973,4158,3881,1626,2614,1873,3936,3395,2471,2037,3146,2449,3975,4355,2582,3849,2054,4207,1948,3444,2239,3031,1583,4458,2665,3672,1905,1420,3981,2503,1277,2124,2234,3921,1340,3455,1472,3278,4581,2567,2715,1961,4360,3112,2375,3082,1252,1753,3872,2689,4045,2942,2298,3391,3737,3376,3640,1516,2863,1225,4366,2060,4272,1566,2143,2012,3904,3260,3754,1368,3228,4469,1780,1531,4324,3608,1230,4593,2888,3019,4409,2092,3273,4020,3554,3202,1235,4145,3623,3359,4117,1716,2454,3305,1432,3818,3774,1830,3127,1658,2322,2486,4241,2903,1218,3041,3853,4164,3715,3107,3970,4436,4106,2579,4538,1797,4267,2939,1372,4516,4217,1404,1358,1898,1257,3124,2426,2992,1981,1221,4488,2279,4510,2357,3388,1504,4235,1585,4093,2949,2722,2807,3156,4257,3398,2435,3589,3067,4419,1844,2194,1412,2215,1866,4061,3039,3168,1940,3433,4548,4289,4278,1839,3620,1918,1316,1649,3565,3401,1817,2960,3533,3447,2743,1448,2490,2187,3346,2919,2342,1575,4463,3056,2643,1998,4574,1646,4121,2174,2098,2532,1481,3748,2971,2431,3368,3252,2934,2594,1721,1903,2406,2811,3104,2004,1854,4338,1244,1822,4495,1523,2394,3085,2944,3978,4293,4321,4153,1706,1513,1661,2120,2095,4372,3181,2475,3598,1294,4387,2066,3793,2680,2183,1893,2294,4098,4570,4306,3552,3420,1614,2287,2683,3705,3291,3601,1546,2522,3521,1248,3379,3992,1908,2123,2258,4014,1578,4472,4399,2385,3785,3511,4378,3232,2534,2255,2983,2719,4254,3733,1395,3987,3373,1593,3837,2951,4523,2815,1303,1986,3790,3337,4357,3496,4491,1757,4579,3690,4455,3062,1436,3956,4029,3897,4350,4281,1789,2366,3323,4442,2619,2040,3875,4474,4007,2746,1693,2070,3479,2417,1288,1710,2795,3633,2340,2668,3506,3843,2021,1346,2063,3805,2651,4318,2549,2847,1550,4506,2507,4229,1299,3076,4501,1399,4363,1930,2353,2159,3362,1352,3974,3025,1827,1261,2966,3543,3570,1384,1537,4484,3489,1500,3965,1923,3538,1925,4330,3939,3740,1880,2484,1885,2699,3812,3526,3950,3580,3096,1848,4423,4056,3047,1606,3474,3528,4335,2879,2640,3924,3626,1945,3299,1463,2998,2018,2866,4161,3316,4189,2191,1204,2106,2087,3933,3721,4174,2980,3575,2177,4002,1870,3669,2771])). 39.32/11.37 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.32/11.37 % [INFO] Killing All external provers ... 39.32/11.37 FINAL WATCH: 39.2 CPU 11.3 WC 39.32/11.37 EOF