0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : java -Xss128m -Xmx4g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar %s -t %d -p --atp cvc4=/export/starexec/sandbox2/solver/bin/externals/cvc4 --atp e=/export/starexec/sandbox2/solver/bin/externals/eprover --atp iprover=/export/starexec/sandbox2/solver/bin/externals/iprover 0.03/0.29 % Computer : n149.star.cs.uiowa.edu 0.03/0.29 % Model : x86_64 x86_64 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.29 % Memory : 32218.625MB 0.03/0.29 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.29 % CPULimit : 300 0.03/0.29 % DateTime : Sat Jul 14 05:17:55 CDT 2018 0.03/0.29 % CPUTime : 31.73/11.41 % [INFO] Running in sequential loop mode. 32.50/11.62 % [CONFIG] Using configuration: timeout(300) with strategy 32.68/11.70 % [INFO] iprover registered as external prover. 32.68/11.70 % [INFO] e registered as external prover. 32.68/11.71 % [INFO] cvc4 registered as external prover. 32.68/11.71 % [INFO] Parsing finished. Scanning for conjecture ... 33.41/11.88 % [INFO] Found a conjecture and 5479 axioms. Running axiom selection ... 41.51/14.53 % [INFO] Axiom selection finished. Selected 4947 axioms (removed 532 axioms). 46.00/16.28 % [INFO] Type checking passed. Searching for refutation ... 115.67/52.93 % [INFO] Killing All external provers ... 115.67/52.94 % Time passed: 52554ms 115.67/52.94 % Effective reasoning time: 41523ms 115.67/52.94 % Solved by strategy 115.68/52.97 % Axioms used in derivation (4947): fact_1958_diff__eq__diff__eq, fact_1293_power__eq__0__iff, fact_1976_double__zero__sym, fact_388_semiring__norm_I110_J, fact_4144_sin__n__Im__cis__pow__n, fact_1765_less__diff__conv, fact_2117_mult__1, fact_2192_zero__less__double__add__iff__zero__less__single__add, fact_4400_real__of__int__abs, fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_5007_divides__mult__int, fact_2374_mod__0, fact_4225_div__neg__pos, fact_3485_abs__le__interval__iff, fact_3113_power__le__imp__le__base, fact_3842_exp__gt__one, fact_2604_nonneg1__imp__zdiv__pos__iff, fact_5092_bset_I8_J, fact_1879_add__strict__increasing2, fact_1258_less__add__one, fact_1599_nat__le__linear, fact_3552_zdiv__zminus2__eq__if, fact_4141_Re_Ononneg__bounded, fact_4011_coprime__mul, fact_1319_mult__left__le__imp__le, fact_4569_div__code__int__def, fact_3090_even__power, fact_1064_mult__mono_H, fact_3114_power__le__imp__le__base, fact_3386_natfloor__mono, fact_1917_add__imp__eq, fact_2296_mult_Oadd__left, fact_3178_lemma__realpow__diff, fact_2398_zmod__simps_I4_J, fact_919_dvd__triv__right, fact_1436_power__0__left, fact_2155_add__increasing, fact_4975_gcd__zero__int, fact_223_sum__power2__le__zero__iff, fact_1681_unity__coeff__ex, fact_2383_mod__mult__left__eq, fact_3877_DERIV__real__sqrt, fact_5157_increasing__LIMSEQ, fact_3298_nat__number__of__add__1, fact_2066_add__less__cancel__left, fact_4394_real__number__of, fact_3964_complex__diff, fact_1116_mult__le__0__iff, fact_443_zprime__zdvd__power, fact_4562_minus__code__int__def, fact_2076_right__minus__eq, fact_2501_mod__by__1, fact_4466_real__of__int__div__aux, fact_837_mult__eq__0__iff, fact_326_add__numeral__0__right, fact_3758_even__zero__nat, fact_754_zprime__zdvd__zmult, fact_811_zcong__trans, fact_3802_fact__mono__nat, fact_3620_tan__30, fact_3141_zero__code__numeral__code, fact_3561_cos__minus, fact_117_semiring__norm_I113_J, fact_3755_odd__add, fact_4110_complex__inverse__def, fact_2037_add__less__imp__less__left, fact_1968_add__0__right, fact_1360_mult__less__le__imp__less, fact_1211_zero__le__one, fact_3273_not__neg__number__of__Pls, fact_1109_mult__nonneg__nonpos, fact_4587_card__nor__eq__noX, fact_2998_zle__int, fact_4838_sum2sq__def, fact_3732_sin__monotone__2pi_H, fact_1242_zero__le__power, fact_523_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_170_number__of__reorient, fact_4026_divides__mul, fact_3826_INVERSE__ZERO, fact_1254_zero__less__power, fact_3855_real__inv__sqrt__pow2, fact_1670_mult__less__cancel2, fact_2456_dvd__mod__imp__dvd, fact_2119_mult__1__left, fact_3204_Suc__nat__eq__nat__zadd1, fact_2810_of__nat__double, fact_1226_zero__less__one, fact_1184_mult__pos__neg, fact_157_add1__zle__eq, fact_2274_pinf_I9_J, fact_303_power2__eq__square, fact_4833_rat__floor__code, fact_4216_divmod__nat__eq, fact_1389_mult__right__le__one__le, fact_379_semiring__numeral__1__eq__1, fact_2075_add__less__cancel__right, fact_1478_power__strict__decreasing, fact_307_even__less__0__iff, fact_1296_power__0, fact_797_dvd__refl, fact_830_no__zero__divisors, fact_2021_add__right__mono, fact_1508_zprime__factor__exists, fact_731_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_1982_add__0, fact_1635_less__imp__le__nat, fact_1402_power__decreasing, fact_4353_gcd__mult__cancel__nat, fact_3935_real__root__pos__unique, fact_2897_EvenOdd_Oeven__plus__even, fact_3886_DERIV__local__const, fact_1502__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_2660_split__zmod, fact_4391_real__of__int__power, fact_2050_add__strict__mono, fact_2840_of__nat__Suc, fact_2490_StandardRes__prop1, fact_4348_gcd__add__mult__nat, fact_1515_nat__dvd__1__iff__1, fact_2921_of__nat__less__0__iff, fact_4335_gcd__lcm__complete__lattice__nat_Oinf__bot__left, fact_4525_zcong__cancel, fact_247_double__eq__0__iff, fact_2986_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_4539_make__zrelprime, fact_123_le__special_I2_J, fact_1198_mult__less__cancel__right__disj, fact_3409_natceiling__add__one, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_013, fact_733_q__neg__lemma, fact_2489_odd__mult__odd__prop, fact_3174_lemma__realpow__diff, fact_1678_unity__coeff__ex, fact_3306_MultInvPair__prop2, fact_3739_minus__sin__cos__eq, fact_2088_diff__0__right, fact_1405_power__decreasing, fact_1754_le__diff__iff, fact_1260_less__add__one, fact_4473_log__powr, fact_2560_div__mult__div__if__dvd, fact_2122_mult__1__left, fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_1133_comm__mult__strict__left__mono, fact_4681_rat__number__of__def, fact_4976_gcd__exp__int, fact_1253_zero__less__power, fact_2321_negDivAlg__eqn__1__number__of, fact_3788_lemma__even__div2, fact_2209_le__iff__diff__le__0, fact_3269_not__neg__int, fact_4443_number__of__less__real__of__int__iff, fact_2515_dvd__imp__mod__0, fact_1031_zcong__zmult__self, fact_5005_coprime__dvd__mult__int, fact_4534_zcong__lineq__ex, fact_867_combine__common__factor, fact_2441_dvd__mod__iff, fact_557_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_655_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_2789_zmult2__lemma, fact_2580_div__add, fact_4155_bezw__0, fact_1650_add__mult__distrib2, fact_5184_max__number__of__Suc, fact_1624_not__add__less1, fact_2442_dvd__mod__iff, fact_3547_neg__zminus__int, fact_2971_of__nat__1, fact_2472_div__by__0, fact_1141_mult__strict__left__mono, fact_5193_max__Suc__Suc, fact_3756_even__add, fact_4366_coprime__minus__one__nat, fact_3167_nat__eq__iff, fact_2143_add__nonpos__nonpos, fact_3002_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_2853_Zero__not__Suc, fact_273_double__number__of__Bit0, fact_2123_mult__1__left, fact_5187_lessThan__Suc__atMost, fact_1231_not__one__less__zero, fact_159_semiring__add__number__of, fact_3418_zdvd__antisym__abs, fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_4663_rat__zero__code, fact_1994_add__le__imp__le__left, fact_4561_plus__code__int__def, fact_1159_mult__less__cancel__left__neg, fact_626_crossproduct__noteq, fact_3365_real__average__minus__first, fact_2085_diff__self, fact_3542_zabs__def, fact_3140_mod__mult__self4, fact_1931_add__right__cancel, fact_1723_dvd_Oless__imp__triv, fact_2313_gcd__lcm__complete__lattice__nat_Obot__least, fact_1896_zero__reorient, fact_2758_Suc__n__div__2__gt__zero, fact_868_combine__common__factor, fact_3127_n__less__n__mult__m, fact_2756_MultInv__def, fact_862_one__neq__zero, fact_4214_divmod__nat__rel__add1__eq, fact_2172_double__add__le__zero__iff__single__add__le__zero, fact_1859_add__pos__nonneg, fact_1780_nat__diff__split__asm, fact_1794_divides__mul__l, fact_3610_tan__periodic, fact_612_add__0__iff, fact_1791_real__mult__less__mono2, fact_3585_cos__30, fact_4339_gcd__0__nat, fact_2052_add__strict__left__mono, fact_477_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_2736_mod__lemma, fact_1477_power__strict__decreasing, fact_956_dvd__mult__right, fact_4175_prime__dvd__power, fact_1199_mult__less__cancel__right__disj, fact_2020_add__right__mono, fact_272_double__number__of__Bit0, fact_3367_real__sum__of__halves, fact_4699_one__real__code, help_fequal_1_1_fequal_000tc__Rat__Orat_T, fact_2240_MultInv__prop2, fact_1173_mult__pos__neg2, fact_4185_divides__primepow, fact_3089_exp__mono__le, fact_4263_Im__rcis, fact_3201_expand__Suc, fact_3520_uminus__dvd__conv_I1_J, fact_4501_zgcd__geq__zero, fact_4316_dvd__gcd__D2__nat, fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_339_add__number__of__eq, fact_124_nat__1__add__1, fact_4298_gcd__dvd2__nat, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___023, fact_3915_real__root__inverse, fact_3506_arcsin__lt__bounded, fact_2574_dvd__mult__div__cancel, fact_5155_bijzcong__zcong__prod, fact_2643_dvd__div__eq__mult, fact_3429_ln__less__cancel__iff, fact_1591_nat__add__commute, fact_2100_mult_Ocomm__neutral, fact_1273_power__increasing, fact_3807_fact__less__mono__nat, fact_459_zprime__2, fact_3435_zero__le__zpower__abs, fact_937_mult__dvd__mono, fact_2173_double__add__le__zero__iff__single__add__le__zero, fact_4274_fact__less__mono__int, fact_2508_mod__mult__self2, fact_1069_mult__right__mono__neg, fact_1034_zcong__scalar, fact_1114_mult__nonneg__nonneg, fact_1464_convex__bound__le, fact_3859_reals__Archimedean, fact_54_zmult__commute, fact_3498_ln__one__minus__pos__upper__bound, fact_3166_nat__eq__iff2, fact_2638_dvd__div__div__eq__mult, fact_3936_real__root__pow__pos, fact_1467_power__Suc__less, fact_5181_lemma__isCont__inj2, fact_2925_of__nat__0, fact_329_add__numeral__0__right, fact_546_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_3675_le__natfloor, fact_1107_mult__nonneg__nonpos, fact_456_zdvd__mult__cancel, fact_3976_complex__i__not__one, fact_2735_split__mod, fact_1680_unity__coeff__ex, fact_2593_StandardRes__prop3, fact_2709_ex__nat, fact_374_number__of__Bit0, fact_1143_mult__strict__right__mono, fact_1749_diff__le__mono2, fact_292_semiring__mult__2__right, fact_2624_div__mult__self2, fact_911_dvd__triv__left, fact_1127_mult__strict__left__mono__neg, fact_1924_add__left__imp__eq, fact_1135_comm__mult__strict__left__mono, fact_2659_zmult2__lemma__aux3, fact_32_zero__power2, fact_1801_realpow__minus__mult, fact_4988_gcd__abs2__int, fact_5096_aset_I3_J, fact_1030_zcong__1, fact_4458_real__of__int__ceiling__diff__one__le, fact_4115_complex__Re__cnj, gsy_c_Code__Numeral_Oint__of, fact_2514_dvd__imp__mod__0, fact_4235_mod__pos__pos, fact_2270_pinf_I9_J, fact_1805_power__eq__if, fact_42_add__special_I2_J, fact_1942_add__left__cancel, fact_2121_mult__1__left, help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_, fact_1669_mult__less__cancel1, fact_2130_inv__distinct, fact_519_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_3385_zero__le__natfloor, fact_2573_dvd__mult__div__cancel, fact_2479_div__by__1, fact_3654_power__real__of__nat, fact_1400_power__less__imp__less__base, fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_3651_real__of__nat__mult, fact_1632_add__lessD1, fact_3373_arctan__half, fact_2029_add__le__cancel__right, fact_4271_fact__int__def, fact_2366_mod__self, fact_1295_power__eq__0__iff, fact_1220_not__one__le__zero, fact_3274_neg__number__of__Bit0, fact_1677_unity__coeff__ex, fact_2461_zmod__simps_I3_J, fact_1382_mult__le__cancel__left__pos, fact_1163_zero__less__mult__pos2, fact_2858_less__trans__Suc, fact_1186_mult__pos__pos, fact_3683_cos__diff, fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_252_rel__simps_I49_J, fact_244_mult__Bit1, fact_4951_atLeast0LessThan, fact_4505_zgcd__1__power__distrib, fact_2586_split__pos__lemma, fact_1707_dvd_Ole__imp__less__or__eq, fact_2404_mod__mult__cong, fact_113_rel__simps_I27_J, fact_1855_is__sum2sq__def, fact_3218_of__nat__number__of__lemma, fact_3350_real__sqrt__sum__squares__ge__zero, help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_3051_add__is__1, fact_3838_real__mult__inverse__cancel2, fact_3008_power__Suc2, fact_968_dvd__add, fact_2675_mod__div__decomp, fact_3238_even__prod__div__2, fact_5097_aset_I4_J, fact_1587_less__irrefl__nat, fact_4099_complex__Im__number__of, fact_3360_real__0__le__divide__iff, fact_2359_zdiv__zmult1__eq, fact_2863_Suc__less__eq, fact_1445_power__less__imp__less__exp, fact_2157_add__increasing, fact_901_power__commutes, fact_3942_DERIV__real__root, fact_4704_real__divide__code, fact_1998_add__le__imp__le__right, fact_1072_comm__mult__left__mono, fact_921_dvd__mult2, fact_392_odd__less__0, fact_2262_minf_I9_J, fact_4653_rat__sgn__code, fact_3150_odd__minus__one__even, fact_1320_mult__left__le__imp__le, fact_1869_add__strict__increasing, fact_5191_max__0R, fact_1170_zero__less__mult__pos, fact_717_power__eq__0__iff__number__of, fact_4065_complex__cnj__zero__iff, fact_4465_real__of__int__div3, fact_4779_eq__number__of__Suc, fact_2424_mod__add__left__eq, fact_1085_mult__right__mono, fact_3522_zdiv__zminus2, fact_4446_int__less__real__le, fact_934_mult__dvd__mono, fact_390_semiring__norm_I110_J, fact_360_power2__eq__square__number__of, fact_1817_mult__diff__mult, fact_2311_gcd__lcm__complete__lattice__nat_Otop__le, fact_1039_zcong__zpower, fact_1006_le__imp__power__dvd, fact_3242_neg__one__power__parity, fact_1763_diff__is__0__eq, fact_2910_of__nat__0__le__iff, fact_4192_divmod__int__correct, fact_769_rel__simps_I37_J, fact_4030_coprime__exp2, fact_5170_isCont__root__neg, fact_2631_div__add__self1, fact_2678_Euler__part1, fact_972_power__one, fact_1375_mult__strict__mono, fact_331_less__number__of, fact_1500_neg__one__power__eq__mod__m, fact_984_dvd__power__same, fact_1729_real__zero__not__eq__one, fact_4596_Bnor__in__RsetR, fact_3594_tan__double, fact_1174_mult__pos__neg2, fact_1645_add__le__mono1, fact_183_left__distrib__number__of, fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_3142_of__nat__0__less__iff, fact_774_rel__simps_I24_J, fact_1095_mult__nonpos__nonneg, fact_5140_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J, fact_5183_SetInterval_Otransfer__nat__int__set__functions_I1_J, fact_3444_ln__less__zero, fact_598_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_1063_mult__mono_H, fact_3015_power__Suc, fact_5093_aset_I7_J, fact_4556_of__int__int__of, fact_4033_floor__minus__real__of__nat, fact_71_zadd__left__mono, fact_1935_add__right__cancel, fact_748_power__strict__mono, fact_2445_mod__mod__cancel, fact_2179_add__neg__neg, fact_4948_BseqI2, fact_3762_real__of__nat__fact__not__zero, fact_4644_Frct__code__post_I3_J, fact_534_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_153_int__one__le__iff__zero__less, fact_3171_Suc3__eq__add__3, gsy_c_Archimedean__Field_Oceiling_000tc__RealDef__Oreal, fact_3389_natceiling__zero, fact_1814_nat__power__eq__0__iff, fact_4697_Ratreal__number__collapse_I3_J, fact_185_left__distrib__number__of, fact_86_arith__simps_I32_J, fact_383_semiring__numeral__1__eq__1, fact_4971_coprime__minus__one__int, fact_750_convex__bound__lt, fact_365_power2__eq__square__number__of, fact_3853_exp__ge__add__one__self__aux, fact_3062_Suc__le__eq, fact_4553_mod__code__int__def, fact_707_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_1297_power__0, fact_4102_complex__Im__of__nat, fact_4673_rat__number__collapse_I1_J, fact_2103_mult_Ocomm__neutral, fact_1722_dvd_Oless__imp__not__eq2, fact_2662_div__pos__neg__trivial, fact_3507_arcsin__bounded, fact_510_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_3162_power__Suc__less__one, fact_1166_zero__less__mult__pos2, fact_2935_less__imp__of__nat__less, fact_776_rel__simps_I9_J, fact_870_combine__common__factor, fact_1809_add__diff__add, fact_389_semiring__norm_I110_J, fact_1449_power__less__imp__less__exp, fact_4273_fact__1__int, fact_4494_zgcd__left__commute, fact_1553_diff__bin__simps_I10_J, fact_820_order__le__neq__implies__less, fact_2251_minf_I10_J, fact_2668_negDivAlg__eqn__number__of, fact_155_Numeral1__eq1__nat, fact_2774_nat__mod__eq__lemma, fact_2990_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_3358_SetS__elems__finite, fact_2071_add__less__cancel__right, fact_3434_dvd__imp__le__int, fact_2547_div__mult__self2__is__id, fact_2412_zmod__simps_I1_J, fact_3993_complex__of__real__add__Complex, fact_999_dvd__power__le, fact_3048_less__Suc0, fact_4281_fact__gt__zero__int, fact_1343_mult__less__imp__less__right, fact_3858_lemma__exp__total, fact_25_one__power2, fact_88_number__of__mult, fact_1160_mult__less__cancel__left__neg, fact_1384_mult__left__le__one__le, fact_4435_powr__divide, fact_2541_div__mult__self1__is__id, fact_1876_add__strict__increasing2, fact_2836_Suc__n__not__n, fact_3748_reals__Archimedean6, fact_1489_one__less__power, fact_1561_le__add__iff1, fact_3415_machin, fact_3847_exp__ln__iff, fact_2545_div__mult__self2__is__id, fact_2540_div__mult__mult2, fact_1136_comm__mult__strict__left__mono, fact_2016_add__right__mono, fact_4922_image__add__int__atLeastLessThan, fact_4441_real__of__int__le__zero__cancel__iff, fact_4194_prime__divprod__pow, fact_3601_tan__periodic__n, fact_384_numeral__1__eq__1, fact_1895_zero__reorient, fact_4727_one__le__Fract__iff, fact_2622_div__mult__self1, fact_3988_complex__of__real__def, fact_4217_divmod__nat__rel__divmod__nat, fact_1112_mult__nonneg__nonneg, fact_2203_add__less__le__mono, fact_2392_mod__mult__mult1, fact_4014_coprime__1, fact_347_rel__simps_I16_J, fact_2795_divmod__int__rel__div, fact_2650_StandardRes__prop2, fact_5008_gcd__cases__int, fact_236_mult__numeral__1, fact_1727_dvd_Oless__trans, fact_2447_mod__mod__cancel, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___024, fact_2162_add__nonneg__eq__0__iff, fact_1509_not__real__square__gt__zero, fact_4272_fact__mono__int, fact_2352_div__mod__equality2, fact_3216_of__nat__less__two__power, fact_2113_mult__1, fact_995_power__le__dvd, fact_39_zero__eq__power2, fact_498_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_1430_power__gt1__lemma, fact_2133_add__diff__cancel, fact_3387_natfloor__number__of__eq, fact_1007_le__imp__power__dvd, fact_2687_mult__div__cancel, fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_5145_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J, 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fact_3558_arctan__inverse, fact_2170_add__nonneg__nonneg, fact_1324_mult__right__le__imp__le, fact_1266_dvd__mult__cancel__left, fact_3026_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_555_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_2558_div__mult__div__if__dvd, fact_3551_nat__mult__distrib__neg, fact_891_dvd__0__left, fact_3894_DERIV__real__root__generic, fact_218_power2__less__imp__less, fact_2903_even__odd__conj, fact_177_rel__simps_I51_J, fact_3197_add__2__eq__Suc, help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_001, fact_1225_zero__less__one, fact_969_power__one, fact_3678_natfloor__power, fact_3067_mult__Suc, fact_4517_zrelprime__zdvd__zmult, fact_503_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_96_sum__squares__ge__zero, fact_4154_cis__real__of__nat__Suc__mult, fact_3279_eq__nat__number__of, fact_2960_of__nat__mult, fact_3265_gr0__implies__Suc, fact_2418_mod__add__eq, 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fact_3293_succ__Bit0, fact_3010_power__Suc2, fact_2764_StandardRes__SRStar__prop1, fact_3170_numeral__1__eq__Suc__0, fact_2600_neg__imp__zdiv__nonneg__iff, help_fEx_1_1_fEx_000tc__Int__Oint_U, fact_3524_zmod__zminus2, fact_3019_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_2439_mod__diff__left__eq, fact_2026_add__le__cancel__left, fact_4679_Fract__of__int__eq, fact_5119_min__number__of__Suc, fact_4213_divmod__nat__rel__mult2__eq, fact_3740_arcsin__sin, fact_2128_inv__not__p__minus__1, fact_1015_power__mult, fact_1493_dvd__power, fact_983_dvd__power__same, fact_1864_add__nonneg__pos, fact_3353_not0__implies__Suc, fact_4254_code__int_Oint__of__inject, fact_1241_zero__le__power, fact_1706_dvd_Oantisym__conv, fact_2015_add__left__mono, fact_1701_dvd_Oless__le, fact_1586_linorder__neqE__nat, fact_2448_mod__mod__cancel, fact_1682_number__of2, fact_1718_dvd_Oless__not__sym, fact_556_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_2907_zero__le__imp__of__nat, fact_1922_add__left__imp__eq, fact_4346_gcd__le2__nat, fact_4176_prime__exp, fact_2316_gcd__lcm__complete__lattice__nat_Ole__bot, fact_2569_div__mult__swap, fact_1081_mult__left__mono, fact_2874_le__SucE, fact_1775_le__add__diff__inverse, fact_3674_real__natfloor__le, fact_3575_real__sgn__def, fact_1084_mult__right__mono, fact_4010_coprime__rmul2, fact_1721_dvd_Oless__imp__not__eq, fact_3933_real__root__pos2, fact_2480_div__by__1, fact_2261_minf_I9_J, fact_2492_mod__mult__self1__is__0, fact_2896_EvenOdd_Oeven__product, fact_2380_mod__mult__right__eq, fact_2149_add__increasing2, fact_441_s1, fact_4403_powr__ge__pzero, fact_863_one__neq__zero, fact_1192_mult__less__cancel__left__pos, fact_4019_coprime__exp, fact_963_dvd__add, fact_710_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_4002_complex__split__polar, fact_1847_nat__mult__less__cancel1, fact_17_power2__less__0, fact_1995_add__le__imp__le__left, fact_294_semiring__mult__2__right, 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fact_3227_even__def, fact_3320_real__sqrt__eq__1__iff, fact_4970_coprime__plus__one__int, fact_2865_not__less__eq, fact_78_semiring__mult__number__of, fact_3738_sin__3over2__pi, fact_3839_real__mult__inverse__left, fact_1828_realpow__pos__nth, fact_1648_add__leD1, fact_4367_divides__mult__nat, fact_3669_sin__periodic__pi2, fact_3713_add__tan__eq, fact_5104_bset_I9_J, fact_266_Bit0__def, fact_3676_natceiling__le, fact_2027_add__le__cancel__left, fact_2924_of__nat__0, fact_4566_fact_Osimps_I2_J, fact_4168_prime__g__zero, fact_642_crossproduct__eq, fact_4104_complex__In__mult__cnj__zero, fact_2946_of__nat__less__iff, fact_4560_times__code__int__def, fact_3406_real__sqrt__ge__abs1, fact_4642_Frct__code__post_I2_J, fact_4752_diff__nat__eq__if, fact_3053_mult__eq__1__iff, fact_3626_tan__total__pos, fact_3852_ln__inverse, fact_508_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_1518_dvd__diff, fact_341_number__of__add, fact_1704_dvd_Oneq__le__trans, fact_2538_div__mult__mult2, fact_2626_div__mult__self2, fact_5024_quotient__of__unique, fact_3207_div__Suc__eq__div__add3, fact_975_power__one, fact_1747_diff__add__inverse2, fact_4772_noXRRset__def, fact_4643_Frct__code__post_I1_J, fact_3426_int__nat__abs, fact_62_zle__trans, fact_1045_split__mult__neg__le, fact_3812_dvd__fact__nat, fact_766_rel__simps_I47_J, fact_4347_coprime__Suc__nat, fact_1842_diff__commute, fact_2899_even__minus__even, fact_1674_zdvd__mono, fact_1005_le__imp__power__dvd, fact_4352_coprime__mul__eq__nat, fact_367_power2__sum, fact_1091_mult__nonpos__nonpos, fact_465_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_4028_coprime, gsy_c_Quickcheck__Narrowing_Oint__of, fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_4372_coprime__Suc__0__nat, fact_3268_not__neg__1, fact_2411_zmod__simps_I1_J, fact_3540_negative__zle__0, fact_50_p, fact_1492_dvd__power, fact_2449_dvd__mod, fact_4786_le__number__of__Suc, fact_2156_add__increasing, fact_744_power__strict__mono, fact_4307_gcd__semilattice__nat_Oinf_Oleft__idem, fact_3757_even__sum__nat, fact_4177_coprime__prime, fact_1167_zero__less__mult__pos, fact_2520_div__neg__pos__less0, fact_3848_exp__ln, fact_213_power2__le__imp__le, fact_3929_real__root__pos__pos, fact_4655_quotient__of__inject__eq, fact_2843_of__nat__Suc, fact_2744_nat__add__distrib, fact_2745_transfer__nat__int__relations_I4_J, fact_2982_of__nat__power, fact_4123_complex__Re__one, fact_2333_mod__div__trivial, fact_4604_transfer__int__nat__set__return__embed, fact_2107_mult__1__right, fact_3614_tan__gt__zero, fact_1970_add__0__right, fact_377_number__of__Bit1, fact_785_rel__simps_I28_J, fact_129_zmult__1, fact_3270_neg__def, fact_705_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_3030_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_4341_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff, fact_2163_add__nonneg__eq__0__iff, fact_2769_posDivAlg__eqn, fact_2281_mult_Oprod__diff__prod, fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_1208_pos__add__strict, fact_683_zero__le__even__power_H, fact_2364_mod__self, fact_2247_minf_I10_J, fact_2994_power__0__Suc, fact_2828_of__nat__eq__iff, fact_4567_fact__le, fact_2694_mod__mult__distrib2, fact_3307_real__lbound__gt__zero, fact_4118_complex__Re__le__cmod, fact_1442_power__strict__increasing, fact_3064_less__eq__Suc__le, fact_166_eq__number__of, fact_1422_power__less__power__Suc, fact_3291_succ__Pls, fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_4549_DERIV__nonpos__imp__nonincreasing, fact_4503_zgcd__zmult__distrib2__abs, fact_2927_of__nat__0, fact_1086_mult__right__mono, fact_4636_iszero__rat, fact_2536_div__mult__mult1, fact_4083_complex__cnj, fact_3075_zdiv__int, fact_2760_Int2_Oaux__1, fact_2009_add__mono, fact_883_field__power__not__zero, fact_3923_real__root__le__1__iff, fact_2216_MultInvPair__distinct, 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fact_3474_abs__ln__one__plus__x__minus__x__bound__nonneg, fact_2809_of__nat__double, fact_3042_int__1, fact_3549_not__zle__0__negative, fact_3283_power__nat__number__of__number__of, fact_3736_sin__less__zero, fact_3339_real__sqrt__two__gt__one, fact_1390_zero__less__two, fact_2908_zero__le__imp__of__nat, fact_51_qf1pt, fact_1759_diff__less, fact_1140_mult__strict__left__mono, fact_4117_complex__eqI, fact_4037_coprime__bezout__strong, fact_2108_mult__1__right, fact_4226_div__pos__pos, fact_3916_real__root__ge__0__iff, fact_4418_real__le__floor, fact_4079_complex__cnj__divide, fact_254_rel__simps_I38_J, fact_2077_right__minus__eq, fact_2110_mult__1__right, fact_1793_real__mult__le__cancel__iff1, fact_4490_zgcd0, fact_2696_nat__div__distrib, fact_1050_split__mult__pos__le, fact_3130_prod__mn__less__k, fact_3553_zdiv__zminus1__eq__if, fact_4031_coprime__minus1, fact_2584_div__power, fact_2623_div__mult__self1, fact_5122_min__0R, 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fact_1984_add__0, fact_1705_dvd_Oeq__refl, fact_2465_Residues_Oaux, fact_4088_cnj_Obounded, fact_743_pos2, fact_1417_power__increasing__iff, fact_4558_number__of__code__int__def, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J, fact_496_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_30_zero__power2, fact_1416_power__increasing__iff, fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_530_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_3766_even__nat__def, fact_3280_nat__number__of__add__left, fact_1022_power__one__right, fact_145_Collect__def, fact_1164_zero__less__mult__pos2, fact_2570_div__mult__swap, fact_2078_right__minus__eq, fact_4433_powr__le__cancel__iff, fact_1054_mult__mono, fact_3572_cos__monotone__0__pi, fact_2665_negDivAlg__minus1, fact_3240_even__sum__div__2, fact_1292_power__eq__0__iff, fact_4687_eq__rat_I1_J, fact_2891_even__sum, fact_4260_cis__rcis__eq, fact_4210_divmod__nat__base, fact_846_mult__zero__left, fact_3154_realpow__Suc__le__self, fact_4173_prime__divexp__n, fact_4084_complex__cnj__i, fact_971_power__one, fact_15_sum__power2__eq__zero__iff, fact_2332_mod__div__trivial, fact_2350_div__mod__equality2, fact_255_Bit0__Pls, fact_4159_termination__basic__simps_I5_J, fact_2091_diff__0__right, fact_202_power2__eq__imp__eq, fact_59_le__number__of, fact_128_zmult__1__right, fact_3780_odd__nat__div__two__times__two__plus__one, fact_264_add__Pls, fact_2408_mod__add__cong, fact_4993_gcd__proj2__if__dvd__int, fact_4584_complex__number__of__def, fact_3767_real__of__nat__fact__ge__zero, fact_1698_dvd_Oless__irrefl, fact_2079_right__minus__eq, fact_3190_realpow__two__diff, fact_2388_mod__mult__eq, fact_4571_weak__decr__stable, fact_1286_power__inject__exp, fact_3475_best__odd__division__abs, fact_2680_posDivAlg__eqn__1__number__of, fact_4813_SetS__setprod__prop, fact_3603_arccos__cos, fact_605_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_1886_add__neg__nonpos, fact_1961_add_Ocomm__neutral, fact_2405_mod__add__cong, fact_2139_inv__not__0, fact_132_zadd__zmult__distrib2, fact_4414_powr__minus, fact_1588_less__not__refl2, fact_2685_div__mult1__eq, fact_1000_dvd__power__le, fact_1843_mult__sum2sq, fact_2186_add__pos__pos, fact_5029_zOdd__def, fact_1639_le__add2, fact_726_power__0__left__number__of, fact_2264_minf_I9_J, fact_3617_tan__monotone_H, fact_1041_power__m1__even, fact_2641_dvd__div__eq__mult, fact_2265_d22set__le__swap, fact_3998_cmod__complex__polar, fact_3321_real__sqrt__one, fact_2975_int__eq__0__conv, fact_1696_dvd_Oorder__refl, fact_3093_even__plus__odd__prop1, fact_3782_pos__int__even__equiv__nat__even, fact_2895_even__times__either, fact_239_mult__numeral__1__right, fact_1572_dvd__mult__cancel1, fact_3856_exp__bound, fact_5158_isCont__ln, fact_2248_minf_I10_J, fact_2257_pinf_I10_J, fact_246_double__eq__0__iff, fact_2837_n__not__Suc__n, fact_1158_mult__less__cancel__left__neg, fact_1565_le__add__iff2, fact_3851_inv__real__of__nat__fact__gt__zero, fact_2228_MultInv__prop1, fact_5020_transfer__nat__int__gcd_I1_J, fact_529_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_1110_mult__nonneg__nonneg, fact_1934_add__right__cancel, fact_5074_fact__altdef__nat, fact_2204_add__less__le__mono, fact_3945_MVT2, fact_4563_zero__code__int__def, fact_2802_zmult1__lemma, fact_2669_negDivAlg__eqn, fact_652_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_2557_div__mult__div__if__dvd, fact_251_rel__simps_I50_J, fact_3502_arctan__bounded, fact_2721_div__mult__self__is__m, fact_3930_real__root__less__mono__lemma, fact_935_mult__dvd__mono, fact_4504_zgcd__1__power__left__distrib, fact_3734_sin__cos__eq, fact_793_linorder__neqE__linordered__idom, fact_2148_add__increasing2, fact_2421_mod__add__left__eq, fact_409_less__special_I4_J, fact_1056_mult__mono, fact_5118_gcd__coprime__exists__int, fact_3854_ln__x__over__x__mono, fact_3232_tsub__def, fact_3323_real__sqrt__ge__zero, fact_4410_powr__less__mono, fact_3946_pdivmod__def, fact_627_crossproduct__noteq, fact_295_mult__2__right, fact_4426_floor__subtract, fact_2730_posDivAlg__0, fact_2554_div__self, fact_4238_mod__neg__neg, fact_1979_add__0, fact_2096_diff__eq__diff__less, fact_265_add__Bit0__Bit0, fact_3958_complex__zero__def, fact_4253_less__code__int__def, fact_473_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_1671_mult__less__mono1, fact_1585_nat__neq__iff, fact_1637_less__or__eq__imp__le, fact_3086_Divides_Otransfer__int__nat__functions_I2_J, fact_1503__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_, fact_1009_le__imp__power__dvd, fact_1247_less__1__mult, fact_2184_add__pos__pos, fact_1357_mult__le__less__imp__less, fact_2726_nat__0__iff, fact_2434_mod__add__self2, fact_4052_complex__expi__Ex, fact_2334_mod__div__trivial, fact_3682_cos__diff2, fact_333_add__number__of__left, fact_2053_add__strict__left__mono, fact_26_one__power2, fact_4509_zgcd__zmult__eq__self, fact_1350_mult__right__less__imp__less, fact_4559_fact__mono, fact_2024_add__le__cancel__left, fact_781_rel__simps_I26_J, help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__Nat__Onat_000tc__RealDef__Orea, fact_2996_power__0__Suc, fact_2034_add__less__imp__less__left, fact_3286_Suc__nat__number__of__add, fact_2697_Divides_Otransfer__nat__int__functions_I1_J, fact_2361_zdiv__zmod__equality2, fact_1692_incr__mult__lemma, fact_2338_semiring__div__class_Omod__div__equality_H, fact_755_zcong__zprime__prod__zero__contra, fact_1972_add__0__right, fact_87_number__of__mult, fact_91_sum__squares__le__zero__iff, fact_803_dvd__trans, fact_3495_real__abs__def, fact_140_mem__def, fact_708_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_3364_lemma__real__divide__sqrt__less, fact_890_dvd__0__left, fact_1115_mult__nonneg__nonneg, fact_2370_mod__by__0, fact_2302_mult_Odiff__left, gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oint, fact_4523_zgcd__zcong__zgcd, fact_2811_of__nat__double, fact_2605_pos__imp__zdiv__pos__iff, fact_724_power__0__left__number__of, fact_4116_complex__eq__iff, fact_3006_power__Suc2, fact_4684_inverse__rat, fact_1471_power__Suc__less, fact_2762_Euler_Oaux____2, fact_1554_diff__bin__simps_I3_J, fact_4707_zero__rat, fact_4486_zgcd__zgcd__zmult, fact_3496_abs__sum__triangle__ineq, fact_617_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_3148_power__preserves__even, fact_512_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_3544_zmod__zminus2__eq__if, fact_3443_ln__less__zero__iff, fact_287_mult__2, fact_1826_divides__div__not, fact_3846_exp__real__of__nat__mult, fact_875_comm__semiring__class_Odistrib, fact_1636_le__neq__implies__less, fact_2360_zdiv__zmod__equality, fact_1487_one__less__power, fact_4280_transfer__int__nat__factorial, fact_4659_rat__one__code, fact_5144_SetInterval_Otransfer__int__nat__set__function__closures, fact_3779_even__num__iff, fact_949_dvd__mult__left, fact_3038_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_4500_zgcd__pos, fact_4008_coprime__sos, fact_4152_cis__def, fact_4995_gcd__pos__int, fact_1710_dvd_Oord__le__eq__trans, fact_3671_real__of__nat__diff, help_If_2_1_If_000tc__RealDef__Oreal_T, fact_2718_SRStar__SR__prop, fact_4061_nat_Osize_I1_J, fact_1372_mult__strict__mono, fact_5162_isCont__arctan, fact_3527_even__neg, fact_3378_natceiling__add__number__of, fact_2724_mod__le__divisor, fact_3102_int__le__0__conv, fact_659_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_2200_add__le__less__mono, fact_3031_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_4788_RsetR__zmult__mono, fact_3951_DERIV__isconst__all, fact_3944_pdivmod__posDivAlg, fact_3580_cos__two__less__zero, fact_4690_mult__rat, fact_414__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096, fact_3334_real__sqrt__gt__1__iff, fact_2671_zOddE, fact_976_one__dvd, fact_4174_prime__divexp, fact_799_dvd__refl, fact_4047_add__Min__right, fact_4998_coprime__mult__int, fact_3375_arctan__monotone_H, fact_168_eq__number__of, fact_3259_nonneg__eq__int, help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_, fact_2036_add__less__imp__less__left, fact_4974_gcd__1__int, fact_1421_power__less__power__Suc, fact_1804_mult__eq__if, fact_1250_less__1__mult, fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_660_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_3965_complex__mult, fact_4691_abs__rat, fact_662_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_3531_not__int__zless__negative, fact_2263_minf_I9_J, fact_2876_Suc__mult__cancel1, fact_877_comm__semiring__class_Odistrib, fact_4087_cnj_Ononneg__bounded, fact_195_right__distrib__number__of, fact_3730_sin__squared__eq, fact_2618_zmod__minus1__right, fact_4297_bezw__aux, fact_3471_arctan__ubound, fact_4017_coprime__divisors, fact_3176_lemma__realpow__diff, fact_1902_ab__semigroup__mult__class_Omult__ac_I1_J, fact_4288_fact__reduce__int, fact_1946_ab__semigroup__add__class_Oadd__ac_I1_J, fact_2378_mod__mult__right__eq, fact_2941_of__nat__less__iff, fact_2799_posDivAlg__correct, fact_199_zadd__commute, fact_735_zdiv__mono2__lemma, fact_1538_eq__add__iff2, fact_282_semiring__mult__2, fact_4041_pred__Bit0, fact_284_semiring__mult__2, fact_1614_add__eq__self__zero, fact_3904_real__root__eq__0__iff, fact_1334_mult__less__imp__less__left, fact_2416_zmod__simps_I2_J, fact_835_mult__eq__0__iff, fact_1065_mult__left__mono__neg, fact_1176_mult__pos__neg2, fact_494_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_4349_coprime__common__divisor__nat, fact_3928_real__root__pos, fact_623_crossproduct__noteq, fact_83_arith__simps_I32_J, fact_1904_ab__semigroup__mult__class_Omult__ac_I1_J, fact_575_power__even__eq, fact_945_dvdI, fact_993_power__le__dvd, fact_4598_Nitpick_Oint__lcm__def, fact_2259_minf_I9_J, fact_2775_phi__prime, fact_3550_power3__minus, fact_12_sum__power2__gt__zero__iff, fact_489_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_3398_abs__add__one__gt__zero, fact_2611_neg__mod__conj, fact_3094_even__plus__odd__prop2, fact_943_dvdI, fact_4607_SetS__def, fact_4467_floor__eq2, fact_2318_zmod__number__of__Bit1, fact_2292_mult_Oadd__right, fact_2961_of__nat__mult, fact_3442_ln__eq__zero__iff, fact_4617_nat__gcd_Osimps, fact_240_mult__numeral__1__right, fact_3066_diff__less__Suc, fact_1921_add__imp__eq, fact_1621_mult__is__0, fact_889_dvd__0__left, fact_5017_quotient__of__coprime, fact_4815_Union__SetS__setprod__prop2, fact_1567_less__add__iff2, fact_3639_natceiling__real__of__nat, fact_1354_mult__le__less__imp__less, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__RealDef__Oreal_J_000tc__fun_, fact_869_combine__common__factor, fact_2979_of__nat__power, fact_848_mult__zero__left, fact_5021_gcd__int__def, fact_219_power2__less__imp__less, fact_3607_cos__arccos, fact_747_power__strict__mono, fact_3576_sgn__real__def, fact_2104_mult_Ocomm__neutral, fact_856_zero__neq__one, fact_2497_mod__mult__self2__is__0, fact_3642_real__of__nat__def, fact_1457_four__x__squared, fact_3994_i__mult__eq, fact_1177_mult__pos__neg2, fact_3503_arctan__lbound, fact_4711_quotient__of__Fract, fact_857_zero__neq__one, fact_3890_DERIV__pos__inc__right, fact_897_power__mult__distrib, fact_904_power__commutes, fact_156_zless__imp__add1__zle, fact_4070_cnj_Ominus, fact_3449_zdvd__mult__cancel1, fact_2543_div__mult__self1__is__id, fact_3202_div2__Suc__Suc, fact_554_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_5080_atLeastLessThanPlusOne__atLeastAtMost__int, fact_2686_div__mod__equality_H, fact_616_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_2377_mod__mult__right__eq, fact_1810_add__diff__add, fact_3456_ln__div, fact_2127_inv__g__1, fact_4668_Ratreal__number__of__quotient2, fact_1043_power__m1__even, fact_1691_ex__least__nat__less, fact_4357_coprime__rmult__nat, fact_3777_even__power__nat, help_fTrue_1_1_U, fact_1249_less__1__mult, fact_1080_mult__left__mono, fact_462_le__nat__number__of, fact_762_dvd__0__right, fact_864_one__neq__zero, fact_4510_zgcd__zmult__distrib2, fact_4533_zcong__lineq__unique, fact_2784_posDivAlg_Opsimps, fact_2537_div__mult__mult2, fact_1581_diff__bin__simps_I5_J, fact_82_mult__number__of__left, fact_3432_ln__eq__minus__one, fact_2860_less__SucI, fact_3873_log__mult, fact_3863_log__one, fact_1499__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_3765_Parity_Otransfer__int__nat__relations, fact_1463_zcong__zmult__prop3, fact_3719_sin__pi__half, fact_3795_odd__square, fact_1526_zdvd__zdiffD, fact_3110_power__le__imp__le__base, fact_1237_power__mono, fact_3587_cos__double__less__one, fact_2644_zdiv__leq__prop, fact_1197_mult__less__cancel__right__disj, fact_5164_isCont__sin, fact_2341_semiring__div__class_Omod__div__equality_H, fact_3308_real__sqrt__sum__squares__mult__ge__zero, fact_4954_image__atLeastZeroLessThan__int, fact_4315_gcd__semilattice__nat_Ole__infE, fact_3248_zEvenE, fact_1627_trans__less__add1, fact_2436_mod__add__self2, fact_4336_gcd__1__nat, fact_4716_Fract__less__zero__iff, fact_3351_lemma__sqrt__hcomplex__capprox, fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_4195_prime__ge__2, fact_2039_add__less__imp__less__left, fact_2576_dvd__mult__div__cancel, fact_0__096t_A_060_A0_096, fact_3960_complex__one__def, fact_1269_dvd__mult__cancel__right, fact_3987_complex__eq__cancel__iff2, fact_1963_add_Ocomm__neutral, fact_3927_real__root__strict__decreasing, fact_2568_dvd__div__mult__self, fact_2551_div__mult__mult1__if, fact_1331_mult__less__imp__less__left, fact_1884_add__neg__nonpos, fact_3525_zmod__zminus__zminus, fact_4007_plusinfinity, fact_4130_complex__Im__mult, fact_535_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_2914_of__nat__0__le__iff, fact_3001_zmult__int, fact_843_mult__zero__right, fact_2363_zmult__div__cancel, fact_410_less__special_I4_J, fact_978_one__dvd, fact_2068_add__less__cancel__left, fact_1786_real__two__squares__add__zero__iff, fact_4255_Quickcheck__Narrowing_Oint__of__inject, fact_5186_atLeast0AtMost, fact_3573_cos__monotone__minus__pi__0_H, fact_349_rel__simps_I10_J, fact_2327_mod__mod__trivial, fact_178_rel__simps_I48_J, fact_3206_Suc__div__eq__add3__div, fact_2305_mult_Odiff__right, fact_3793_sin__zero__lemma, fact_2712_mod__if, fact_4468_less__floor__eq, fact_5067_finite__atLeastAtMost__int, help_COMBI_1_1_COMBI_000tc__Int__Oint_U, fact_1543_eq__add__iff1, fact_401_semiring__one__add__one__is__two, fact_1783_real__mult__commute, fact_1157_mult__neg__pos, fact_1562_le__add__iff1, fact_3535_mult__Min, fact_4521_zprime__imp__zrelprime, fact_2653_divmod__int__rel__div__eq, help_If_2_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T, fact_3905_real__root__less__iff, fact_371_number__of__Bit0, fact_676_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_1812_nat__mult__dvd__cancel__disj_H, fact_2396_mod__mult__mult2, fact_188_left__distrib__number__of, fact_4972_coprime__divisors__nat, fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_3403_le__mult__natfloor, fact_1545_right__diff__distrib__number__of, fact_2793_divmod__int__rel__0, fact_474_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_2035_add__less__imp__less__left, fact_1409_power__le__imp__le__exp, fact_2776_negDivAlg_Opsimps, fact_2808_of__nat__double, fact_2695_mod__mult__distrib, fact_4729_Rat__induct__pos, fact_1947_ab__semigroup__add__class_Oadd__ac_I1_J, fact_1851_nat__le__add__iff2, fact_4219_mod__eq, fact_2167_add__nonneg__nonneg, fact_4206_divmod__nat__step, fact_1147_mult__strict__right__mono, fact_1076_comm__mult__left__mono, fact_2787_nat__mod__eq__iff, fact_5003_Fract__coprime, fact_2001_add__le__imp__le__right, fact_2082_eq__iff__diff__eq__0, fact_4669_quotient__of__eq, fact_4256_int__of__number, fact_4586_norR__mem__unique, fact_4_calculation_I2_J, fact_2700_div__less, fact_3804_Fact_Ofact__0__nat, fact_248_double__eq__0__iff, fact_3924_real__root__decreasing, fact_2125_mult__1__left, fact_4138_cmod__def, fact_3966_cmod__unit__one, fact_2822_number__of__int, fact_400_semiring__one__add__one__is__two, fact_2006_add__mono, fact_513_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_1216_not__one__le__zero, fact_216_zero__le__power2, fact_2920_of__nat__less__0__iff, fact_2509_mod__mult__self2, fact_5177_DERIV__isconst2, fact_795_dvd__refl, fact_4076_complex__mod__cnj, fact_2499_mod__by__1, fact_2741_nat__mult__distrib, fact_4397_ceiling__real__of__int, fact_570_nat__mult__2, fact_3706_natceiling__add, fact_2613_mod__pos__pos__trivial, fact_1362_mult__less__le__imp__less, fact_4077_cnj_Odiff, fact_4257_zero__code__int__code, fact_3203_mod2__Suc__Suc, fact_1865_add__nonneg__pos, fact_3182_div__geq, fact_1829_realpow__num__eq__if, fact_1244_zero__le__power, fact_3581_cos__pi__half, fact_1227_not__one__less__zero, fact_4515_zcong__zgcd__zmult__zmod, fact_3967_complex__inverse, fact_1153_mult__neg__pos, fact_1155_mult__neg__pos, fact_181_sum__squares__eq__zero__iff, fact_3903_real__root__le__mono, fact_3696_real__of__nat__div, fact_2444_dvd__mod__iff, fact_4811_Bnor__prod__zgcd, fact_4107_Im_Opos__bounded, fact_974_power__one, fact_3003_zle__iff__zadd, fact_1948_ab__semigroup__add__class_Oadd__ac_I1_J, fact_802_dvd__trans, fact_2771_mod__exhaust__less__4, fact_3483_real__add__minus__iff, fact_2553_div__self, fact_1640_le__add1, fact_46_add__special_I3_J, fact_2980_of__nat__power, fact_121_le__special_I2_J, fact_4963_invertible__coprime__int, fact_1880_add__strict__increasing2, fact_1262_less__add__one, fact_2182_add__neg__neg, fact_4437_powr__def, fact_3829_real__sqrt__inverse, fact_4045_pred__def, fact_1983_add__0, fact_1339_mult__left__less__imp__less, fact_1183_mult__pos__neg, fact_4695_zero__real__code, fact_545_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_1119_zero__le__mult__iff, fact_5121_min__diff, fact_144_mem__def, fact_4981_dvd__gcd__D1__int, fact_4114_Re__complex__of__real, fact_4314_gcd__semilattice__nat_Oless__infI1, fact_986_dvd__power__same, fact_2336_StandardRes__def, fact_1915_add__imp__eq, fact_3586_cos__45, fact_3932_real__root__pos__mult__exp, fact_3068_mult__Suc__right, fact_296_mult__2__right, fact_1967_add_Ocomm__neutral, fact_4147_Im__cis, fact_1623_mult__cancel2, fact_3401_natceiling__le__eq__one, fact_958_dvd__mult__right, fact_2633_div__add__self2, fact_671_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_2939_less__imp__of__nat__less, fact_1694_realpow__two__sum__zero__iff, fact_2210_less__iff__diff__less__0, fact_2051_add__strict__mono, fact_3536_diff__int__def, fact_4380_powr__one__eq__one, fact_624_crossproduct__noteq, fact_1831_realpow__num__eq__if, fact_3655_real__of__nat__power, fact_3977_complex__i__not__number__of, fact_3333_real__sqrt__lt__1__iff, fact_3952_reals__Archimedean2, fact_596_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_1732_real__add__left__mono, fact_1073_comm__mult__left__mono, fact_4371_invertible__coprime__nat, fact_1987_add__0__left, fact_1206_pos__add__strict, fact_739_s, fact_3215_of__nat__less__two__power, fact_2751_Euler_Oaux__1, fact_2471_div__by__0, fact_2882_odd__one__int, fact_1154_mult__neg__pos, fact_1825_real__squared__diff__one__factored, fact_1029_IntPrimes_Ozcong__zero, fact_1517_dvd__diff, fact_1606_not__less0, fact_4463_lemma__floor, fact_1290_power__eq__0__iff, fact_1740_diff__0__eq__0, fact_690_add__scale__eq__noteq, fact_3723_fact__lemma, fact_4767_zpower__number__of__even, fact_2174_zero__le__double__add__iff__zero__le__single__add, fact_2504_mod__mult__self1, fact_4150_cis__inverse, fact_2783_negDivAlg_Opinduct, fact_3347_real__sqrt__sum__squares__eq__cancel2, fact_107_le__number__of__eq__not__less, fact_2872_Suc__le__mono, fact_1534_inf__period_I4_J, fact_5150_vanishes__def, fact_2339_semiring__div__class_Omod__div__equality_H, fact_4086_cnj_Opos__bounded, fact_2310_gcd__lcm__complete__lattice__nat_Otop__unique, fact_1235_power__mono, fact_1602_nat__mult__assoc, fact_4228_div__pos__neg, fact_1368_mult__strict__mono_H, fact_3814_fact__mod, fact_2663_zmod__minus1, fact_4568_one__code__int__def, fact_4250_Quickcheck__Narrowing_Oint__of__code, fact_4090_complex__diff__cnj, fact_4710_Fract__number__of__quotient, fact_1104_mult__nonneg__nonpos, fact_29_zero__power2, fact_136_rel__simps_I33_J, fact_194_right__distrib__number__of, fact_4453_floor__eq, fact_5014_coprime__crossproduct__int, fact_2849_Zero__neq__Suc, fact_3239_even__div__2__prop2, fact_2976_transfer__int__nat__numerals_I1_J, fact_1771_le__imp__diff__is__add, fact_3175_lemma__realpow__diff, fact_4025_coprime__0_H, fact_4919_card__atLeastZeroLessThan__int, fact_914_dvd__triv__right, fact_2525_zdiv__number__of__Bit0, fact_1897_zero__reorient, fact_3250_realpow__pos__nth2, fact_3774_even__nat__mod__two__eq__zero, fact_4035_floor__eq4, fact_3257_int__int__eq, fact_981_one__dvd, fact_4399_real__of__int__minus, fact_768_Bit1__Min, fact_1833_realpow__num__eq__if, fact_1204_pos__add__strict, fact_898_power__mult__distrib, fact_509_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_3200_one__less__nat__eq, fact_2923_of__nat__0, fact_2655_divmod__int__rel__mod__eq, fact_316_number__of__Pls, fact_3600_tan__periodic__pi, fact_2432_mod__add__self1, fact_3192_realpow__two__diff, fact_855_zero__neq__one, fact_3505_nat__intermed__int__val, fact_1305_power__add, fact_233_not__sum__squares__lt__zero, fact_2905_zero__le__imp__of__nat, fact_1535_inf__period_I4_J, fact_5163_isCont__real__sqrt, fact_76_semiring__mult__number__of, fact_1026_power__one__right, fact_21_zero__less__power2, fact_1991_add__0__left, fact_4877_less__eq__nat_Osimps_I2_J, fact_1279_one__le__power, fact_1883_add__neg__nonpos, fact_3743_sin__arccos__abs, fact_1769_add__diff__assoc2, fact_2938_less__imp__of__nat__less, fact_2385_mod__mult__eq, fact_1579_zle__diff1__eq, fact_2661_neq__one__mod__two, fact_3613_lemma__tan__add1, fact_5171_isCont__root__pos, fact_853_zero__neq__one, fact_342_number__of__add, fact_2280_dvd__pos__nat, fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_2928_of__nat__0, fact_2295_mult_Oadd__left, fact_1048_split__mult__neg__le, fact_2533_div__mult__mult1, fact_3773_odd__nat__mod__two__eq__one, fact_2690_div__le__dividend, fact_35_zero__power2, fact_4300_gcd__dvd__prod__nat, fact_3711_two__realpow__gt, fact_70_zless__le, fact_957_dvd__mult__right, fact_3493_real__0__less__add__iff, fact_3840_one__le__exp__iff, fact_4196_prime__odd, fact_903_power__commutes, fact_1672_mult__less__mono2, fact_1461_zpower__zdvd__prop1, fact_3567_cos__ge__minus__one, fact_3209_Suc__mod__eq__add3__mod, fact_3455_ln__add__one__self__le__self, fact_1932_add__right__cancel, fact_234_not__sum__squares__lt__zero, fact_1735_real__le__linear, fact_4332_gcd__add2__nat, fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_2379_mod__mult__right__eq, fact_4266_rcis__def, fact_260_less__int__code_I13_J, fact_3643_real__eq__of__nat, fact_871_combine__common__factor, fact_1712_dvd_Oantisym, fact_1905_ab__semigroup__mult__class_Omult__ac_I1_J, fact_2433_mod__add__self2, fact_369_power2__sum, fact_1387_mult__right__le__one__le, fact_1752_eq__diff__iff, fact_1693_two__realpow__ge__one, fact_2854_nat__int, fact_2942_of__nat__less__iff, fact_1522_zdiff__zmult__distrib, fact_4374_bezout__nat, fact_4156_termination__basic__simps_I4_J, fact_4230_bezw_Osimps, fact_4741_less__eq__Suc__le__raw, fact_3352_Union__SetS__finite, fact_372_number__of__Bit0, fact_3363_SRStar__finite, fact_5146_transfer__int__nat__gcd__closures_I1_J, fact_668_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_1651_add__mult__distrib, fact_4722_one__less__Fract__iff, fact_2116_mult__1, fact_505_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_310_semiring__numeral__0__eq__0, fact_1531_inf__period_I3_J, fact_283_semiring__mult__2, fact_1717_dvd_Oless__imp__neq, fact_4412_powr__add, fact_1715_dvd_Oord__eq__less__trans, fact_3770_even__nat__equiv__def2, fact_1569_less__add__iff1, fact_467_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_2972_of__nat__1, fact_2786_mod__eqD, fact_2625_div__mult__self2, fact_2873_le__SucI, fact_275_power3__eq__cube, fact_1893_inv__inv, fact_4482_Euler__Fermat, fact_1345_mult__less__imp__less__right, fact_5100_bset_I7_J, fact_1329_mult__right__le__imp__le, fact_1302_power__0, fact_1993_add__le__imp__le__left, fact_1596_le__antisym, fact_115_zadd__zless__mono, fact_2852_nat_Osimps_I2_J, fact_3519_zcong__zminus, fact_3468_pi__half__less__two, fact_361_power2__eq__square__number__of, fact_279_power3__eq__cube, fact_3621_tan__less__zero, fact_2207_le__iff__diff__le__0, fact_3328_real__sqrt__lt__0__iff, fact_4180_prime__impl__zprime__int, fact_2047_add__strict__mono, fact_2518_dvd__eq__mod__eq__0, fact_57_less__eq__number__of__int__code, fact_2652_div__prop2, fact_2269_pinf_I9_J, fact_328_add__numeral__0__right, fact_1094_mult__nonpos__nonneg, fact_1862_add__pos__nonneg, fact_1248_less__1__mult, fact_2221_aux______1, fact_3088_divides__rexp, fact_1105_mult__nonneg__nonpos, fact_5135_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J, fact_2328_mod__mod__trivial, fact_2847_int__Suc, fact_201_zmult__zless__mono2, fact_825_divisors__zero, fact_191_right__distrib__number__of, fact_2138_diff__add__cancel, fact_2651_zmod__number__of__Bit0, fact_4097_complex__Im__one, fact_3701_real__of__nat__div3, fact_866_one__neq__zero, fact_3624_arccos, fact_4726_rat__floor__lemma, fact_169_eq__number__of, fact_1456_power__strict__increasing__iff, fact_1827_realpow__pos__nth__unique, fact_3186_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, fact_3153_realpow__Suc__le__self, fact_4855_negateSnd__def, fact_3649_sin__pi, fact_688_add__scale__eq__noteq, fact_1547_right__diff__distrib__number__of, fact_4973_coprime__exp__int, fact_1607_neq0__conv, fact_2145_add__nonpos__nonpos, fact_4204_prime__power__exp, fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_4440_real__of__int__ge__zero__cancel__iff, fact_1830_realpow__num__eq__if, fact_4318_gcd__semilattice__nat_Oinf__mono, fact_1649_add__leE, fact_4962_coprime__exp2__int, fact_397_less__special_I1_J, fact_3199_Suc__diff__eq__diff__pred, fact_2252_minf_I10_J, fact_3457_ln__add__one__self__le__self2, fact_4169_prime__divprod__eq, fact_4113_Re, fact_1366_mult__strict__mono_H, fact_3491_real__add__le__0__iff, fact_2585_split__neg__lemma, fact_806_dvd__trans, fact_495_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_3821_exp__ln__eq, fact_3109_power__le__imp__le__base, fact_3898_real__root__commute, fact_1122_zero__le__square, fact_915_dvd__triv__right, fact_2666_negDivAlg_Osimps, fact_362_power2__eq__square__number__of, fact_1519_dvd__diff, fact_3024_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_1676_unity__coeff__ex, fact_3836_exp__eq__one__iff, fact_3596_tan__minus, fact_197_zadd__assoc, fact_3419_zdvd__self__abs2, help_COMBI_1_1_COMBI_000tc__Nat__Onat_U, fact_1395_zero__less__two, fact_4100_Im_Ominus, fact_2486_xzgcda__linear__aux2, fact_4476_ln__powr__bound2, fact_738_quartic__square__square, fact_3255_int__if__cong, fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_36_zero__eq__power2, fact_3045_zdvd__int, fact_1055_mult__mono, fact_2055_add__strict__left__mono, fact_3647_not__real__of__nat__less__zero, fact_3630_tan__half, fact_3214_of__nat__less__two__power, fact_992_power__le__dvd, fact_4319_gcd__semilattice__nat_Oinf__greatest, fact_2495_mod__mult__self2__is__0, gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint, fact_5141_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J, fact_5075_atLeastLessThanSuc__atLeastAtMost, fact_1660_nat__mult__eq__1__iff, fact_1420_power__less__power__Suc, fact_3021_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_3095_even__minus__odd, fact_3559_cos__arcsin, fact_1889_add__nonpos__neg, fact_1773_le__diff__conv2, fact_1955_one__reorient, fact_1071_comm__mult__left__mono, fact_2841_of__nat__Suc, fact_3087_exp__mono__lt, fact_270_double__number__of__Bit0, fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_1378_mult__le__cancel__left__neg, fact_3744_arcsin__pi, fact_152_less__nat__number__of, fact_403_semiring__one__add__one__is__two, fact_4564_fact__lt, fact_1604_zcong__square__zless, fact_353_add__Bit1__Bit0, fact_4581_of__int__int__eq, fact_1333_mult__less__imp__less__left, fact_2375_mod__0, fact_2502_mod__by__1, fact_1702_dvd_Oless__le__not__le, fact_2705_nat__0, fact_5101_periodic__finite__ex, fact_4078_complex__cnj__power, fact_970_power__one, fact_2649_Euler_Oaux__2, fact_4201_xzgcd__def, fact_359_power2__eq__square__number__of, fact_2287_mult_Ozero__right, fact_2507_mod__mult__self1, fact_470_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_2535_div__mult__mult1, fact_1429_power__gt1__lemma, fact_4551_gcd__nat__induct, fact_923_dvd__mult2, fact_19_zero__less__power2, fact_3421_abs__zmult__eq__1, fact_5026_Rat__cases, fact_461_is__mult__sum2sq, fact_4544_polar__Ex, fact_1661_power2__diff, fact_4080_complex__cnj__complex__of__real, fact_3996_i__complex__of__real, fact_4027_coprime__divprod, fact_3715_cos__npi, fact_3256_Nat__Transfer_Otransfer__int__nat__relations_I1_J, fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_4122_Re_Oadd, fact_3400_le__natfloor__eq__one, help_fequal_1_1_fequal_000tc__RealDef__Oreal_T, fact_1040_power__m1__even, fact_1608_less__nat__zero__code, fact_2491_mod__mult__self1__is__0, fact_2463_zdiff__zmod__right, fact_2676_mod__div__decomp, fact_3452_ln__ge__zero__imp__ge__one, fact_2933_of__nat__less__imp__less, fact_3980_i__def, fact_1156_mult__neg__pos, fact_4529_int__relprime__odd__power__divisors, fact_1483_power__eq__imp__eq__base, fact_633_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_5105_aset_I9_J, fact_2196_add__le__less__mono, fact_89_number__of__mult, fact_3811_fact__ge__Suc__0__nat, fact_1257_less__add__one, fact_4654_quotient__of__inject, fact_3104_power__inject__base, fact_1058_mult__mono, fact_1485_one__less__power, fact_2215_wset__inv__mem__mem, fact_1202_not__square__less__zero, fact_3688_tan__npi, fact_3077_div__1, fact_4044_pred__Min, fact_5138_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J, fact_472_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_1776_le__add__diff, fact_550_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_2790_unique__remainder, fact_3849_inv__real__of__nat__fact__ge__zero, fact_3446_ln__le__minus__one, fact_2212_less__iff__diff__less__0, fact_4324_gcd__semilattice__nat_Ole__infI2, fact_3345_real__sqrt__sum__squares__ge2, fact_3453_ln__ge__zero__iff, fact_2250_minf_I10_J, fact_2577_div__add, fact_2243_mono__nat__linear__lb, fact_720_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_3414_abs__ln__one__plus__x__minus__x__bound, fact_4982_gcd__greatest__int, fact_2126_inv__less__p__minus__1, fact_4389_real__of__int__diff, fact_4990_gcd__neg1__int, fact_3497_realpow__square__minus__le, fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_1288_power__inject__exp, fact_53_number__of__is__id, fact_1540_eq__add__iff1, fact_1120_zero__le__mult__iff, fact_1900_zero__reorient, fact_4390_power__real__of__int, fact_2435_mod__add__self2, fact_1659_nat__mult__1__right, fact_4233_mod__int__def, fact_2511_mod__mult__self2, fact_3278_neg__imp__number__of__eq__0, fact_1446_power__less__imp__less__exp, fact_1768_diff__add__assoc2, fact_4594_is__RRset__def, fact_180_sum__squares__eq__zero__iff, fact_3016_power__Suc, fact_3156_realpow__Suc__le__self, fact_4531_int__relprime__power__divisors, fact_522_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_411_less__special_I2_J, fact_3494_abs__real__def, fact_3431_ln__one, fact_1532_inf__period_I4_J, fact_2968_of__nat__1, fact_725_power__0__left__number__of, fact_3149_zero__less__int__conv, fact_2733_split__div, fact_4395_real__of__one, fact_190_right__distrib__number__of, fact_4275_fact__neg__int, fact_1175_mult__pos__neg2, fact_2782_eq__diff__eq_H, fact_2307_gcd__lcm__complete__lattice__nat_Onot__top__less, fact_4688_divide__rat, fact_1755_dvd__diffD, fact_1950_one__reorient, fact_2213_zfact_Osimps, fact_4675_eq__rat_I3_J, fact_946_dvdI, fact_3562_cos__le__one, fact_2481_div__by__1, fact_2105_mult__1__right, fact_1129_mult__strict__right__mono__neg, fact_2446_mod__mod__cancel, fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_1370_mult__strict__mono_H, fact_1629_add__less__mono1, fact_2098_mult_Ocomm__neutral, fact_625_crossproduct__noteq, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Int__Oint, fact_1342_mult__less__imp__less__right, fact_3590_cos__ge__zero, fact_3014_power__Suc, fact_2276_pow__divides__pow__int, fact_1758_diff__mult__distrib2, fact_902_power__commutes, fact_3061_le__imp__less__Suc, fact_271_double__number__of__Bit0, fact_4058_code__numeral_Osize_I1_J, fact_4676_of__nat__rat, fact_3825_exp__less__cancel__iff, 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fact_1102_mult__nonneg__nonpos2, fact_4125_complex__Re__number__of, fact_164_add__nat__number__of, fact_3459_abs__power2__distrib, fact_4183_prime__factor__lt, fact_1369_mult__strict__mono_H, fact_2922_of__nat__0, fact_2289_mult__right_Ozero, fact_4407_powr__mono, fact_760_dvd__0__right, fact_861_one__neq__zero, fact_1075_comm__mult__left__mono, fact_3644_sin__le__one, fact_4181_prime__g__one, fact_777_rel__simps_I3_J, fact_3912_real__root__divide, fact_3597_tan__zero, fact_4082_code__numeral_Osimps_I2_J, fact_2353_div__mod__equality2, fact_4289_length__around__zero, fact_4145_cos__n__Re__cis__pow__n, fact_4548_int__of__nat__induct, fact_3125_zdiff__int, fact_5123_min__0L, fact_2965_of__nat__mult, fact_4812_Bnor__prod__power, fact_3143_of__nat__0__less__iff, fact_2397_zmod__simps_I4_J, fact_1096_mult__nonpos__nonneg, fact_2883_Parity_Oeven__product, fact_2300_mult__left_Odiff, fact_2473_div__by__0, fact_4379_powr__not__zero, fact_3727_sin__cos__squared__add2__mult, fact_2732_StandardRes__SRStar__prop1a, fact_4618_transfer__nat__int__set__return__embed, fact_3225_less__2__cases, fact_433_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_4351_coprime__plus__one__nat, fact_615_add__0__iff, fact_2582_div__power, fact_4193_prime__dvd__square, fact_415_zadd__power3, fact_4536_int__triple__relprime__odd__power__divisors, fact_3231_power__odd__eq, fact_2347_mod__div__equality, fact_2917_of__nat__less__0__iff, fact_2562_dvd__div__mult, fact_800_dvd__refl, fact_1187_mult__pos__pos, fact_1563_le__add__iff2, fact_5000_coprime__mul__eq__int, fact_52_zle__refl, fact_130_plus__numeral__code_I9_J, fact_2646_div__eq__minus1, fact_3709_sin__cos__npi, fact_3752_lemma__STAR__cos, fact_3818_aux4, fact_2115_mult__1, fact_3009_power__Suc2, fact_134_rel__simps_I5_J, fact_2271_pinf_I9_J, fact_1997_add__le__imp__le__left, fact_673_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_2588_dvd__eq__mod__eq__0__number__of, fact_3511_negative__zless, fact_4422_ceiling__le__eq, fact_2043_add__less__imp__less__right, fact_1872_add__strict__increasing, fact_2881_even__zero__int, fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_3753_sin__zero__iff, fact_2977_of__nat__power, fact_2957_of__nat__add, fact_5161_isCont__cos, fact_1564_le__add__iff2, fact_2919_of__nat__less__0__iff, fact_315_number__of__Pls, fact_1530_inf__period_I3_J, fact_2294_mult__right_Oadd, fact_3516_minus__numeral__code_I5_J, fact_3410_le__natfloor__eq__number__of, fact_2997_power__0__Suc, fact_1240_zero__le__power, fact_5027_Rat__induct, fact_3792_lemma__even__mod__4__div__2, fact_796_dvd__refl, fact_4326_gcd__unique__nat, fact_5168_isCont__abs, fact_1044_split__mult__neg__le, fact_1899_zero__reorient, fact_93_sum__squares__le__zero__iff, fact_2916_of__nat__less__0__iff, fact_4809_Union__SetS__setprod__prop1, fact_1711_dvd__antisym, fact_3254_inc__induct, fact_1824_real__squared__diff__one__factored, fact_5182_lemma__isCont__inj, fact_317_number__of__Pls, fact_399_semiring__one__add__one__is__two, fact_2530_zmod__eq__0__iff, fact_2298_mult__left_Oadd, fact_1210_zero__le__one, fact_4481_prime__power__mult, fact_5035_LIMSEQ__le__const2, fact_580_even__power__le__0__imp__0, fact_1908_add__right__imp__eq, fact_1152_mult__neg__pos, fact_2140_inv__is__inv, fact_3081_power__Suc__0, fact_4507_zgcd__0, fact_3337_real__sqrt__two__ge__zero, fact_1383_mult__le__cancel__left__pos, fact_2524_Divides_Otransfer__nat__int__function__closures_I1_J, fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_1444_power__strict__increasing, fact_3404_less__one__imp__sqr__less__one, fact_2422_mod__add__left__eq, fact_1190_mult__pos__pos, fact_3879_DERIV__arctan, fact_37_zero__eq__power2, fact_3319_real__sqrt__power, fact_2326_mod__mod__trivial, fact_337_add__number__of__eq, fact_1549_left__diff__distrib__number__of, fact_3263_dvd_Olift__Suc__mono__less, fact_4108_Im_Ononneg__bounded, fact_3132_one__less__m, fact_2693_mod__less__eq__dividend, fact_2868_add__Suc__right, fact_788_rel__simps_I25_J, fact_1800_realpow__minus__mult, fact_135_less__eq__int__code_I15_J, fact_4048_add__Min, fact_4328_gcd__greatest__iff__nat, fact_4474_ceiling__eq, fact_1191_mult__less__cancel__left__pos, fact_2962_of__nat__mult, fact_1978_add__0, fact_3741_sin__cos__add, fact_2645_power__preserves__odd, fact_1326_mult__right__le__imp__le, fact_4448_int__le__real__less, fact_4532_xzgcd__correct__aux2, fact_263_add__Pls__right, fact_1363_mult__less__le__imp__less, fact_1404_power__decreasing, fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, help_COMBC_1_1_COMBC_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin, fact_3831_real__divide__def, fact_3247_inv__is__inv__aux, fact_313_semiring__numeral__0__eq__0, fact_2855_Suc__less__SucD, fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_4059_nat__size, fact_3982_Complex__mult__i, fact_2420_mod__add__eq, fact_1070_mult__right__mono__neg, fact_2304_mult__right_Odiff, fact_2945_of__nat__less__iff, fact_4383_powr__powr, fact_2763_StandardRes__SRStar__prop4, fact_3424_pi__gt__zero, fact_812_zcong__neg__1__impl__ne__1, fact_2062_add__strict__right__mono, fact_1582_diff__bin__simps_I6_J, fact_2413_zmod__simps_I2_J, fact_2909_zero__le__imp__of__nat, fact_3115_power__gt1, fact_4599_ResSet__image, fact_4682_real__floor__code, fact_7_not__sum__power2__lt__zero, fact_4629_finite__greaterThanLessThan__int, fact_3992_Complex__add__complex__of__real, fact_99_le__special_I3_J, fact_734_unique__quotient__lemma, fact_1544_right__diff__distrib__number__of, fact_900_power__commutes, fact_936_mult__dvd__mono, fact_1700_dvd_Ole__less, fact_133_rel__simps_I29_J, fact_2114_mult__1, fact_3376_arctan__zero__zero, fact_1181_mult__pos__neg, fact_4139_complex__Re__inverse, fact_3920_real__root__lt__0__iff, fact_4359_gcd__diff1__nat, fact_576_power__even__eq, fact_2151_add__increasing2, fact_1228_not__one__less__zero, fact_2308_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_3775_odd__nat__equiv__def, fact_357_odd__nonzero, fact_4968_gcd__add1__int, fact_3091_IntNatAux_Oodd__plus__odd, fact_4142_Re_Obounded, fact_3917_real__root__le__0__iff, fact_67_rel__simps_I19_J, fact_813_order__le__neq__implies__less, fact_3776_even__nat__equiv__def, fact_3126_one__less__mult, fact_413_less__special_I2_J, fact_952_dvd__mult__left, fact_2201_add__less__le__mono, fact_954_dvd__mult__left, fact_1687_QuadRes__def, fact_2636_dvd__div__div__eq__mult, fact_3112_power__le__imp__le__base, fact_212_power2__le__imp__le, fact_1912_add__right__imp__eq, fact_4419_le__floor__eq, fact_3724_natfloor__div__nat, fact_689_add__scale__eq__noteq, fact_2770_posDivAlg__eqn__number__of, fact_1209_zero__le__one, fact_578_power__even__eq, fact_3865_DERIV__cos, fact_2679_posDivAlg_Osimps, fact_1117_mult__le__0__iff, fact_3282_div__nat__number__of, fact_3954_complex__norm, fact_3011_power__Suc, fact_4388_real__of__int__le__iff, fact_95_sum__squares__ge__zero, fact_840_mult__zero__right, fact_2581_div__power, fact_2348_mod__div__equality, fact_4483_zgcd__zdvd1, fact_3708_sin__gt__zero, fact_2805_two__times__odd__div__two__plus__one, fact_962_dvd__add, fact_3681_sin__zero__abs__cos__one, fact_4985_abs__gcd__int, fact_5033_LIMSEQ__realpow__zero, fact_2564_dvd__div__mult, fact_2146_add__nonpos__nonpos, fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_924_dvd__mult2, fact_1684_mult__le__cancel2, fact_209_power2__le__imp__le, fact_453_zpower__zpower, fact_1802_realpow__minus__mult, fact_1720_dvd_Oless__imp__not__less, fact_4202_xzgcda__linear, fact_1307_power__add, fact_1215_not__one__le__zero, fact_2534_div__mult__mult1, fact_245_pos__zmult__eq__1__iff, fact_1145_mult__strict__right__mono, fact_2512_dvd__imp__mod__0, fact_2419_mod__add__eq, fact_5153_zcongm__def, fact_764__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_, fact_4401_real__of__int__floor__le, fact_1349_mult__right__less__imp__less, fact_4285_transfer__nat__int__factorial, fact_2729_transfer__nat__int__relations_I3_J, fact_1448_power__less__imp__less__exp, fact_1849_nat__eq__add__iff2, fact_775_rel__simps_I13_J, fact_532_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_2032_add__le__cancel__right, fact_2803_Nat__Transfer_Otransfer__nat__int__functions_I3_J, fact_3043_transfer__int__nat__numerals_I2_J, fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_780_bin__less__0__simps_I2_J, fact_3888_DERIV__neg__dec__left, fact_1837_norR__mem__unique__aux, fact_1137_mult__strict__left__mono, fact_2229_wset__mem, fact_2510_mod__mult__self2, fact_3751_reals__Archimedean3, fact_3466_pi__half__le__two, fact_994_power__le__dvd, fact_1317_zprime__zdvd__zmult__better, fact_3377_arctan__monotone, fact_2839_of__nat__Suc, fact_249_rel__simps_I46_J, fact_1281_one__le__power, fact_4678_of__int__rat, fact_4101_Im_Odiff, fact_1857_add__pos__nonneg, fact_2120_mult__1__left, fact_1501_one__not__neg__one__mod__m, fact_4329_gcd__semilattice__nat_Ole__iff__inf, fact_718_power__eq__0__iff__number__of, fact_3100_of__nat__diff, fact_1742_less__imp__diff__less, fact_577_power__even__eq, fact_3989_sgn__eq, fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_2344_mod__div__equality2, fact_407_one__add__one__is__two, fact_1964_add_Ocomm__neutral, fact_1513_number__of__diff, fact_257_less__int__code_I16_J, fact_4649_abs__rat__def, fact_482_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_1098_mult__nonneg__nonpos2, fact_3768_real__of__nat__fact__gt__zero, fact_4006_minusinfinity, fact_1584_less__not__refl, fact_4231_bezw__non__0, fact_5009_gcd__unique__int, fact_2175_zero__le__double__add__iff__zero__le__single__add, fact_3830_divide__real__def, fact_3372_lemma__MVT, fact_2351_div__mod__equality2, fact_358_zless__add1__eq, fact_2286_mult__left_Ozero, fact_3764_even__difference__nat, fact_3523_zdiv__zminus__zminus, fact_3871_log__le__cancel__iff, fact_539_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_4284_dvd__fact__int, fact_452_zprime__power__zdvd__cancel__left, fact_3177_lemma__realpow__diff, fact_5094_bset_I5_J, fact_3382_real__norm__def, fact_3111_power__le__imp__le__base, fact_4051_Suc__diff__number__of, fact_3679_real__of__nat__gt__zero__cancel__iff, fact_4370_div__gcd__coprime__nat, fact_4965_gcd__coprime__int, fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_1011_nat__power__less__imp__less, fact_1592_nat__add__left__commute, fact_1595_nat__add__right__cancel, fact_1138_mult__strict__left__mono, fact_1097_mult__nonpos__nonneg, fact_2494_mod__mult__self1__is__0, fact_276_power3__eq__cube, fact_2912_of__nat__0__le__iff, fact_1367_mult__strict__mono_H, fact_2846_zless__iff__Suc__zadd, fact_1551_left__diff__distrib__number__of, fact_1221_zero__less__one, fact_3548_negative__zless__0, fact_382_semiring__numeral__1__eq__1, fact_2195_add__le__less__mono, fact_1099_mult__nonneg__nonpos2, fact_179_zless__linear, fact_2880_exp__mono__eq, fact_4334_gcd__mult__distrib__nat, fact_3000_int__mult, fact_4614_nat__set__def, fact_4128_abs__Re__le__cmod, fact_3985_i__mult__eq2, fact_291_semiring__mult__2__right, fact_3479_nat0__intermed__int__val, fact_4032_floor__eq3, fact_1728_dvd_Oless__asym, fact_4807_norm__frac_Osimps, fact_4612_gcd__eq__nitpick__gcd, fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_327_add__numeral__0__right, fact_4657_less__rat__def, fact_3746_sin__arccos__lemma1, fact_20_zero__less__power2, fact_888_dvd__0__left, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__HOL__026, fact_2859_Suc__lessI, fact_3991_complex__of__real__mult__Complex, fact_2778_transfer__morphismI, fact_4717_zero__less__Fract__iff, gsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_000tc__Int__Oint_000tc_, fact_4680_Fract__of__int__quotient, fact_4580_complex__cnj__of__int, fact_3463_power2__eq1__iff, fact_1933_add__right__cancel, fact_2282_mult_Oprod__diff__prod, fact_2777_transfer__morphism__nat__int, fact_3819_exp__less__mono, fact_3198_add__2__eq__Suc_H, fact_4060_nat_Osize_I3_J, fact_574_power__even__eq, fact_4593_RRset2norRR__correct1, fact_540_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_3781_even__nat__div__two__times__two, fact_193_right__distrib__number__of, fact_1057_mult__mono, fact_1352_mult__right__less__imp__less, fact_5116_trivial__limit__sequentially, fact_4997_coprime__lmult__int, fact_1415_power__increasing__iff, fact_3165_split__nat, fact_4665_obtain__pos__sum, fact_4783_less__number__of__Suc, fact_2345_mod__div__equality2, fact_3179_Suc__pred_H, fact_3261_zero__le__imp__eq__int, fact_4650_sgn__rat__def, fact_3195_numeral__2__eq__2, fact_2953_of__nat__add, fact_3243_odd__equiv__def, fact_2519_dvd__eq__mod__eq__0, fact_1960_diff__eq__diff__eq, fact_3931_real__root__mult__lemma, fact_2505_mod__mult__self1, fact_3425_zdvd1__eq, fact_2168_add__nonneg__nonneg, fact_2734_zero__less__nat__eq, fact_1601_nat__mult__commute, fact_2879_mod__Suc__eq__Suc__mod, fact_3172_lemma__realpow__diff, fact_967_dvd__add, fact_2627_div__mult__self2, fact_1666_zdiff__power3, fact_3628_lemma__tan__total1, fact_2713_mod__mult__self3, fact_2244_d22set__eq__wset, fact_2124_mult__1__left, fact_790_pos__zmult__eq__1__iff__lemma, fact_1945_ab__semigroup__add__class_Oadd__ac_I1_J, fact_1767_diff__less__mono, fact_1433_power__0__left, fact_3164_power__Suc__less__one, fact_5028_card__setsum__aux, fact_3032_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_950_dvd__mult__left, fact_3866_DERIV__ln, fact_4121_Re_Ozero, fact_1018_power__mult, fact_3311_real__sqrt__eq__iff, fact_475_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_3571_real__sgn__pos, fact_3526_zminus__zmod, fact_1223_zero__less__one, fact_2040_add__less__imp__less__right, fact_2097_diff__eq__diff__less, fact_2823_number__of__int, fact_1019_power__mult, fact_5006_coprime__dvd__mult__iff__int, fact_56_times__numeral__code_I5_J, fact_1665_zdiff__power2, fact_4049_diff__bin__simps_I8_J, fact_1139_mult__strict__left__mono, fact_2884_even__times__anything, fact_2273_pinf_I9_J, fact_6_p0, fact_4331_gcd__semilattice__nat_Oinf__le1, fact_2211_less__iff__diff__less__0, fact_672_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_2012_add__left__mono, fact_3667_sin__diff, fact_4081_code__numeral_Osimps_I3_J, fact_1815_divides__rev, fact_1103_mult__nonneg__nonpos2, fact_3224_zEvenI, fact_3533_zmod__zminus1__not__zero, fact_1719_dvd_Oless__imp__le, fact_2704_transfer__nat__int__numerals_I1_J, fact_1779_nat__diff__split, fact_1910_add__right__imp__eq, fact_5012_gcd__le2__int, gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint, fact_4354_coprime__mult__nat, fact_4969_gcd__add2__int, fact_343_number__of__add, fact_4488_zgcd__1, fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_2291_mult_Oadd__right, fact_3820_ln__unique, fact_163_semiring__add__number__of, fact_203_power2__eq__imp__eq, fact_1437_power__0__left, fact_765__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_1750_diff__le__mono, fact_737_zdiv__mono2__neg__lemma, fact_3615_arccos__bounded, fact_2689_div__le__mono, fact_2900_not__odd__impl__even, fact_102_le__special_I1_J, fact_3827_exp__inj__iff, fact_704_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_5180_isCont__inv__fun__inv, fact_208_power2__le__imp__le, fact_2373_mod__0, fact_2080_eq__iff__diff__eq__0, fact_3999_expi__two__pi__i, fact_1874_add__strict__increasing, fact_4131_complex__Re__mult, fact_4093_complex__Im__cnj, fact_3532_Int_OMin__def, fact_3641_sin__npi, fact_1265_dvd__mult__cancel__left, fact_965_dvd__add, fact_172_number__of__reorient, fact_1321_mult__left__le__imp__le, fact_3122_int__eq__iff, fact_804_dvd__trans, fact_231_sum__squares__gt__zero__iff, fact_1479_power__eq__imp__eq__base, fact_787_rel__simps_I11_J, fact_1012_nat__zero__less__power__iff, fact_274_power3__eq__cube, fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_3937_real__root__increasing, fact_3948_polar__ex1, fact_2268_d22set__mem, fact_3181_add__eq__if, fact_23_one__power2, fact_2454_dvd__mod__imp__dvd, fact_267_zadd__0__right, fact_1371_mult__strict__mono_H, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U, fact_1861_add__pos__nonneg, fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, fact_4705_real__times__code, fact_4265_rcis__divide, fact_913_dvd__triv__right, fact_1132_comm__mult__strict__left__mono, fact_1603_power__dvd__imp__le, fact_3860_log__base__10__eq1, fact_1523_zdiff__zmult__distrib2, gsy_v_s____, fact_3726_sin__gt__zero2, fact_224_sum__power2__le__zero__iff, fact_2940_less__imp__of__nat__less, fact_3098_of__nat__diff, fact_2806_Code__Numeral_Oint__of__code, fact_417_int__pos__lt__two__imp__zero__or__one, fact_619_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_5002_gcd__0__int, fact_4158_termination__basic__simps_I2_J, fact_398_less__special_I1_J, fact_1787_real__mult__right__cancel, fact_3473_ln__one__plus__pos__lower__bound, fact_10_sum__power2__gt__zero__iff, fact_330_less__number__of, fact_3235_even__div__2__prop1, fact_527_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_1246_less__1__mult, fact_3926_real__root__lt__1__iff, fact_2617_zmod__zdvd__zmod, fact_985_dvd__power__same, fact_528_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_2158_add__increasing, fact_348_bin__less__0__simps_I4_J, fact_4497_zgcd__zminus, fact_4269_nat__of__def, fact_3017_power__Suc, fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_4375_Cauchy__iff2, fact_2303_mult__right_Odiff, fact_1486_one__less__power, fact_2757_posDivAlg__div__mod, fact_2664_zdiv__number__of__Bit1, fact_2457_zdiv__zero, fact_838_mult__eq__0__iff, fact_3249_mod__induct__0, fact_3275_neg__nat, fact_1271_power__increasing, fact_987_dvd__power__same, fact_4302_gcd__exp__nat, fact_4162_divmod__int__def, fact_3210_mod__Suc__eq__mod__add3, fact_3570_cos__periodic__pi, fact_833_no__zero__divisors, fact_1217_not__one__le__zero, fact_1516_dvd__diff, fact_722_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_696_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_2306_mult_Odiff__right, fact_1605_zcong__square, fact_4646_Frct__code__post_I5_J, fact_1121_zero__le__mult__iff, fact_789_zmult__eq__1__iff, fact_526_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_2791_unique__quotient, fact_2827_Suc__inject, fact_706_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_4986_gcd__idem__int, fact_4585_phi__def, fact_237_mult__numeral__1, fact_2983_of__nat__power, fact_560_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_3884_DERIV__local__min, fact_1803_divides__exp, fact_2312_gcd__lcm__complete__lattice__nat_Onot__less__bot, fact_3868_log__less__cancel__iff, fact_3119_power__gt1, fact_1891_add__nonpos__neg, fact_4140_Re_Opos__bounded, fact_114_rel__simps_I21_J, fact_5083_fact__div__fact, fact_782_rel__simps_I30_J, fact_3908_real__root__mult__exp, fact_3040_zadd__int__left, fact_1124_zero__le__square, fact_376_number__of__Bit1, fact_2320_StandardRes__prop4, fact_988_dvd__power__same, fact_3716_cos__npi2, fact_2242_int__gr__induct, fact_2949_of__nat__le__iff, fact_2109_mult__1__right, fact_2969_of__nat__1, fact_2528_zmod__le__nonneg__dividend, fact_3331_real__sqrt__le__1__iff, fact_2000_add__le__imp__le__right, fact_2272_pinf_I9_J, fact_613_add__0__iff, fact_2698_nat__mod__distrib, fact_3869_log__ln, fact_4522_zgcd1__iff__no__common__primedivisor, fact_931_dvd__mult, fact_2428_mod__add__right__eq, fact_1318_mult__left__le__imp__le, fact_3963_complex__minus, fact_3791_lemma__odd__mod__4__div__2, fact_4290_Bnor__prime, fact_381_semiring__numeral__1__eq__1, fact_1965_add_Ocomm__neutral, fact_1820_mult__diff__mult, help_fdisj_2_1_U, fact_2150_add__increasing2, fact_2792_self__remainder, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo, fact_3123_nat__0__le, fact_98_le__special_I3_J, fact_3950_z3div__def, fact_1617_less__eq__nat_Osimps_I1_J, fact_2225_wset__g__1, fact_4728_Fract__le__one__iff, fact_3325_real__sqrt__ge__0__iff, fact_1875_add__strict__increasing2, fact_3537_diff__int__def__symmetric, fact_1609_gr__implies__not0, fact_4311_gcd__assoc__nat, fact_2193_zero__less__double__add__iff__zero__less__single__add, fact_1344_mult__less__imp__less__right, fact_1546_right__diff__distrib__number__of, fact_4264_rcis__mult, fact_1113_mult__nonneg__nonneg, fact_2070_add__less__cancel__right, fact_3861_DERIV__arccos, fact_828_no__zero__divisors, fact_2013_add__left__mono, fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_3619_tan__inverse, fact_741_zprime__def, fact_2386_mod__mult__eq, fact_3911_real__root__eq__1__iff, fact_4520_zgcd__code, fact_1385_mult__left__le__one__le, fact_2743_Nat__Transfer_Otransfer__nat__int__functions_I1_J, fact_198_zadd__left__commute, fact_3481_arctan__minus, fact_2065_add__less__cancel__left, fact_2947_of__nat__le__iff, fact_3226_nat__2, fact_3810_fact__ge__one__nat, fact_3317_real__sqrt__less__iff, fact_2185_add__pos__pos, gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint, fact_926_dvd__mult2, fact_3234_Suc__Suc__mult__two__diff__two, fact_3700_real__of__nat__number__of, fact_4991_gcd__neg2__int, fact_841_mult__zero__right, fact_2245_ex__least__nat__le, fact_1401_power__less__imp__less__base, fact_2254_pinf_I10_J, fact_4188_prime__coprime, fact_4003_DERIV__pos__imp__increasing, fact_4570_euclid__bound, fact_232_not__sum__squares__lt__zero, fact_5169_isCont__root__zero, fact_3907_real__root__mult, fact_2223_wset__mem__mem, fact_3034_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_402_semiring__one__add__one__is__two, fact_3808_Fact_Ofact__Suc, fact_3295_succ__Min, fact_11_sum__power2__gt__zero__iff, fact_1304_power__add, fact_2500_mod__by__1, fact_1697_real__le__eq__diff, fact_3103_power__inject__base, fact_3326_real__sqrt__gt__zero, fact_3301_MultInvPair__card__two, fact_4514_zgcd__non__0, fact_3193_realpow__two__diff, fact_2283_mult_Ozero__left, fact_3393_natceiling__one, fact_1268_dvd__mult__cancel__right, fact_3284_power__nat__number__of, fact_966_dvd__add, fact_3975_complex__i__not__zero, fact_49__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_, fact_4442_number__of__less__real__of__int__iff2, fact_3343_real__sqrt__pow2__gt__zero, fact_2926_of__nat__0, fact_1610_gr0I, fact_2952_of__nat__le__iff, fact_4578_complex__Im__of__int, fact_3786_even__even__mod__4__iff, fact_3070_Suc__eq__plus1, fact_1219_not__one__le__zero, fact_3180_Suc__diff__1, fact_2595_zdiv__mono1__neg, fact_2166_add__nonneg__nonneg, fact_2684_mod__mult2__eq, fact_4356_coprime__lmult__nat, fact_2356_div__mod__equality, fact_2384_mod__mult__left__eq, fact_476_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_3118_power__gt1, fact_1731_real__le__trans, fact_2591_StandardRes__ubound, fact_2737_transfer__nat__int__numerals_I4_J, fact_288_mult__2, fact_3397_natfloor__neg, fact_4129_Re__sgn, fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_2038_add__less__imp__less__left, fact_2041_add__less__imp__less__right, fact_2346_mod__div__equality, fact_497_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_1890_add__nonpos__neg, fact_3492_real__add__less__0__iff, fact_2866_add__Suc__shift, fact_1291_power__eq__0__iff, fact_3733_cos__sin__eq, fact_4124_Re_Ominus, fact_3304_Suc__lessE, fact_4209_divmod__nat__zero, fact_4377_ln__powr__bound, fact_3501_minus__pi__half__less__zero, fact_230_sum__squares__gt__zero__iff, fact_4207_bezout__prime, fact_3294_succ__def, fact_4023_coprime__Suc0, fact_3490_real__0__le__add__iff, fact_3939_sqrt__def, fact_3004_power__Suc2, fact_3673_tan__def, fact_1236_power__mono, fact_1975_double__zero__sym, fact_1524_Int2_Oaux1, fact_2607_zdiv__eq__0__iff, fact_4310_gcd__semilattice__nat_Oinf__left__commute, fact_2129_inv__not__1, fact_1397_power__less__imp__less__base, fact_4396_real__of__int__mult, fact_632_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_4538_int__triple__relprime__power__divisors, fact_395_less__special_I3_J, fact_2719_div__le__mono2, fact_406_one__add__one__is__two, fact_175_number__of__reorient, fact_4992_gcd__proj1__if__dvd__int, fact_1748_Nat_Odiff__le__self, fact_2513_dvd__imp__mod__0, fact_3065_Suc__mult__less__cancel1, fact_860_one__neq__zero, fact_2681_Euler__part3, fact_1906_ab__semigroup__mult__class_Omult__ac_I1_J, fact_3564_cos__arctan__not__zero, fact_4001_expi__zero, fact_2749_add__self__div__2, fact_2132_add__diff__cancel, fact_418_s0p, fact_4075_complex__cnj__of__nat, fact_1733_less__eq__real__def, fact_8_not__sum__power2__lt__zero, fact_1101_mult__nonneg__nonpos2, fact_3543_minus__numeral__code_I6_J, fact_2046_add__strict__mono, fact_4966_transfer__int__nat__gcd_I1_J, fact_1301_power__0, fact_1083_mult__right__mono, fact_1951_one__reorient, fact_842_mult__zero__right, fact_1252_zero__less__power, fact_171_number__of__reorient, fact_44_add__special_I3_J, fact_2642_dvd__div__eq__mult, fact_892_power__mult__distrib, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__025, fact_1458_Int2_Ozcong__zero, fact_964_dvd__add, fact_1025_power__one__right, fact_4714_Ratreal__number__of__quotient, fact_723_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_2739_nat__less__eq__zless, fact_1261_less__add__one, fact_3627_tan__total, fact_2060_add__strict__right__mono, fact_2943_of__nat__less__iff, fact_3875_log__inverse, fact_4378_real__of__int__less__iff, fact_1658_nat__1__eq__mult__iff, fact_2476_div__0, fact_3394_rabs__ratiotest__lemma, fact_3510_negative__zle, fact_2817_lessI, fact_3116_power__gt1, fact_1577_add__number__of__diff1, fact_4148_cis__mult, fact_492_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_2451_dvd__mod, fact_2898_even__diff, fact_1459_zcong__zless__0, fact_5004_div__gcd__coprime__int, fact_533_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_3962_complex__add, fact_1450_power__less__imp__less__exp, fact_491_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_3027_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_4212_divmod__nat__rel__mult1__eq, fact_2277_pow__divides__eq__nat, fact_312_semiring__numeral__0__eq__0, fact_3073_diff__Suc__1, fact_3366_real__average__minus__second, fact_2241_MultInv__prop2a, fact_3919_real__root__gt__0__iff, fact_468_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_1709_dvd_Oord__eq__le__trans, fact_1052_split__mult__pos__le, fact_3436_nat__abs__mult__distrib, fact_298_mult__2__right, fact_2703_mod__less__divisor, fact_1224_zero__less__one, fact_1480_power__eq__imp__eq__base, fact_3241_one__div__nat__number__of, fact_719_pos__zmult__pos, fact_2092_diff__eq__diff__less__eq, fact_997_dvd__power__le, fact_4055_ResSet__SRStar__prop, fact_873_combine__common__factor, fact_259_rel__simps_I2_J, fact_661_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_2829_of__nat__eq__iff, fact_4345_gcd__le1__nat, fact_2614_pos__mod__conj, fact_3427_ln__less__self, fact_2738_transfer__nat__int__relations_I2_J, fact_3262_less__imp__Suc__add, fact_1194_mult__less__cancel__left__disj, fact_33_zero__power2, fact_2315_gcd__lcm__complete__lattice__nat_Obot__unique, fact_100_le__special_I1_J, fact_4409_powr__less__cancel__iff, fact_3482_real__minus__mult__self__le, fact_2601_div__pos__pos__trivial, fact_5090_aset_I8_J, fact_2003_add__le__imp__le__right, fact_2701_nat__mult__div__cancel__disj, fact_1239_zero__le__power, fact_1284_power__inject__exp, fact_4980_dvd__gcd__D2__int, fact_2218_d22set__induct__old, fact_4921_atLeastPlusOneLessThan__greaterThanLessThan__int, fact_2785_posDivAlg_Opinduct, fact_60_le__number__of, fact_2189_double__add__less__zero__iff__single__add__less__zero, fact_3264_dvd_Olift__Suc__mono__less__iff, fact_3158_realpow__Suc__le__self, fact_2987_transfer__int__nat__quantifiers_I2_J, fact_2632_div__add__self2, fact_2395_mod__mult__mult2, fact_4677_Fract__of__nat__eq, fact_2890_Parity_Oeven__plus__even, fact_5095_bset_I3_J, fact_2399_zmod__simps_I4_J, fact_1053_mult__mono, fact_2153_add__increasing, fact_1311_zcong__not__zero, fact_940_mult__dvd__mono, fact_5037_monoseq__le, fact_2011_add__left__mono, fact_4063_complex__mod__mult__cnj, fact_2450_dvd__mod, fact_1061_mult__mono_H, fact_80_mult__number__of__left, fact_3290_Suc__le__D, fact_221_power2__less__imp__less, fact_783_rel__simps_I23_J, fact_3041_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_3844_one__less__exp__iff, fact_2231_MultInv__prop3, fact_4702_real__minus__code, fact_3023_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_4085_Suc__code__numeral__minus__one, fact_3828_abs__exp__cancel, fact_1811_divides__ge, fact_1278_one__le__power, fact_973_power__one, fact_2057_add__strict__left__mono, fact_2197_add__le__less__mono, fact_3271_not__neg__eq__ge__0, fact_4211_divmod__nat__div__mod, fact_3653_real__of__nat__1, fact_416_zadd__power2, fact_2406_mod__add__cong, fact_2180_add__neg__neg, fact_4470_ceiling__eq3, fact_3080_nat__power__eq__Suc__0__iff, fact_2877_diff__Suc__Suc, fact_319_semiring__norm_I112_J, fact_4262_Re__rcis, fact_192_right__distrib__number__of, fact_4153_DeMoivre, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Rat__Orat_000tc__HOL__Obool_U, fact_2748_nat__power__eq, fact_3623_arctan__tan, fact_1440_power__strict__increasing, fact_3806_fact__gt__zero__nat, fact_980_one__dvd, fact_1200_not__square__less__zero, fact_2816_Suc__mono, fact_3514_zminus__0, fact_1725_dvd_Oless__le__trans, fact_79_mult__number__of__left, fact_756_zcong__zprime__prod__zero, fact_2483_div__dvd__div, fact_2194_zero__less__double__add__iff__zero__less__single__add, fact_4671_one__rat, fact_1093_mult__nonpos__nonneg, fact_4406_powr__less__mono2__neg, fact_2324_pos__zdiv__mult__2, fact_3101_of__nat__diff, fact_4796_diff__nat__number__of, fact_3984_i__squared, fact_916_dvd__triv__right, fact_3568_abs__cos__le__one, fact_4312_gcd__semilattice__nat_Oinf__assoc, fact_2159_add__nonneg__eq__0__iff, fact_3356_real__sqrt__divide, fact_3205_Suc__div__eq__add3__div__number__of, fact_4645_Frct__code__post_I6_J, fact_1881_add__neg__nonpos, fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_493_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_1348_mult__right__less__imp__less, fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_2532_zmod__eq__dvd__iff, fact_373_number__of__Bit0, fact_2901_even__odd__disj, fact_2429_mod__add__self1, fact_1611_plus__nat_Oadd__0, fact_3117_power__gt1, fact_4430_powr__mono2, fact_5102_aset_I10_J, fact_490_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_3076_Divides_Otransfer__int__nat__functions_I1_J, fact_1618_le__0__eq, fact_4747_nat__number__of__Bit0, fact_1004_le__imp__power__dvd, fact_1282_one__le__power, fact_3687_le__natfloor__eq, fact_3272_neg__number__of__Bit1, fact_116_nat__number__of__Pls, fact_4590_RRset__zcong__eq, fact_2230_MultInv__zcong__prop1, fact_2073_add__less__cancel__right, fact_4282_fact__ge__one__int, fact_3798_cos__coeff__def, fact_3430_abs__div, fact_2279_mult__left__cancel, fact_4126_Re_Odiff, fact_4179_coprime__prime__eq, fact_3832_not__exp__le__zero, fact_1414_power__increasing__iff, fact_1925_add__left__imp__eq, fact_1557_dvd__mult__cancel, fact_4299_gcd__dvd1__nat, fact_2094_diff__eq__diff__less__eq, fact_2527_pos__mod__bound, fact_770_rel__simps_I40_J, fact_3593_cos__is__zero, fact_912_dvd__triv__left, fact_1756_dvd__diffD1, fact_3416_pi__neq__zero, fact_4672_rat__number__collapse_I2_J, fact_955_dvd__mult__right, fact_1230_not__one__less__zero, fact_387_numeral__1__eq__1, fact_4337_gcd__lcm__complete__lattice__nat_Oinf__bot__right, fact_2640_dvd__div__eq__mult, fact_1594_nat__add__left__cancel, fact_3188_tsub__eq, fact_478_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_686_add__scale__eq__noteq, fact_2549_div__mult__mult1__if, fact_3129_mn__eq__m__one, fact_334_add__number__of__left, fact_925_dvd__mult2, fact_1441_power__strict__increasing, fact_1046_split__mult__neg__le, fact_1892_add__nonpos__neg, fact_3467_pi__half__neq__zero, fact_2844_of__nat__Suc, fact_3609_arccos__cos2, fact_1985_add__0__left, fact_1256_zero__less__power, fact_1294_power__eq__0__iff, fact_792_linorder__neqE__linordered__idom, fact_1412_power__le__imp__le__exp, fact_1298_power__0, fact_3388_natfloor__one, fact_3338_real__sqrt__two__gt__zero, fact_1233_power__mono, fact_355_int__0__less__1, fact_487_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_325_add__numeral__0, fact_2217_int__le__induct, fact_4597_RRset2norRR__eq__norR, fact_4454_tan__periodic__int, fact_3943_exp__total, fact_4360_gcd__nat_Osimps, help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__fun_Itc__Int__Oint, fact_2290_mult__right_Ozero, fact_4042_le__iff__pred__less, fact_551_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_1212_zero__le__one, fact_2232_MultInv__prop4, fact_499_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_2579_div__add, fact_2191_double__add__less__zero__iff__single__add__less__zero, fact_3396_sin__bound__lemma, fact_4295_Bnor__mem__zg, fact_2575_dvd__mult__div__cancel, fact_4385_real__of__int__inject, fact_3185_div__Suc, fact_1128_mult__strict__right__mono__neg, fact_3399_natceiling__neg, fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_2190_double__add__less__zero__iff__single__add__less__zero, fact_3677_sin__2npi, fact_4524_zless__zprime__imp__zrelprime, fact_3761_even__product__nat, fact_2008_add__mono, fact_3824_exp__less__cancel, fact_4487_zgcd__eq, fact_3625_tan__total__pi4, fact_1928_add__left__imp__eq, fact_763_dvd__0__right, help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__Int__Oint_U, fact_3735_cos__2npi, fact_3478_int__val__lemma, fact_3107_power__inject__base, fact_2288_mult_Ozero__right, fact_293_semiring__mult__2__right, fact_3137_diff__Suc__diff__eq1, fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_2699_Divides_Otransfer__nat__int__functions_I2_J, 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fact_2531_zdvd__mult__div__cancel, fact_1887_add__nonpos__neg, fact_2937_less__imp__of__nat__less, fact_3128_n__less__m__mult__n, fact_187_left__distrib__number__of, fact_2235_Int2_Oaux____2, fact_2630_div__add__self1, fact_1303_power__add, fact_4146_Re__cis, fact_4723_Fract__add__one, fact_1616_imp__le__cong, fact_43_add__special_I2_J, fact_3518_zminus__zminus, fact_4024_coprime__0, fact_3322_real__sqrt__eq__zero__cancel, fact_4221_divmod__nat__rel__ex, fact_4191_two__is__prime, fact_481_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_1878_add__strict__increasing2, fact_2594_int__div__less__self, fact_1555_less__bin__lemma, fact_3957_Complex__eq__0, fact_2325_mod__mod__trivial, fact_3789_lemma__STAR__sin, fact_1753_Nat_Odiff__diff__eq, fact_1988_add__0__left, fact_4537_zgcd__ex__linear, fact_3355_real__divide__square__eq, fact_4127_complex__Re__of__nat, fact_1316_zcong__zero__equiv__div, fact_1514_dvd__reduce, fact_549_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_3310_zero__induct, fact_5149_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J, fact_3512_minus__Pls, fact_1310_zcong__not, fact_948_dvd__mult__left, fact_1558_xzgcda__linear__aux1, fact_4917_Sup__atLeastLessThan, fact_454_zdvd__not__zless, fact_5160_isCont__tan, fact_2838_of__nat__Suc, fact_5154_cpmi, fact_4398_real__of__int__ceiling__cancel, fact_3556_zminus1__lemma, fact_1521_diff__bin__simps_I7_J, fact_2355_div__mod__equality, fact_368_power2__sum, fact_1374_mult__strict__mono, fact_332_less__number__of, fact_1633_nat__less__le, fact_547_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_3784_nat__even__iff__2__dvd, fact_3237_int__power__div__base, fact_1131_comm__mult__strict__left__mono, fact_4270_around__zero_Opinduct, fact_1819_mult__diff__mult, fact_4039_succ__pred, fact_4977_gcd__commute__int, fact_504_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_2608_div__prop1, fact_3955_exists__least__lemma, fact_1274_power__increasing, fact_713_power__eq__0__iff__number__of, fact_4784_less__Suc__number__of, fact_2692_div__mult2__eq, fact_4424_ceiling__le__real, fact_2864_less__Suc__eq, fact_4376_ceiling__eq2, fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_4182_prime__nd__one, fact_363_power2__eq__square__number__of, fact_22_one__power2, fact_4495_zgcd__commute, fact_2323_pos__zmod__mult__2, fact_960_dvd__mult__right, fact_4996_coprime__rmult__int, fact_4451_real__of__int__floor__add__one__ge, fact_3665_sin__add, fact_2807_EvenOdd_Oneg__one__even__power, fact_45_add__special_I3_J, fact_1_calculation_I1_J, fact_518_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_1737_diffs0__imp__equal, fact_951_dvd__mult__left, fact_3922_real__root__ge__1__iff, fact_4753_finite__divisors__int, fact_3439_ln__ge__zero, fact_4034_le__mult__floor, fact_881_field__power__not__zero, fact_2255_pinf_I10_J, 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fact_1171_zero__less__mult__pos, fact_4436_powr__minus__divide, fact_3500_m2pi__less__pi, fact_3759_even__Suc, fact_3447_zero__less__zpower__abs__iff, fact_1074_comm__mult__left__mono, fact_3318_real__sqrt__mult, fact_1078_mult__left__mono, fact_697_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_893_power__mult__distrib, fact_3783_even__dvd, fact_844_mult__zero__right, fact_2002_add__le__imp__le__right, fact_2592_StandardRes__eq__zcong, fact_4112_complex__Im__inverse, fact_2754_div__2__gt__zero, fact_2131_add__diff__cancel, fact_3632_sin__arccos, fact_3486_real__diff__def, fact_1914_add__right__imp__eq, fact_2667_zprime__zOdd__eq__grt__2, fact_4459_powr__realpow, fact_2019_add__right__mono, help_fdisj_3_1_U, fact_1527_nat__dvd__not__less, fact_778_rel__simps_I6_J, fact_3060_Suc__leI, fact_2468_zdvd__zmod__imp__zdvd, fact_47_add__special_I3_J, fact_982_one__dvd, fact_4386_real__of__int__zero, fact_9_not__sum__power2__lt__zero, fact_753_zpower__zdvd__prop2, 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fact_4439_real__of__int__gt__zero__cancel__iff, fact_2014_add__left__mono, fact_1901_ab__semigroup__mult__class_Omult__ac_I1_J, fact_1619_mult__0, fact_1259_less__add__one, fact_4120_complex__surj, fact_711_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_648_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_2498_mod__mult__self2__is__0, fact_2415_zmod__simps_I2_J, fact_205_power2__eq__imp__eq, fact_3565_real__sgn__eq, fact_822_divisors__zero, fact_5001_gcd__0__left__int, fact_1403_power__decreasing, fact_3099_of__nat__diff, fact_3815_fact__num__eq__if__nat, fact_4438_real__of__int__lt__zero__cancel__iff, fact_1172_zero__less__mult__pos, fact_2358_zmod__zdiv__equality, help_fequal_1_1_fequal_000tc__Int__Oint_T, fact_3340_real__sqrt__unique, fact_77_semiring__mult__number__of, fact_3465_incr__lemma, fact_1832_realpow__num__eq__if, fact_3050_dvd__1__iff__1, fact_281_semiring__mult__2, fact_3054_less__iff__Suc__add, fact_1427_power__gt1__lemma, 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fact_3245_even__plus__one__div__two, fact_1667_add__gr__0, fact_4651_divide__rat__def, fact_4074_code__numeral_Oinject, fact_375_number__of__Bit1, fact_1539_eq__add__iff2, fact_1506_number__of1, fact_685_zero__le__even__power_H, fact_699_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_4062_code__numeral_Osize_I2_J, fact_3539_int__zle__neg, fact_4016_coprime__commute, fact_1161_zero__less__mult__pos2, fact_1574_add__number__of__diff1, fact_3595_cos__arccos__lemma1, fact_4452_real__of__int__floor__add__one__gt, fact_2902_odd__iff__not__even, fact_1795_divides__mul__r, fact_3346_real__sqrt__sum__squares__ge1, fact_2049_add__strict__mono, fact_2707_transfer__nat__int__relations_I1_J, fact_285_semiring__mult__2, fact_3332_real__sqrt__ge__1__iff, fact_3285_mod__nat__number__of, fact_3408_arctan__add, fact_419_cube__square, fact_2367_mod__self, fact_1079_mult__left__mono, fact_3606_arccos__lbound, fact_553_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_4719_add__rat, fact_678_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_1990_add__0__left, fact_1323_mult__left__le__imp__le, fact_2546_div__mult__self2__is__id, fact_3330_real__sqrt__ge__one, fact_1714_dvd__diff__nat, fact_3582_cos__two__pi, fact_4320_gcd__semilattice__nat_Ole__infI, fact_2999_Nat__Transfer_Otransfer__int__nat__relations_I3_J, fact_1566_less__add__iff2, fact_4338_gcd__0__left__nat, fact_2443_dvd__mod__iff, fact_2727_zless__nat__conj, fact_4365_gcd__coprime__nat, fact_4171_prime__dvd__mult, fact_3801_fact__nonzero__nat, fact_3379_real__sqrt__sum__squares__less, fact_4387_real__of__int__zero__cancel, fact_4652_normalize__negative, fact_34_zero__power2, fact_4259_complex__mod__rcis, fact_1971_add__0__right, fact_3448_abs__power3__distrib, fact_3995_complex__of__real__i, fact_2706_mod__eq__0__iff, fact_2889_Parity_Oeven__plus__odd, fact_1550_left__diff__distrib__number__of, fact_4994_gcd__mult__distrib__int, fact_1866_add__nonneg__pos, fact_4109_Im_Obounded, fact_1100_mult__nonneg__nonpos2, fact_3213_le__div__geq, fact_4573_upto_Opinduct, fact_3685_nat__less__real__le, fact_2022_add__le__cancel__left, fact_1734_real__less__def, fact_817_order__le__neq__implies__less, fact_3772_even__nat__plus__one__div__two, fact_241_mult__numeral__1__right, fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_66_rel__simps_I34_J, fact_2144_add__nonpos__nonpos, fact_5099_aset_I5_J, fact_1764_add__diff__inverse, fact_880_comm__semiring__class_Odistrib, fact_2615_pos__mod__sign, fact_2267_d22set__g__1, help_If_1_1_If_000tc__Nat__Onat_T, fact_2470_div__by__0, fact_1966_add_Ocomm__neutral, fact_3159_power__Suc__less__one, fact_463_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_1023_power__one__right, fact_308_even__less__0__iff, fact_165_le__imp__0__less, fact_28_one__power2, fact_4064_complex__cnj__inverse, fact_922_dvd__mult2, fact_3822_ln__exp, fact_1823_real__squared__diff__one__factored, fact_1882_add__neg__nonpos, fact_207_power2__eq__imp__eq, fact_2555_div__self, fact_1306_power__add, fact_4535_xzgcd__correct__aux1, fact_451_zprime__power__zdvd__cancel__right, help_If_2_1_If_000tc__Int__Oint_T, fact_3891_DERIV__const__ratio__const2, fact_154_nat__numeral__1__eq__1, fact_728_power__0__left__number__of, fact_4420_floor__add, fact_3039_zadd__int, help_fFalse_1_1_U, fact_1784_real__mult__assoc, fact_74_semiring__mult__number__of, fact_4020_floor__real__of__nat, fact_108_le__number__of__eq__not__less, fact_2058_add__strict__right__mono, fact_4322_gcd__proj2__if__dvd__nat, fact_1299_power__0, fact_4303_gcd__semilattice__nat_Oinf_Oidem, fact_2369_mod__by__0, fact_3145_of__nat__0__less__iff, fact_1766_less__diff__iff, fact_2893_odd__pow, fact_5178_DERIV__isconst__end, fact_2673_mod__div__decomp, fact_3834_exp__gt__zero, fact_918_dvd__triv__right, fact_1916_add__imp__eq, fact_5045_LIMSEQ__rabs__realpow__zero2, fact_4098_Im_Oadd, fact_1839_nat__less__add__iff2, 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fact_4550_DERIV__nonneg__imp__nonincreasing, fact_932_dvd__mult, fact_2571_div__mult__swap, fact_1973_add__0__right, fact_2030_add__le__cancel__right, fact_928_dvd__mult, fact_3078_mod__1, fact_5025_Rat__cases__nonzero, fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_4343_gcd__Suc__0, fact_1885_add__neg__nonpos, fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_1454_power__strict__increasing__iff, fact_1283_power__inject__exp, fact_939_mult__dvd__mono, fact_3433_zabs__less__one__iff, fact_5179_DERIV__isconst1, fact_1435_power__0__left, fact_2765_SRStar__mult__prop1, fact_111_less__eq__int__code_I14_J, fact_2918_of__nat__less__0__iff, fact_3417_abs__int__eq, fact_1927_add__left__imp__eq, fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_3072_Suc__diff__le, fact_1327_mult__right__le__imp__le, fact_324_add__numeral__0, fact_1438_power__0__left, fact_1854_nat__le__add__iff1, fact_977_one__dvd, fact_1037_zcong__zadd, fact_620_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_345_rel__simps_I12_J, fact_63_zle__antisym, fact_5015_gcd__code__int, fact_1285_power__inject__exp, fact_3097_odd__minus__odd, fact_5120_min__Suc__number__of, fact_1977_double__zero__sym, fact_3046_nat__lt__two__imp__zero__or__one, fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_1821_exp__eq__1, fact_2894_one__not__even, fact_1201_not__square__less__zero, fact_5071_SetInterval_Otransfer__nat__int__set__functions_I2_J, fact_158_zle__add1__eq__le, fact_3309_nat_Oexhaust, fact_740_Euler_Oaux____1, fact_1207_pos__add__strict, fact_2821_code__numeral__zero__minus__one, fact_2602_div__nonneg__neg__le0, fact_4499_zgcd__self, fact_1957_diff__eq__diff__eq, fact_3428_ln__inj__iff, fact_4054_ResSet__def, fact_2813_of__nat__double, fact_2826_number__of__int, help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc__, fact_568_zero__less__power__nat__eq__number__of, fact_2824_number__of__int, fact_1341_mult__left__less__imp__less, fact_4215_divmod__nat__rel__unique, fact_1460_zcong__zless__imp__eq, fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, help_If_2_1_If_000tc__Nat__Onat_T, fact_3680_sin__cos__squared__add3, fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, help_fequal_2_1_fequal_000tc__Int__Oint_T, fact_1642_nat__add__left__cancel__le, fact_917_dvd__triv__right, fact_222_power2__less__imp__less, fact_3785_even__mult__two__ex, fact_3276_neg__number__of__Min, fact_2455_dvd__mod__imp__dvd, fact_40_add__special_I2_J, gsy_v_m, fact_823_divisors__zero, fact_814_order__le__neq__implies__less, fact_3742_sin__cos__minus, fact_1162_zero__less__mult__pos2, fact_3121_int__nat__eq, fact_879_comm__semiring__class_Odistrib, fact_1182_mult__pos__neg, fact_4199_xzgcd__linear, fact_4133_complex__mod__sqrt__Re__mult__cnj, fact_2587_dvd__eq__mod__eq__0__number__of, fact_2831_of__nat__eq__iff, fact_2517_dvd__eq__mod__eq__0, fact_3611_tan__45, fact_2978_of__nat__power, fact_4036_coprime__bezout, fact_3656_real__natceiling__ge, fact_1468_power__Suc__less, fact_2005_add__mono, fact_3557_negD, fact_1641_le__iff__add, fact_5151_vanishesD, fact_5176_isCont__inv__fun, fact_1656_mult__le__mono, fact_761_dvd__0__right, fact_5128_SetInterval_Otransfer__int__nat__set__functions, fact_1528_inf__period_I3_J, fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_3686_nat__le__real__less, fact_306_even__less__0__iff, fact_3749_reals__Archimedean4, fact_3287_SRStar__card, fact_3887_DERIV__pos__inc__left, fact_3874_log__divide, fact_859_zero__neq__one, fact_4709_rat__number__collapse_I3_J, fact_4574_small__lazy_H_Opinduct, fact_2565_dvd__div__mult__self, fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_1203_pos__add__strict, fact_4670_eq__rat_I2_J, fact_1556_dvd__imp__le, fact_3521_uminus__dvd__conv_I2_J, fact_3979_inverse__i, fact_3196_semiring__norm_I115_J, fact_1868_add__nonneg__pos, fact_930_dvd__mult, fact_3534_zmod__zminus2__not__zero, fact_1944_ab__semigroup__add__class_Oadd__ac_I1_J, fact_4277_transfer__nat__int__factorial__closure, fact_1002_dvd__power__le, fact_3423_pi__not__less__zero, fact_4358_gcd__diff2__nat, fact_3058_Suc__le__lessD, fact_2410_zmod__simps_I1_J, fact_4363_ceiling__real__of__nat, fact_1038_zcong__shift, fact_2552_div__mult__mult1__if, help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Int__Oint_U, fact_2198_add__le__less__mono, fact_4423_ceiling__le, fact_5082_card__atLeastAtMost__int, fact_663_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_1690_decr__mult__lemma, fact_2559_div__mult__div__if__dvd, fact_2720_nat__mult__div__cancel1, fact_2861_less__antisym, fact_3684_cos__add, fact_2069_add__less__cancel__left, fact_322_add__numeral__0, fact_4983_gcd__greatest__iff__int, fact_127_less__number__of__int__code, fact_3120_power__gt1, fact_4530_xzgcd__correct, fact_55_zle__linear, fact_4457_real__of__int__ceiling__le__add__one, fact_2224_wset__subset, fact_4258_rcis__zero__arg, fact_84_arith__simps_I32_J, fact_4236_mod__pos__pos__1__number__of, fact_2382_mod__mult__left__eq, fact_143_mem__def, fact_2725_nat__le__0, fact_131_zadd__zmult__distrib, fact_2672_SRStar__mult__prop2, fact_2931_of__nat__less__imp__less, fact_2766_Euler__part2, fact_2368_mod__by__0, fact_2814_of__nat__double, fact_2869_Suc__n__not__le__n, fact_2112_mult__1, fact_679_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_3638_natfloor__real__of__nat, fact_3374_lemma__f__mono__add, fact_3313_real__sqrt__le__iff, fact_3513_minus__Bit0, help_If_1_1_If_000tc__Int__Oint_T, fact_1713_dvd_Oorder__trans, fact_2044_add__less__imp__less__right, fact_2152_add__increasing2, fact_4692_normalize__eq, fact_4989_gcd__abs1__int, fact_1287_power__inject__exp, fact_58_le__number__of, fact_1853_nat__diff__add__eq1, fact_4591_RRset2norRR__correct, fact_3646_real__of__nat__zero, fact_525_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_1008_le__imp__power__dvd, fact_5143_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J, fact_831_no__zero__divisors, fact_1398_power__less__imp__less__base, fact_4506_zgcd__0__left, fact_3253_dvd_Olift__Suc__mono__le, fact_4685_minus__rat__cancel, fact_4445_number__of__le__real__of__int__iff, fact_771_rel__simps_I45_J, fact_444_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_5013_gcd__le1__int, fact_2993_power__0__Suc, fact_1484_power__eq__imp__eq__base, fact_1408_power__le__imp__le__exp, fact_5152_vanishesI, fact_882_field__power__not__zero, fact_5142_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J, fact_1425_power__less__power__Suc, fact_3160_power__Suc__less__one, fact_1578_Euler_Oaux1, fact_1593_nat__add__assoc, fact_3303_lessE, fact_1410_power__le__imp__le__exp, fact_1151_mult__neg__neg, fact_2885_anything__times__even, fact_3959_Complex__eq__number__of, fact_751_convex__bound__lt, fact_1871_add__strict__increasing, fact_4718_le__rat, fact_380_semiring__numeral__1__eq__1, fact_1845_left__add__mult__distrib, fact_2337_zdiv__zadd1__eq, fact_1376_mult__strict__mono, fact_4344_gcd__pos__nat, fact_3845_exp__ge__add__one__self, fact_4750_Bseq__realpow, fact_1589_less__not__refl3, fact_1806_diff__square, fact_1699_dvd_Oeq__iff, fact_3636_real__of__nat__inject, fact_151_rel__simps_I15_J, fact_1394_zero__less__two, fact_757_dvd__0__right, fact_3047_less__Suc__eq__0__disj, fact_3057_One__nat__def, fact_791_linorder__neqE__linordered__idom, fact_3220_of__nat__number__of__lemma, fact_2028_add__le__cancel__right, fact_887_dvd__0__left, fact_2469_zpower__zmod, fact_1836__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096, fact_1272_power__increasing, fact_3885_DERIV__local__max, fact_3584_cos__60, fact_3648_real__of__nat__less__iff, fact_2342_mod__div__equality2, fact_715_power__eq__0__iff__number__of, fact_3146_of__nat__0__less__iff, fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_4785_le__Suc__number__of, fact_3878_DERIV__tan, fact_4369_coprime__dvd__mult__nat, fact_4415_real__of__int__div4, fact_2956_of__nat__add, fact_1507_less__zeroE, fact_1373_mult__strict__mono, fact_1981_add__0, fact_824_divisors__zero, fact_3392_natceiling__number__of__eq, fact_391_semiring__norm_I110_J, fact_1218_not__one__le__zero, fact_3602_zsgn__def, fact_4978_gcd__int_Oleft__commute, fact_1234_power__mono, fact_4462_log__powr__cancel, fact_3763_odd__pos, fact_3230_power__odd__eq, fact_421_self__quotient__aux1, fact_3695_sin__expansion__lemma, fact_3947_polar__ex2, fact_3925_real__root__gt__1__iff, fact_2964_of__nat__mult, fact_2862_not__less__less__Suc__eq, fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_3978_complex__i__mult__minus, fact_3694_natceiling__subtract, fact_1888_add__nonpos__neg, fact_2202_add__less__le__mono, fact_3659_real__of__nat__le__zero__cancel__iff, fact_300_power2__eq__square, fact_3509_arcsin__ubound, fact_4721_Fract__less__one__iff, fact_4546_dist__complex__def, fact_2670_neg__zdiv__mult__2, fact_3702_natfloor__add, fact_2753_Little__Fermat, fact_3168_int__eq__iff__number__of, fact_927_dvd__mult, fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_2683_nat__if__cong, fact_2723_div__less__dividend, fact_2954_of__nat__add, fact_3035_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_2178_add__neg__neg, fact_2106_mult__1__right, fact_24_one__power2, fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_3052_one__is__add, fact_2892_even__difference, fact_3155_realpow__Suc__le__self, fact_4689_minus__rat, fact_4066_cnj_Ozero, fact_4222_euclid, fact_2482_div__dvd__div, fact_4317_dvd__gcd__D1__nat, fact_4475_powr__realpow2, fact_3144_of__nat__0__less__iff, fact_3329_real__sqrt__gt__0__iff, fact_1144_mult__strict__right__mono, fact_3267_not__neg__0, fact_544_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_1736_real__le__refl, fact_2484_div__dvd__div, fact_1315_zcong__eq__zdvd__prop, fact_126_mult__Bit0, help_fequal_2_1_fequal_000tc__RealDef__Oreal_T, fact_2183_add__pos__pos, fact_4628_card__greaterThanLessThan__int, fact_4178_prime__coprime__strong, fact_4431_powr__mult, fact_4012_coprime__mul__eq, fact_3025_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_2387_mod__mult__eq, fact_2794_self__quotient, gsy_v_s1____, fact_4278_fact__nonzero__int, fact_1797_realpow__minus__mult, fact_4293_Bnor__mem__zle, fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_2583_div__power, fact_2007_add__mono, fact_1580_diff__bin__simps_I4_J, fact_4105_Im__sgn, fact_320_semiring__norm_I112_J, fact_4092_Im, fact_2597_div__neg__neg__trivial, fact_5098_bset_I4_J, fact_3710_sin__double, fact_1679_unity__coeff__ex, fact_5165_cnj_OisCont, fact_2226_wset__less, fact_4218_div__eq, fact_3412_lemma__interval, fact_3703_sin__arcsin, fact_2856_Suc__lessD, fact_3799_fact__add__num__eq__if2__nat, fact_2086_diff__self, fact_4009_coprime__lmul2, fact_1469_power__Suc__less, fact_1844_nat__mult__eq__cancel__disj, fact_3805_fact__Suc__0__nat, fact_2206_add__less__le__mono, fact_4428_floor__minus__real__of__int, fact_836_mult__eq__0__iff, fact_3728_sin__cos__squared__add, fact_3084_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_1703_divides__antisym, fact_2761_WilsonRuss_Oinv__def, fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_1494_dvd__power, fact_256_Pls__def, fact_884_field__power__not__zero, fact_1559_zcong__def, fact_3138_diff__Suc__diff__eq2, fact_810_zcong__eq__trans, fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_2621_div__mult__self1, fact_4404_powr__gt__zero, fact_1431_power__gt1__lemma, fact_1573_dvd__mult__cancel2, fact_5016_coprime__common__divisor__int, fact_896_power__mult__distrib, fact_1788_real__mult__left__cancel, fact_2752_EvenOdd_Oneg__one__odd__power, fact_4000_expi__add, fact_3629_lemma__tan__total, fact_991_power__le__dvd, fact_2716_le__mod__geq, fact_3221_even__equiv__def, fact_2951_of__nat__le__iff, fact_4361_gcd__non__0__nat, fact_4172_prime__product, fact_4165_primes__eq, fact_2995_power__0__Suc, fact_3663_abs__sin__le__one, fact_1907_ab__semigroup__mult__class_Omult__ac_I1_J, fact_13_sum__power2__eq__zero__iff, fact_4449_real__nat__eq__real, fact_2205_add__less__le__mono, fact_5136_Divides_Otransfer__int__nat__function__closures_I2_J, fact_1898_zero__reorient, fact_3124_zless__nat__eq__int__zless, fact_3697_ln__realpow, fact_2599_div__nonpos__pos__le0, fact_2371_mod__by__0, fact_3289_zero__induct__lemma, fact_4518_zrelprime__dvd__mult, fact_938_mult__dvd__mono, fact_3135_one__le__mult__iff, fact_2888_odd__plus__even 115.68/52.97 % No. of inferences in proof: 9898 115.68/52.97 % No. of processed clauses: 50 115.68/52.97 % No. of generated clauses: 59 115.68/52.97 % No. of forward subsumed clauses: 14 115.68/52.97 % No. of backward subsumed clauses: 0 115.68/52.97 % No. of ground rewrite rules in store: 31 115.68/52.97 % No. of non-ground rewrite rules in store: 3 115.68/52.97 % No. of positive (non-rewrite) units in store: 0 115.68/52.97 % No. of negative (non-rewrite) units in store: 15 115.68/52.97 % No. of choice functions detected: 0 115.68/52.97 % No. of choice instantiations: 0 115.68/52.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 52554 ms resp. 41523 ms w/o parsing 120.83/55.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 120.83/55.28 thf(ord_less_int_type, type, ord_less_int: $i). 120.83/55.28 thf(plus_plus_int_type, type, plus_plus_int: $i). 120.83/55.28 thf(power_power_int_type, type, power_power_int: $i). 120.83/55.28 thf(s_type, type, s: $i). 120.83/55.28 thf(hAPP_int_fun_nat_int_type, type, hAPP_int_fun_nat_int: ($i > ($i > $i))). 120.83/55.28 thf(number_number_of_nat_type, type, number_number_of_nat: $i). 120.83/55.28 thf(bit0_type, type, bit0: $i). 120.83/55.28 thf(bit1_type, type, bit1: $i). 120.83/55.28 thf(pls_type, type, pls: $i). 120.83/55.28 thf(hAPP_int_int_type, type, hAPP_int_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_int_nat_type, type, hAPP_int_nat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_int_type, type, hAPP_nat_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_int_fun_int_int_type, type, hAPP_int_fun_int_int: ($i > ($i > $i))). 120.83/55.28 thf(one_one_int_type, type, one_one_int: $i). 120.83/55.28 thf(hAPP_i1948725293t_bool_type, type, hAPP_i1948725293t_bool: ($i > ($i > $i))). 120.83/55.28 thf(zero_zero_int_type, type, zero_zero_int: $i). 120.83/55.28 thf(hAPP_int_bool_type, type, hAPP_int_bool: ($i > ($i > $i))). 120.83/55.28 thf(hBOOL_type, type, hBOOL: ($i > $o)). 120.83/55.28 thf(times_times_complex_type, type, times_times_complex: $i). 120.83/55.28 thf(of_real_complex_type, type, of_real_complex: ($i > $i)). 120.83/55.28 thf(hAPP_c172932010omplex_type, type, hAPP_c172932010omplex: ($i > ($i > $i))). 120.83/55.28 thf(complex_type, type, complex: $i). 120.83/55.28 thf(cos_type, type, cos: $i). 120.83/55.28 thf(hAPP_real_real_type, type, hAPP_real_real: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_r265291036omplex_type, type, hAPP_r265291036omplex: ($i > ($i > $i))). 120.83/55.28 thf(sin_type, type, sin: $i). 120.83/55.28 thf(hAPP_real_complex_type, type, hAPP_real_complex: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_complex_complex_type, type, hAPP_complex_complex: ($i > ($i > $i))). 120.83/55.28 thf(cnj_type, type, cnj: $i). 120.83/55.28 thf(ii_type, type, ii: $i). 120.83/55.28 thf(uminus473333897omplex_type, type, uminus473333897omplex: $i). 120.83/55.28 thf(minus_minus_complex_type, type, minus_minus_complex: $i). 120.83/55.28 thf(plus_plus_complex_type, type, plus_plus_complex: $i). 120.83/55.28 thf(zero_zero_complex_type, type, zero_zero_complex: $i). 120.83/55.28 thf(zero_zero_real_type, type, zero_zero_real: $i). 120.83/55.28 thf(divmod_nat_type, type, divmod_nat: ($i > ($i > $i))). 120.83/55.28 thf(divmod_nat_rel_type, type, divmod_nat_rel: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P1555980039t_bool_type, type, hAPP_P1555980039t_bool: ($i > ($i > $i))). 120.83/55.28 thf(product_Pair_nat_nat_type, type, product_Pair_nat_nat: $i). 120.83/55.28 thf(hAPP_n1865633855at_nat_type, type, hAPP_n1865633855at_nat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_n1289843868at_nat_type, type, hAPP_n1289843868at_nat: ($i > ($i > $i))). 120.83/55.28 thf(one_one_real_type, type, one_one_real: $i). 120.83/55.28 thf(uminus_uminus_real_type, type, uminus_uminus_real: $i). 120.83/55.28 thf(minus_minus_real_type, type, minus_minus_real: $i). 120.83/55.28 thf(times_times_real_type, type, times_times_real: $i). 120.83/55.28 thf(hAPP_r1250527377l_real_type, type, hAPP_r1250527377l_real: ($i > ($i > $i))). 120.83/55.28 thf(plus_plus_real_type, type, plus_plus_real: $i). 120.83/55.28 thf(inverse_divide_real_type, type, inverse_divide_real: $i). 120.83/55.28 thf(power_power_real_type, type, power_power_real: $i). 120.83/55.28 thf(hAPP_r474017924t_real_type, type, hAPP_r474017924t_real: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_real_type, type, hAPP_nat_real: ($i > ($i > $i))). 120.83/55.28 thf(invers1449016382omplex_type, type, invers1449016382omplex: $i). 120.83/55.28 thf(one_one_complex_type, type, one_one_complex: $i). 120.83/55.28 thf(div_div_nat_type, type, div_div_nat: $i). 120.83/55.28 thf(hAPP_nat_fun_nat_nat_type, type, hAPP_nat_fun_nat_nat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_nat_type, type, hAPP_nat_nat: ($i > ($i > $i))). 120.83/55.28 thf(div_mod_nat_type, type, div_mod_nat: ($i > $i)). 120.83/55.28 thf(re_type, type, re: $i). 120.83/55.28 thf(hAPP_complex_real_type, type, hAPP_complex_real: ($i > ($i > $i))). 120.83/55.28 thf(im_type, type, im: $i). 120.83/55.28 thf(cOMBC_real_nat_real_type, type, cOMBC_real_nat_real: $i). 120.83/55.28 thf(hAPP_f248847589l_real_type, type, hAPP_f248847589l_real: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_n546711566l_real_type, type, hAPP_n546711566l_real: ($i > ($i > $i))). 120.83/55.28 thf(abs_abs_real_type, type, abs_abs_real: $i). 120.83/55.28 thf(norm_norm_real_type, type, norm_norm_real: $i). 120.83/55.28 thf(cis_type, type, cis: ($i > $i)). 120.83/55.28 thf(norm_norm_complex_type, type, norm_norm_complex: $i). 120.83/55.28 thf(sqrt_type, type, sqrt: $i). 120.83/55.28 thf(number528085621omplex_type, type, number528085621omplex: $i). 120.83/55.28 thf(hAPP_int_complex_type, type, hAPP_int_complex: ($i > ($i > $i))). 120.83/55.28 thf(number267125858f_real_type, type, number267125858f_real: $i). 120.83/55.28 thf(hAPP_int_real_type, type, hAPP_int_real: ($i > ($i > $i))). 120.83/55.28 thf(ord_less_eq_real_type, type, ord_less_eq_real: $i). 120.83/55.28 thf(hAPP_r1134773055l_bool_type, type, hAPP_r1134773055l_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_real_bool_type, type, hAPP_real_bool: ($i > ($i > $i))). 120.83/55.28 thf(dvd_dvd_real_type, type, dvd_dvd_real: $i). 120.83/55.28 thf(div_mo231679042de_int_type, type, div_mo231679042de_int: ($i > $i)). 120.83/55.28 thf(hAPP_Q1762011733de_int_type, type, hAPP_Q1762011733de_int: ($i > ($i > $i))). 120.83/55.28 thf(quickcheck_of_int_type, type, quickcheck_of_int: $i). 120.83/55.28 thf(quickcheck_int_of_type, type, quickcheck_int_of: ($i > $i)). 120.83/55.28 thf(div_mod_int_type, type, div_mod_int: ($i > $i)). 120.83/55.28 thf(hAPP_i1732201573de_int_type, type, hAPP_i1732201573de_int: ($i > ($i > $i))). 120.83/55.28 thf(ord_less_real_type, type, ord_less_real: $i). 120.83/55.28 thf(isCont_real_real_type, type, isCont_real_real: ($i > $i)). 120.83/55.28 thf(arcsin_type, type, arcsin: $i). 120.83/55.28 thf(pi_type, type, pi: $i). 120.83/55.28 thf(ln_type, type, ln: $i). 120.83/55.28 thf(deriv_real_type, type, deriv_real: ($i > ($i > $i))). 120.83/55.28 thf(inverse_inverse_real_type, type, inverse_inverse_real: $i). 120.83/55.28 thf(power_power_complex_type, type, power_power_complex: $i). 120.83/55.28 thf(hAPP_c1088319240omplex_type, type, hAPP_c1088319240omplex: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_complex_type, type, hAPP_nat_complex: ($i > ($i > $i))). 120.83/55.28 thf(real_nat_type, type, real_nat: $i). 120.83/55.28 thf(zero_z891286103de_int_type, type, zero_z891286103de_int: $i). 120.83/55.28 thf(invers1025623611omplex_type, type, invers1025623611omplex: $i). 120.83/55.28 thf(powr_type, type, powr: $i). 120.83/55.28 thf(dvd_dvd_complex_type, type, dvd_dvd_complex: $i). 120.83/55.28 thf(hAPP_c1403687985x_bool_type, type, hAPP_c1403687985x_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_complex_bool_type, type, hAPP_complex_bool: ($i > ($i > $i))). 120.83/55.28 thf(zero_z126310315umeral_type, type, zero_z126310315umeral: $i). 120.83/55.28 thf(div_mo1740067990umeral_type, type, div_mo1740067990umeral: ($i > $i)). 120.83/55.28 thf(hAPP_C498520661umeral_type, type, hAPP_C498520661umeral: ($i > ($i > $i))). 120.83/55.28 thf(arccos_type, type, arccos: $i). 120.83/55.28 thf(arctan_type, type, arctan: $i). 120.83/55.28 thf(is_int_type, type, is_int: ($i > $o)). 120.83/55.28 thf(archim856651990g_real_type, type, archim856651990g_real: ($i > $i)). 120.83/55.28 thf(real_int_type, type, real_int: $i). 120.83/55.28 thf(tan_type, type, tan: $i). 120.83/55.28 thf(min_type, type, min: $i). 120.83/55.28 thf(zero_zero_nat_type, type, zero_zero_nat: $i). 120.83/55.28 thf(size_size_nat_type, type, size_size_nat: $i). 120.83/55.28 thf(natceiling_type, type, natceiling: ($i > $i)). 120.83/55.28 thf(nat_type, type, nat: $i). 120.83/55.28 thf(exp_real_type, type, exp_real: $i). 120.83/55.28 thf(minus_minus_nat_type, type, minus_minus_nat: $i). 120.83/55.28 thf(suc_type, type, suc: $i). 120.83/55.28 thf(plus_p1627245867umeral_type, type, plus_p1627245867umeral: $i). 120.83/55.28 thf(hAPP_C1594335432umeral_type, type, hAPP_C1594335432umeral: ($i > ($i > $i))). 120.83/55.28 thf(times_1655362735umeral_type, type, times_1655362735umeral: $i). 120.83/55.28 thf(div_di1218280263umeral_type, type, div_di1218280263umeral: $i). 120.83/55.28 thf(natfloor_type, type, natfloor: ($i > $i)). 120.83/55.28 thf(inverse_divide_rat_type, type, inverse_divide_rat: $i). 120.83/55.28 thf(number_number_of_rat_type, type, number_number_of_rat: $i). 120.83/55.28 thf(hAPP_int_rat_type, type, hAPP_int_rat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_rat_fun_rat_rat_type, type, hAPP_rat_fun_rat_rat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_rat_rat_type, type, hAPP_rat_rat: ($i > ($i > $i))). 120.83/55.28 thf(ratreal_type, type, ratreal: ($i > $i)). 120.83/55.28 thf(ord_at4362885an_nat_type, type, ord_at4362885an_nat: ($i > $i)). 120.83/55.28 thf(hAPP_n1699378549t_bool_type, type, hAPP_n1699378549t_bool: ($i > ($i > $i))). 120.83/55.28 thf(ord_at238088361st_nat_type, type, ord_at238088361st_nat: ($i > $i)). 120.83/55.28 thf(archim1246769320r_real_type, type, archim1246769320r_real: ($i > $i)). 120.83/55.28 thf(log_type, type, log: ($i > $i)). 120.83/55.28 thf(minus_minus_int_type, type, minus_minus_int: $i). 120.83/55.28 thf(even_odd_even_nat_type, type, even_odd_even_nat: $i). 120.83/55.28 thf(hAPP_nat_bool_type, type, hAPP_nat_bool: ($i > ($i > $i))). 120.83/55.28 thf(ord_less_nat_type, type, ord_less_nat: $i). 120.83/55.28 thf(plus_plus_nat_type, type, plus_plus_nat: $i). 120.83/55.28 thf(semiri2020571505omplex_type, type, semiri2020571505omplex: $i). 120.83/55.28 thf(semiri132038758t_real_type, type, semiri132038758t_real: $i). 120.83/55.28 thf(rcis_type, type, rcis: ($i > ($i > $i))). 120.83/55.28 thf(dvd_dv174992974umeral_type, type, dvd_dv174992974umeral: $i). 120.83/55.28 thf(hAPP_C10902773l_bool_type, type, hAPP_C10902773l_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_C24501650l_bool_type, type, hAPP_C24501650l_bool: ($i > ($i > $i))). 120.83/55.28 thf(semiri1621563631at_int_type, type, semiri1621563631at_int: $i). 120.83/55.28 thf(image_nat_int_type, type, image_nat_int: ($i > ($i > $i))). 120.83/55.28 thf(uminus_uminus_int_type, type, uminus_uminus_int: $i). 120.83/55.28 thf(code_S1047413653umeral_type, type, code_S1047413653umeral: ($i > $i)). 120.83/55.28 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: $i). 120.83/55.28 thf(archim791455193or_rat_type, type, archim791455193or_rat: ($i > $i)). 120.83/55.28 thf(div_div_int_type, type, div_div_int: $i). 120.83/55.28 thf(bseq_real_type, type, bseq_real: ($i > $i)). 120.83/55.28 thf(ord_less_eq_int_type, type, ord_less_eq_int: $i). 120.83/55.28 thf(one_one_rat_type, type, one_one_rat: $i). 120.83/55.28 thf(dist_dist_complex_type, type, dist_dist_complex: ($i > $i)). 120.83/55.28 thf(sgn_sgn_real_type, type, sgn_sgn_real: $i). 120.83/55.28 thf(minus_1690775515umeral_type, type, minus_1690775515umeral: $i). 120.83/55.28 thf(one_on1645066479umeral_type, type, one_on1645066479umeral: $i). 120.83/55.28 thf(times_times_nat_type, type, times_times_nat: $i). 120.83/55.28 thf(uminus_uminus_rat_type, type, uminus_uminus_rat: $i). 120.83/55.28 thf(plus_p1446045655de_int_type, type, plus_p1446045655de_int: $i). 120.83/55.28 thf(hAPP_Q1729056540de_int_type, type, hAPP_Q1729056540de_int: ($i > ($i > $i))). 120.83/55.28 thf(times_123202395de_int_type, type, times_123202395de_int: $i). 120.83/55.28 thf(div_di1430059507de_int_type, type, div_di1430059507de_int: $i). 120.83/55.28 thf(expi_type, type, expi: ($i > $i)). 120.83/55.28 thf(sequentially_type, type, sequentially: $i). 120.83/55.28 thf(tendsto_nat_real_type, type, tendsto_nat_real: ($i > ($i > ($i > $i)))). 120.83/55.28 thf(monoseq_real_type, type, monoseq_real: ($i > $i)). 120.83/55.28 thf(number1226105091de_int_type, type, number1226105091de_int: $i). 120.83/55.28 thf(cauchy_real_type, type, cauchy_real: ($i > $i)). 120.83/55.28 thf(abs_abs_int_type, type, abs_abs_int: $i). 120.83/55.28 thf(fact_fact_nat_type, type, fact_fact_nat: $i). 120.83/55.28 thf(ord_atMost_nat_type, type, ord_atMost_nat: $i). 120.83/55.28 thf(if_Pro1731782967nt_int_type, type, if_Pro1731782967nt_int: $i). 120.83/55.28 thf(fTrue_type, type, fTrue: $i). 120.83/55.28 thf(hAPP_b40753821nt_int_type, type, hAPP_b40753821nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P1145851913nt_int_type, type, hAPP_P1145851913nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P1975530577nt_int_type, type, hAPP_P1975530577nt_int: ($i > ($i > $i))). 120.83/55.28 thf(dvd_dv1760642554de_int_type, type, dvd_dv1760642554de_int: $i). 120.83/55.28 thf(hAPP_Q1010094925t_bool_type, type, hAPP_Q1010094925t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_Q2096512830t_bool_type, type, hAPP_Q2096512830t_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBI_nat_type, type, cOMBI_nat: $i). 120.83/55.28 thf(one_one_nat_type, type, one_one_nat: $i). 120.83/55.28 thf(big_co1705425894at_nat_type, type, big_co1705425894at_nat: ($i > ($i > $i))). 120.83/55.28 thf(times_times_int_type, type, times_times_int: $i). 120.83/55.28 thf(zero_zero_rat_type, type, zero_zero_rat: $i). 120.83/55.28 thf(image_int_nat_type, type, image_int_nat: ($i > ($i > $i))). 120.83/55.28 thf(nat_tr876908586nt_nat_type, type, nat_tr876908586nt_nat: ($i > $i)). 120.83/55.28 thf(hAPP_f448129468l_bool_type, type, hAPP_f448129468l_bool: ($i > ($i > $i))). 120.83/55.28 thf(ring_11397209091omplex_type, type, ring_11397209091omplex: $i). 120.83/55.28 thf(dvd_dvd_rat_type, type, dvd_dvd_rat: $i). 120.83/55.28 thf(hAPP_r2115560837t_bool_type, type, hAPP_r2115560837t_bool: ($i > ($i > $i))). 120.83/55.28 thf(minus_minus_rat_type, type, minus_minus_rat: $i). 120.83/55.28 thf(hAPP_rat_bool_type, type, hAPP_rat_bool: ($i > ($i > $i))). 120.83/55.28 thf(sgn_sgn_complex_type, type, sgn_sgn_complex: $i). 120.83/55.28 thf(times_times_rat_type, type, times_times_rat: $i). 120.83/55.28 thf(cOMBB_1418110531ol_int_type, type, cOMBB_1418110531ol_int: $i). 120.83/55.28 thf(hAPP_f423804115t_bool_type, type, hAPP_f423804115t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f2119767738t_bool_type, type, hAPP_f2119767738t_bool: ($i > ($i > $i))). 120.83/55.28 thf(fFalse_type, type, fFalse: $i). 120.83/55.28 thf(coprime_type, type, coprime: $i). 120.83/55.28 thf(nat_nat_set_type, type, nat_nat_set: $i). 120.83/55.28 thf(code_int_of_type, type, code_int_of: ($i > $i)). 120.83/55.28 thf(cOMBK_1643584600t_bool_type, type, cOMBK_1643584600t_bool: ($i > $i)). 120.83/55.28 thf(hAPP_f957591787ol_nat_type, type, hAPP_f957591787ol_nat: ($i > ($i > $i))). 120.83/55.28 thf(inverse_inverse_rat_type, type, inverse_inverse_rat: $i). 120.83/55.28 thf(if_real_type, type, if_real: $i). 120.83/55.28 thf(hAPP_b646336293l_real_type, type, hAPP_b646336293l_real: ($i > ($i > $i))). 120.83/55.28 thf(nat_lcm_type, type, nat_lcm: ($i > $i)). 120.83/55.28 thf(nat_gcd_type, type, nat_gcd: ($i > $i)). 120.83/55.28 thf(collect_int_type, type, collect_int: ($i > $i)). 120.83/55.28 thf(nat_size_type, type, nat_size: $i). 120.83/55.28 thf(plus_plus_rat_type, type, plus_plus_rat: $i). 120.83/55.28 thf(dvd_dvd_nat_type, type, dvd_dvd_nat: $i). 120.83/55.28 thf(ord_le1304079648umeral_type, type, ord_le1304079648umeral: $i). 120.83/55.28 thf(ord_le565307924umeral_type, type, ord_le565307924umeral: $i). 120.83/55.28 thf(power_power_nat_type, type, power_power_nat: $i). 120.83/55.28 thf(prime_type, type, prime: $i). 120.83/55.28 thf(ord_less_eq_rat_type, type, ord_less_eq_rat: $i). 120.83/55.28 thf(standardRes_type, type, standardRes: ($i > $i)). 120.83/55.28 thf(ord_le1860547276de_int_type, type, ord_le1860547276de_int: $i). 120.83/55.28 thf(one_on1684967323de_int_type, type, one_on1684967323de_int: $i). 120.83/55.28 thf(power_881366806de_int_type, type, power_881366806de_int: $i). 120.83/55.28 thf(hAPP_Q125967240de_int_type, type, hAPP_Q125967240de_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_n522471361de_int_type, type, hAPP_n522471361de_int: ($i > ($i > $i))). 120.83/55.28 thf(root_type, type, root: $i). 120.83/55.28 thf(gcd_gcd_nat_type, type, gcd_gcd_nat: $i). 120.83/55.28 thf(power_2100829034umeral_type, type, power_2100829034umeral: $i). 120.83/55.28 thf(hAPP_C471253896umeral_type, type, hAPP_C471253896umeral: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_n1108039445umeral_type, type, hAPP_n1108039445umeral: ($i > ($i > $i))). 120.83/55.28 thf(ord_less_rat_type, type, ord_less_rat: $i). 120.83/55.28 thf(power_power_rat_type, type, power_power_rat: $i). 120.83/55.28 thf(hAPP_rat_fun_nat_rat_type, type, hAPP_rat_fun_nat_rat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_rat_type, type, hAPP_nat_rat: ($i > ($i > $i))). 120.83/55.28 thf(product_fst_int_int_type, type, product_fst_int_int: $i). 120.83/55.28 thf(bezw_type, type, bezw: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P1175774780nt_int_type, type, hAPP_P1175774780nt_int: ($i > ($i > $i))). 120.83/55.28 thf(product_snd_int_int_type, type, product_snd_int_int: $i). 120.83/55.28 thf(number_number_of_int_type, type, number_number_of_int: $i). 120.83/55.28 thf(fract_type, type, fract: $i). 120.83/55.28 thf(hAPP_int_fun_int_rat_type, type, hAPP_int_fun_int_rat: ($i > ($i > $i))). 120.83/55.28 thf(ord_le258702272de_int_type, type, ord_le258702272de_int: $i). 120.83/55.28 thf(divmod_int_type, type, divmod_int: ($i > ($i > $i))). 120.83/55.28 thf(posDivAlg_type, type, posDivAlg: ($i > ($i > $i))). 120.83/55.28 thf(negateSnd_type, type, negateSnd: $i). 120.83/55.28 thf(negDivAlg_type, type, negDivAlg: ($i > ($i > $i))). 120.83/55.28 thf(product_Pair_int_int_type, type, product_Pair_int_int: $i). 120.83/55.28 thf(hAPP_i1584592887nt_int_type, type, hAPP_i1584592887nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i1524277240nt_int_type, type, hAPP_i1524277240nt_int: ($i > ($i > $i))). 120.83/55.28 thf(semiri1424489471de_int_type, type, semiri1424489471de_int: $i). 120.83/55.28 thf(nat_neg_type, type, nat_neg: $i). 120.83/55.28 thf(pred_type, type, pred: $i). 120.83/55.28 thf(member_int_type, type, member_int: $i). 120.83/55.28 thf(hAPP_i2112223885l_bool_type, type, hAPP_i2112223885l_bool: ($i > ($i > $i))). 120.83/55.28 thf(zEven_type, type, zEven: $i). 120.83/55.28 thf(number1443263063umeral_type, type, number1443263063umeral: $i). 120.83/55.28 thf(hAPP_i769753017umeral_type, type, hAPP_i769753017umeral: ($i > ($i > $i))). 120.83/55.28 thf(semiri984289939at_nat_type, type, semiri984289939at_nat: $i). 120.83/55.28 thf(bnorRset_type, type, bnorRset: ($i > $i)). 120.83/55.28 thf(fact_fact_int_type, type, fact_fact_int: $i). 120.83/55.28 thf(semiri151668891at_rat_type, type, semiri151668891at_rat: $i). 120.83/55.28 thf(quotient_of_type, type, quotient_of: ($i > $i)). 120.83/55.28 thf(zOdd_type, type, zOdd: $i). 120.83/55.28 thf(fact_type, type, fact: $i). 120.83/55.28 thf(finite_finite_int_type, type, finite_finite_int: $i). 120.83/55.28 thf(zprime_type, type, zprime: $i). 120.83/55.28 thf(gcd_gcd_int_type, type, gcd_gcd_int: $i). 120.83/55.28 thf(legacy_zgcd_type, type, legacy_zgcd: ($i > $i)). 120.83/55.28 thf(semiri1619134803umeral_type, type, semiri1619134803umeral: $i). 120.83/55.28 thf(nat_is_nat_type, type, nat_is_nat: $i). 120.83/55.28 thf(sgn_sgn_rat_type, type, sgn_sgn_rat: $i). 120.83/55.28 thf(sgn_sgn_int_type, type, sgn_sgn_int: $i). 120.83/55.28 thf(divmod_int_rel_type, type, divmod_int_rel: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P603027463t_bool_type, type, hAPP_P603027463t_bool: ($i > ($i > $i))). 120.83/55.28 thf(ring_1_of_int_rat_type, type, ring_1_of_int_rat: $i). 120.83/55.28 thf(finite_card_int_type, type, finite_card_int: $i). 120.83/55.28 thf(ord_at641636577an_int_type, type, ord_at641636577an_int: ($i > $i)). 120.83/55.28 thf(ord_max_nat_type, type, ord_max_nat: $i). 120.83/55.28 thf(ord_min_nat_type, type, ord_min_nat: $i). 120.83/55.28 thf(code_c271388182l_size_type, type, code_c271388182l_size: ($i > $i)). 120.83/55.28 thf(zfact_type, type, zfact: $i). 120.83/55.28 thf(cOMBI_int_type, type, cOMBI_int: $i). 120.83/55.28 thf(d22set_type, type, d22set: $i). 120.83/55.28 thf(big_co1548731110nt_int_type, type, big_co1548731110nt_int: ($i > ($i > $i))). 120.83/55.28 thf(frct_type, type, frct: ($i > $i)). 120.83/55.28 thf(if_nat_type, type, if_nat: $i). 120.83/55.28 thf(hAPP_b992065680at_nat_type, type, hAPP_b992065680at_nat: ($i > ($i > $i))). 120.83/55.28 thf(is_RRset_type, type, is_RRset: ($i > $i)). 120.83/55.28 thf(fequal_rat_type, type, fequal_rat: $i). 120.83/55.28 thf(produc282740534nt_int_type, type, produc282740534nt_int: $i). 120.83/55.28 thf(hAPP_i1730167831nt_int_type, type, hAPP_i1730167831nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P408881810nt_int_type, type, hAPP_P408881810nt_int: ($i > ($i > $i))). 120.83/55.28 thf(xzgcda_type, type, xzgcda: ($i > ($i > ($i > ($i > ($i > ($i > ($i > ($i > $i))))))))). 120.83/55.28 thf(if_int_type, type, if_int: $i). 120.83/55.28 thf(hAPP_b1463609396nt_int_type, type, hAPP_b1463609396nt_int: ($i > ($i > $i))). 120.83/55.28 thf(dvd_dvd_int_type, type, dvd_dvd_int: $i). 120.83/55.28 thf(int_gcd_type, type, int_gcd: $i). 120.83/55.28 thf(sRStar_type, type, sRStar: $i). 120.83/55.28 thf(hAPP_f1594865479ol_int_type, type, hAPP_f1594865479ol_int: ($i > ($i > $i))). 120.83/55.28 thf(normalize_type, type, normalize: ($i > $i)). 120.83/55.28 thf(succ_type, type, succ: $i). 120.83/55.28 thf(fEx_int_type, type, fEx_int: $i). 120.83/55.28 thf(cOMBC_983868720t_bool_type, type, cOMBC_983868720t_bool: $i). 120.83/55.28 thf(cOMBB_2027861294ol_int_type, type, cOMBB_2027861294ol_int: $i). 120.83/55.28 thf(cOMBB_int_bool_int_type, type, cOMBB_int_bool_int: $i). 120.83/55.28 thf(hAPP_f1475822739t_bool_type, type, hAPP_f1475822739t_bool: ($i > ($i > $i))). 120.83/55.28 thf(fequal_int_type, type, fequal_int: $i). 120.83/55.28 thf(hAPP_f1251097615t_bool_type, type, hAPP_f1251097615t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f735247205t_bool_type, type, hAPP_f735247205t_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBC_int_int_int_type, type, cOMBC_int_int_int: $i). 120.83/55.28 thf(cOMBB_1496585939nt_int_type, type, cOMBB_1496585939nt_int: $i). 120.83/55.28 thf(hAPP_f1629352853nt_int_type, type, hAPP_f1629352853nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1760145644nt_int_type, type, hAPP_f1760145644nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f2135977429nt_int_type, type, hAPP_f2135977429nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1791153283t_bool_type, type, hAPP_f1791153283t_bool: ($i > ($i > $i))). 120.83/55.28 thf(pdivmod_type, type, pdivmod: ($i > ($i > $i))). 120.83/55.28 thf(nat_tsub_type, type, nat_tsub: ($i > $i)). 120.83/55.28 thf(int_lcm_type, type, int_lcm: ($i > $i)). 120.83/55.28 thf(cOMBB_562416518ol_int_type, type, cOMBB_562416518ol_int: $i). 120.83/55.28 thf(hAPP_f847817363t_bool_type, type, hAPP_f847817363t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f791698359t_bool_type, type, hAPP_f791698359t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i345030060t_bool_type, type, hAPP_i345030060t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f428220345t_bool_type, type, hAPP_f428220345t_bool: ($i > ($i > $i))). 120.83/55.28 thf(norm_frac_rel_type, type, norm_frac_rel: $i). 120.83/55.28 thf(accp_P2006205492nt_int_type, type, accp_P2006205492nt_int: ($i > $i)). 120.83/55.28 thf(fequal_nat_type, type, fequal_nat: $i). 120.83/55.28 thf(s1_type, type, s1: $i). 120.83/55.28 thf(fequal_real_type, type, fequal_real: $i). 120.83/55.28 thf(ord_at875362053st_int_type, type, ord_at875362053st_int: ($i > $i)). 120.83/55.28 thf(even_odd_even_int_type, type, even_odd_even_int: $i). 120.83/55.28 thf(phi_type, type, phi: $i). 120.83/55.28 thf(norRRset_type, type, norRRset: $i). 120.83/55.28 thf(abs_abs_rat_type, type, abs_abs_rat: $i). 120.83/55.28 thf(vanishes_type, type, vanishes: ($i > $i)). 120.83/55.28 thf(produc713050258nt_int_type, type, produc713050258nt_int: ($i > $i)). 120.83/55.28 thf(produc1298267108nt_int_type, type, produc1298267108nt_int: ($i > $i)). 120.83/55.28 thf(cos_coeff_type, type, cos_coeff: $i). 120.83/55.28 thf(zcong_type, type, zcong: ($i > $i)). 120.83/55.28 thf(resSet_type, type, resSet: ($i > $i)). 120.83/55.28 thf(code_nat_of_aux_type, type, code_nat_of_aux: ($i > $i)). 120.83/55.28 thf(xzgcd_type, type, xzgcd: ($i > ($i > $i))). 120.83/55.28 thf(t_type, type, t: $i). 120.83/55.28 thf(nat_case_nat_type, type, nat_case_nat: ($i > ($i > $i))). 120.83/55.28 thf(wset_type, type, wset: ($i > $i)). 120.83/55.28 thf(nat_aux_type, type, nat_aux: ($i > $i)). 120.83/55.28 thf(hAPP_i872162435t_bool_type, type, hAPP_i872162435t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f429935748t_bool_type, type, hAPP_f429935748t_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBS_2011279539nt_int_type, type, cOMBS_2011279539nt_int: $i). 120.83/55.28 thf(hAPP_f434654626nt_int_type, type, hAPP_f434654626nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1574055885nt_int_type, type, hAPP_f1574055885nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i1778081398nt_int_type, type, hAPP_i1778081398nt_int: ($i > ($i > $i))). 120.83/55.28 thf(twoSqu1907779896sum2sq_type, type, twoSqu1907779896sum2sq: $i). 120.83/55.28 thf(minus_534354567de_int_type, type, minus_534354567de_int: $i). 120.83/55.28 thf(member_fun_int_bool_type, type, member_fun_int_bool: $i). 120.83/55.28 thf(hAPP_f628503027l_bool_type, type, hAPP_f628503027l_bool: ($i > ($i > $i))). 120.83/55.28 thf(rsetR_type, type, rsetR: ($i > $i)). 120.83/55.28 thf(hAPP_f215623910l_bool_type, type, hAPP_f215623910l_bool: ($i > ($i > $i))). 120.83/55.28 thf(ord_lessThan_nat_type, type, ord_lessThan_nat: $i). 120.83/55.28 thf(adjust_type, type, adjust: ($i > $i)). 120.83/55.28 thf(negDivAlg_rel_type, type, negDivAlg_rel: $i). 120.83/55.28 thf(setS_type, type, setS: ($i > ($i > $i))). 120.83/55.28 thf(ord_gr1297742076an_int_type, type, ord_gr1297742076an_int: ($i > $i)). 120.83/55.28 thf(hAPP_f659380387ol_int_type, type, hAPP_f659380387ol_int: ($i > ($i > $i))). 120.83/55.28 thf(finite1395289673t_bool_type, type, finite1395289673t_bool: $i). 120.83/55.28 thf(big_co1758102091ol_nat_type, type, big_co1758102091ol_nat: $i). 120.83/55.28 thf(hAPP_f93439879ol_nat_type, type, hAPP_f93439879ol_nat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f521865025ol_nat_type, type, hAPP_f521865025ol_nat: ($i > ($i > $i))). 120.83/55.28 thf(twoSqu1770640450sum2sq_type, type, twoSqu1770640450sum2sq: $i). 120.83/55.28 thf(m_type, type, m: $i). 120.83/55.28 thf(nat_case_bool_type, type, nat_case_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBB_real_bool_int_type, type, cOMBB_real_bool_int: $i). 120.83/55.28 thf(hAPP_f1173902867t_bool_type, type, hAPP_f1173902867t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f429384717t_bool_type, type, hAPP_f429384717t_bool: ($i > ($i > $i))). 120.83/55.28 thf(ord_at1496968948n_real_type, type, ord_at1496968948n_real: ($i > $i)). 120.83/55.28 thf(comple124823625p_real_type, type, comple124823625p_real: ($i > $i)). 120.83/55.28 thf(sin_coeff_type, type, sin_coeff: $i). 120.83/55.28 thf(cOMBC_int_int_bool_type, type, cOMBC_int_int_bool: $i). 120.83/55.28 thf(sr_type, type, sr: $i). 120.83/55.28 thf(noXRRset_type, type, noXRRset: ($i > $i)). 120.83/55.28 thf(image_int_int_type, type, image_int_int: ($i > ($i > $i))). 120.83/55.28 thf(comple219730294t_bool_type, type, comple219730294t_bool: ($i > $i)). 120.83/55.28 thf(z3mod_type, type, z3mod: ($i > $i)). 120.83/55.28 thf(hAPP_P880235623l_bool_type, type, hAPP_P880235623l_bool: ($i > ($i > $i))). 120.83/55.28 thf(member308914164t_bool_type, type, member308914164t_bool: $i). 120.83/55.28 thf(hAPP_P1681069257l_bool_type, type, hAPP_P1681069257l_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1469637905l_bool_type, type, hAPP_f1469637905l_bool: ($i > ($i > $i))). 120.83/55.28 thf(quadRes_type, type, quadRes: $i). 120.83/55.28 thf(inv_type, type, inv: ($i > $i)). 120.83/55.28 thf(multInv_type, type, multInv: ($i > $i)). 120.83/55.28 thf(multInvPair_type, type, multInvPair: ($i > ($i > $i))). 120.83/55.28 thf(cOMBB_int_real_int_type, type, cOMBB_int_real_int: $i). 120.83/55.28 thf(hAPP_f134192053t_real_type, type, hAPP_f134192053t_real: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f563293398t_real_type, type, hAPP_f563293398t_real: ($i > ($i > $i))). 120.83/55.28 thf(z3div_type, type, z3div: ($i > $i)). 120.83/55.28 thf(cOMBB_118231410ol_int_type, type, cOMBB_118231410ol_int: $i). 120.83/55.28 thf(hAPP_f1399575567t_bool_type, type, hAPP_f1399575567t_bool: ($i > ($i > $i))). 120.83/55.28 thf(legendre_type, type, legendre: ($i > $i)). 120.83/55.28 thf(hAPP_f1512942609t_bool_type, type, hAPP_f1512942609t_bool: ($i > ($i > $i))). 120.83/55.28 thf(isCont156215680omplex_type, type, isCont156215680omplex: ($i > $i)). 120.83/55.28 thf(cOMBB_1102189010nt_int_type, type, cOMBB_1102189010nt_int: $i). 120.83/55.28 thf(hAPP_f1228585167nt_int_type, type, hAPP_f1228585167nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f2004554147nt_int_type, type, hAPP_f2004554147nt_int: ($i > ($i > $i))). 120.83/55.28 thf(cOMBB_nat_bool_int_type, type, cOMBB_nat_bool_int: $i). 120.83/55.28 thf(hAPP_f696844121t_bool_type, type, hAPP_f696844121t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1448486952t_bool_type, type, hAPP_f1448486952t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P2110489235nt_int_type, type, hAPP_P2110489235nt_int: ($i > ($i > $i))). 120.83/55.28 thf(cOMBC_1417754532nt_int_type, type, cOMBC_1417754532nt_int: $i). 120.83/55.28 thf(hAPP_f578362681nt_int_type, type, hAPP_f578362681nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i61245889nt_int_type, type, hAPP_i61245889nt_int: ($i > ($i > $i))). 120.83/55.28 thf(quickc1265749348ro_rel_type, type, quickc1265749348ro_rel: $i). 120.83/55.28 thf(accp_int_type, type, accp_int: ($i > $i)). 120.83/55.28 thf(cOMBC_int_nat_int_type, type, cOMBC_int_nat_int: $i). 120.83/55.28 thf(hAPP_f2105620693nt_int_type, type, hAPP_f2105620693nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_nat_fun_int_int_type, type, hAPP_nat_fun_int_int: ($i > ($i > $i))). 120.83/55.28 thf(ring_1_of_int_int_type, type, ring_1_of_int_int: $i). 120.83/55.28 thf(cOMBB_550562460ol_int_type, type, cOMBB_550562460ol_int: $i). 120.83/55.28 thf(hAPP_f983569339t_bool_type, type, hAPP_f983569339t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f725770969t_bool_type, type, hAPP_f725770969t_bool: ($i > ($i > $i))). 120.83/55.28 thf(big_co230513141nt_int_type, type, big_co230513141nt_int: $i). 120.83/55.28 thf(hAPP_f1926459811ol_int_type, type, hAPP_f1926459811ol_int: ($i > ($i > $i))). 120.83/55.28 thf(posDivAlg_rel_type, type, posDivAlg_rel: $i). 120.83/55.28 thf(fdisj_type, type, fdisj: ($i > ($i > $i))). 120.83/55.28 thf(cOMBC_736024425nt_int_type, type, cOMBC_736024425nt_int: $i). 120.83/55.28 thf(cOMBB_1875755114nt_int_type, type, cOMBB_1875755114nt_int: $i). 120.83/55.28 thf(cOMBB_int_int_int_type, type, cOMBB_int_int_int: $i). 120.83/55.28 thf(hAPP_f888249301nt_int_type, type, hAPP_f888249301nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f836602773nt_int_type, type, hAPP_f836602773nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f808647893nt_int_type, type, hAPP_f808647893nt_int: ($i > ($i > $i))). 120.83/55.28 thf(rRset2norRR_type, type, rRset2norRR: ($i > ($i > $i))). 120.83/55.28 thf(lazy_small_lazy_rel_type, type, lazy_small_lazy_rel: $i). 120.83/55.28 thf(cOMBB_int_bool_nat_type, type, cOMBB_int_bool_nat: $i). 120.83/55.28 thf(hAPP_f1361476881t_bool_type, type, hAPP_f1361476881t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1154658180t_bool_type, type, hAPP_f1154658180t_bool: ($i > ($i > $i))). 120.83/55.28 thf(size_size_list_int_type, type, size_size_list_int: $i). 120.83/55.28 thf(quickc666637781d_zero_type, type, quickc666637781d_zero: ($i > $i)). 120.83/55.28 thf(hAPP_list_int_nat_type, type, hAPP_list_int_nat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i744251628nt_int_type, type, hAPP_i744251628nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f747162069nt_int_type, type, hAPP_f747162069nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1356864277nt_int_type, type, hAPP_f1356864277nt_int: ($i > ($i > $i))). 120.83/55.28 thf(trivial_limit_nat_type, type, trivial_limit_nat: ($i > $i)). 120.83/55.28 thf(norm_frac_type, type, norm_frac: ($i > ($i > $i))). 120.83/55.28 thf(iszero_int_type, type, iszero_int: $i). 120.83/55.28 thf(iszero_rat_type, type, iszero_rat: $i). 120.83/55.28 thf(cOMBB_1290694363ol_int_type, type, cOMBB_1290694363ol_int: $i). 120.83/55.28 thf(hAPP_f908327869t_bool_type, type, hAPP_f908327869t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f720654810t_bool_type, type, hAPP_f720654810t_bool: ($i > ($i > $i))). 120.83/55.28 thf(finite1876863882t_bool_type, type, finite1876863882t_bool: $i). 120.83/55.28 thf(cOMBB_int_int_nat_type, type, cOMBB_int_int_nat: $i). 120.83/55.28 thf(hAPP_f1431025877at_int_type, type, hAPP_f1431025877at_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1139079189at_int_type, type, hAPP_f1139079189at_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P62333565t_bool_type, type, hAPP_P62333565t_bool: ($i > ($i > $i))). 120.83/55.28 thf(member2143287562nt_int_type, type, member2143287562nt_int: $i). 120.83/55.28 thf(hAPP_P1062890741l_bool_type, type, hAPP_P1062890741l_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f526364711l_bool_type, type, hAPP_f526364711l_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBB_859312247nt_nat_type, type, cOMBB_859312247nt_nat: $i). 120.83/55.28 thf(hAPP_f125788821nt_int_type, type, hAPP_f125788821nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1935805932nt_int_type, type, hAPP_f1935805932nt_int: ($i > ($i > $i))). 120.83/55.28 thf(image_275383677t_bool_type, type, image_275383677t_bool: ($i > ($i > $i))). 120.83/55.28 thf(zcongm_type, type, zcongm: ($i > $i)). 120.83/55.28 thf(hAPP_i16292313t_bool_type, type, hAPP_i16292313t_bool: ($i > ($i > $i))). 120.83/55.28 thf(cOMBC_int_rat_bool_type, type, cOMBC_int_rat_bool: $i). 120.83/55.28 thf(hAPP_f1480506641t_bool_type, type, hAPP_f1480506641t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_r1900510169t_bool_type, type, hAPP_r1900510169t_bool: ($i > ($i > $i))). 120.83/55.28 thf(produc713279741t_bool_type, type, produc713279741t_bool: $i). 120.83/55.28 thf(hAPP_f1418982953t_bool_type, type, hAPP_f1418982953t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f538843494t_bool_type, type, hAPP_f538843494t_bool: ($i > ($i > $i))). 120.83/55.28 thf(bijR_int_int_type, type, bijR_int_int: ($i > $i)). 120.83/55.28 thf(produc883642259nt_int_type, type, produc883642259nt_int: $i). 120.83/55.28 thf(hAPP_P941956607nt_int_type, type, hAPP_P941956607nt_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_P230595783nt_int_type, type, hAPP_P230595783nt_int: ($i > ($i > $i))). 120.83/55.28 thf(ratrel_type, type, ratrel: $i). 120.83/55.28 thf(big_co1024481617at_int_type, type, big_co1024481617at_int: $i). 120.83/55.28 thf(cOMBC_nat_int_int_type, type, cOMBC_nat_int_int: $i). 120.83/55.28 thf(hAPP_f1673103573at_int_type, type, hAPP_f1673103573at_int: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1599440987ol_int_type, type, hAPP_f1599440987ol_int: ($i > ($i > $i))). 120.83/55.28 thf(cOMBB_int_rat_int_type, type, cOMBB_int_rat_int: $i). 120.83/55.28 thf(hAPP_f1270196437nt_rat_type, type, hAPP_f1270196437nt_rat: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f1900950721nt_rat_type, type, hAPP_f1900950721nt_rat: ($i > ($i > $i))). 120.83/55.28 thf(quickcheck_nat_of_type, type, quickcheck_nat_of: ($i > $i)). 120.83/55.28 thf(cOMBC_241247961t_bool_type, type, cOMBC_241247961t_bool: $i). 120.83/55.28 thf(cOMBB_95956018ol_int_type, type, cOMBB_95956018ol_int: $i). 120.83/55.28 thf(hAPP_f1576199059t_bool_type, type, hAPP_f1576199059t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_f351634443t_bool_type, type, hAPP_f351634443t_bool: ($i > ($i > $i))). 120.83/55.28 thf(hAPP_i627165055t_real_type, type, hAPP_i627165055t_real: ($i > ($i > $i))). 120.83/55.28 thf(upto_rel_type, type, upto_rel: $i). 120.83/55.28 thf(3312,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3802_fact__mono__nat)). 120.83/55.28 thf(16466,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3312])). 120.83/55.28 thf(1703,axiom,(((hAPP_complex_complex @ cnj @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4066_cnj_Ozero)). 120.83/55.28 thf(10822,plain,(((hAPP_complex_complex @ cnj @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703])). 120.83/55.28 thf(725,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((C = D) & (A != B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ A)) != (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ B)))) <= (E != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_add__scale__eq__noteq)). 120.83/55.28 thf(7375,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((C = D) & ~ (A = B)) => (~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ B))))) | (E = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])). 120.83/55.28 thf(4080,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_rel__simps_I21_J)). 120.83/55.28 thf(19204,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit0 @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit0 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4080])). 120.83/55.28 thf(4343,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (((one_one_int = A) | ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int) = A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) @ B)))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1604_zcong__square__zless)). 120.83/55.28 thf(20194,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => ((one_one_int = A) | ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int) = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) @ B)))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4343])). 120.83/55.28 thf(2004,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) = A) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3368_eq__divide__2__times__iff)). 120.83/55.28 thf(11866,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) = A) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ C))) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ C)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004])). 120.83/55.28 thf(1049,axiom,((! [A:$i,B:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1797_realpow__minus__mult)). 120.83/55.28 thf(8536,plain,((! [A:$i,B:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049])). 120.83/55.28 thf(3109,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2427_mod__add__right__eq)). 120.83/55.28 thf(15767,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3109])). 120.83/55.28 thf(4703,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_f659380387ol_int @ (hAPP_f1599440987ol_int @ big_co1024481617at_int @ (hAPP_f1139079189at_int @ (hAPP_f1431025877at_int @ cOMBB_int_int_nat @ (hAPP_int_fun_int_int @ plus_plus_int @ A)) @ (hAPP_int_fun_nat_int @ (hAPP_f1673103573at_int @ cOMBC_nat_int_int @ (hAPP_f1935805932nt_int @ (hAPP_f125788821nt_int @ cOMBB_859312247nt_nat @ times_times_int) @ semiri1621563631at_int)) @ B))) @ (hAPP_n1699378549t_bool @ ord_lessThan_nat @ C))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ one_one_nat))) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4947_arith__series__int)). 120.83/55.28 thf(21624,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_f659380387ol_int @ (hAPP_f1599440987ol_int @ big_co1024481617at_int @ (hAPP_f1139079189at_int @ (hAPP_f1431025877at_int @ cOMBB_int_int_nat @ (hAPP_int_fun_int_int @ plus_plus_int @ A)) @ (hAPP_int_fun_nat_int @ (hAPP_f1673103573at_int @ cOMBC_nat_int_int @ (hAPP_f1935805932nt_int @ (hAPP_f125788821nt_int @ cOMBB_859312247nt_nat @ times_times_int) @ semiri1621563631at_int)) @ B))) @ (hAPP_n1699378549t_bool @ ord_lessThan_nat @ C))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ one_one_nat))) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4703])). 120.83/55.28 thf(2845,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A) = B) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1772_le__add__diff__inverse2)). 120.83/55.28 thf(14852,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2845])). 120.83/55.28 thf(4124,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ lazy_small_lazy_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)) <= (! [D:$i,E:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ one_one_int)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ lazy_small_lazy_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))) <= ((is_int @ E) & (is_int @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4574_small__lazy_H_Opinduct)). 120.83/55.28 thf(19370,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ lazy_small_lazy_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)) | ~ (! [D:$i,E:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ one_one_int)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ lazy_small_lazy_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) | ~ ((is_int @ E) & (is_int @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4124])). 120.83/55.28 thf(1471,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1640_le__add1)). 120.83/55.28 thf(10007,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471])). 120.83/55.28 thf(4729,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_less__int__code_I16_J)). 120.83/55.28 thf(21729,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4729])). 120.83/55.28 thf(3121,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((zero_zero_int != B) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4723_Fract__add__one)). 120.83/55.28 thf(15806,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((~ (zero_zero_int = B)) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3121])). 120.83/55.28 thf(4363,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ sRStar @ C))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) @ (hAPP_i1948725293t_bool @ sRStar @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2765_SRStar__mult__prop1)). 120.83/55.28 thf(20256,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ sRStar @ C))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) @ (hAPP_i1948725293t_bool @ sRStar @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4363])). 120.83/55.28 thf(4191,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_zero__less__mult__pos2)). 120.83/55.28 thf(19597,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4191])). 120.83/55.28 thf(4269,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ uminus_uminus_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3527_even__neg)). 120.83/55.28 thf(19904,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ uminus_uminus_int @ A))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ uminus_uminus_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4269])). 120.83/55.28 thf(724,axiom,(((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ one_one_int) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4707_zero__rat)). 120.83/55.28 thf(7373,plain,(((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ one_one_int) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 120.83/55.28 thf(3754,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2047_add__strict__mono)). 120.83/55.28 thf(17959,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3754])). 120.83/55.28 thf(1876,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2754_div__2__gt__zero)). 120.83/55.28 thf(11472,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876])). 120.83/55.28 thf(3372,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3009_power__Suc2)). 120.83/55.28 thf(16662,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3372])). 120.83/55.28 thf(574,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ norm_norm_complex @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3489_complex__mod__minus__le__complex__mod)). 120.83/55.28 thf(6836,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ norm_norm_complex @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])). 120.83/55.28 thf(2824,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2383_mod__mult__left__eq)). 120.83/55.28 thf(14782,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2824])). 120.83/55.28 thf(737,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = zero_zero_nat) <=> ((zero_zero_nat = A) & (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4340_gcd__zero__nat)). 120.83/55.28 thf(7427,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = zero_zero_nat) => ((zero_zero_nat = A) & (zero_zero_nat = B))) & (((zero_zero_nat = A) & (zero_zero_nat = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 120.83/55.28 thf(51,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3954_complex__norm)). 120.83/55.28 thf(5116,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 120.83/55.28 thf(1583,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ one_one_real) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4434_powr__one__gt__zero__iff)). 120.83/55.28 thf(10410,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ one_one_real) = A)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ one_one_real) = A) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583])). 120.83/55.28 thf(441,axiom,((! [A:$i]: ((is_int @ A) => (A = (archim856651990g_real @ (hAPP_int_real @ real_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4397_ceiling__real__of__int)). 120.83/55.28 thf(6405,plain,((! [A:$i]: ((is_int @ A) => (A = (archim856651990g_real @ (hAPP_int_real @ real_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 120.83/55.28 thf(4122,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.28 thf(19364,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4122])). 120.83/55.28 thf(187,axiom,(((natceiling @ zero_zero_real) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3389_natceiling__zero)). 120.83/55.28 thf(5561,plain,(((natceiling @ zero_zero_real) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 120.83/55.28 thf(3866,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__eq__int__code_I16_J)). 120.83/55.28 thf(18360,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3866])). 120.83/55.28 thf(2702,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (is_RRset @ A) @ B)) <=> (((hAPP_int_nat @ phi @ B) = (hAPP_f957591787ol_nat @ finite_card_int @ A)) & (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (rsetR @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4594_is__RRset__def)). 120.83/55.28 thf(14343,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (is_RRset @ A) @ B)) => (((hAPP_int_nat @ phi @ B) = (hAPP_f957591787ol_nat @ finite_card_int @ A)) & (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (rsetR @ B))))) & ((((hAPP_int_nat @ phi @ B) = (hAPP_f957591787ol_nat @ finite_card_int @ A)) & (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (rsetR @ B)))) => (hBOOL @ (hAPP_int_bool @ (is_RRset @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2702])). 120.83/55.28 thf(3491,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2377_mod__mult__right__eq)). 120.83/55.28 thf(17043,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3491])). 120.83/55.28 thf(693,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3078_mod__1)). 120.83/55.28 thf(7272,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 120.83/55.28 thf(4369,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ pls) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1520_diff__bin__simps_I1_J)). 120.83/55.28 thf(20273,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ pls) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4369])). 120.83/55.28 thf(4582,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2525_zdiv__number__of__Bit0)). 120.83/55.28 thf(21175,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4582])). 120.83/55.28 thf(4406,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ one_one_nat) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.28 thf(20432,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ one_one_nat) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4406])). 120.83/55.28 thf(1261,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3063_less__Suc__eq__le)). 120.83/55.28 thf(9273,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261])). 120.83/55.28 thf(2568,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3453_ln__ge__zero__iff)). 120.83/55.28 thf(13859,plain,((! [A:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2568])). 120.83/55.28 thf(1546,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ zero_zero_nat) @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2475_div__0)). 120.83/55.28 thf(10259,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ zero_zero_nat) @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546])). 120.83/55.28 thf(4871,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2659_zmult2__lemma__aux3)). 120.83/55.28 thf(22210,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4871])). 120.83/55.28 thf(3584,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_less__special_I1_J)). 120.83/55.28 thf(17358,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3584])). 120.83/55.28 thf(1692,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_comm__semiring__class_Odistrib)). 120.83/55.28 thf(10785,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692])). 120.83/55.28 thf(2202,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2906_zero__le__imp__of__nat)). 120.83/55.28 thf(12564,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202])). 120.83/55.28 thf(3499,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2912_of__nat__0__le__iff)). 120.83/55.28 thf(17072,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3499])). 120.83/55.28 thf(850,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.28 thf(7854,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])). 120.83/55.28 thf(4726,axiom,((! [A:$i,B:$i,C:$i]: ((((B = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) => (? [D:$i,E:$i]: ((is_int @ D) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) & (is_int @ E)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4537_zgcd__ex__linear)). 120.83/55.28 thf(21710,plain,((! [A:$i,B:$i,C:$i]: (((B = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) => (? [D:$i,E:$i]: ((is_int @ D) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) & (is_int @ E)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4726])). 120.83/55.28 thf(886,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2024_add__le__cancel__left)). 120.83/55.28 thf(7973,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])). 120.83/55.28 thf(776,axiom,((! [A:$i,B:$i]: (((one_one_real != B) => (A = (hAPP_real_real @ (log @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4462_log__powr__cancel)). 120.83/55.28 thf(7569,plain,((! [A:$i,B:$i]: (((~ (one_one_real = B)) => (A = (hAPP_real_real @ (log @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])). 120.83/55.28 thf(383,axiom,((! [A:$i]: ((image_int_nat @ nat @ (image_nat_int @ semiri1621563631at_int @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4604_transfer__int__nat__set__return__embed)). 120.83/55.28 thf(6231,plain,((! [A:$i]: ((image_int_nat @ nat @ (image_nat_int @ semiri1621563631at_int @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 120.83/55.28 thf(2894,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) => (C = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1912_add__right__imp__eq)). 120.83/55.28 thf(15009,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) => (C = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2894])). 120.83/55.28 thf(3011,axiom,((! [A:$i]: (is_int @ (quickcheck_int_of @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Quickcheck__Narrowing_Oint__of)). 120.83/55.28 thf(15418,plain,((! [A:$i]: (is_int @ (quickcheck_int_of @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3011])). 120.83/55.28 thf(1849,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1491_dvd__power)). 120.83/55.28 thf(11372,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849])). 120.83/55.28 thf(1076,axiom,((zero_zero_complex = (hAPP_int_complex @ number528085621omplex @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_semiring__norm_I112_J)). 120.83/55.28 thf(8663,plain,((zero_zero_complex = (hAPP_int_complex @ number528085621omplex @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076])). 120.83/55.28 thf(921,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (natfloor @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ B)) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3410_le__natfloor__eq__number__of)). 120.83/55.28 thf(8097,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (natfloor @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ B)) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ B)) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (natfloor @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[921])). 120.83/55.28 thf(1369,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_nat_rat @ semiri151668891at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2834_of__nat__eq__iff)). 120.83/55.28 thf(9648,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_nat_rat @ semiri151668891at_rat @ B))) & (((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_nat_rat @ semiri151668891at_rat @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369])). 120.83/55.28 thf(2014,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2762_Euler_Oaux____2)). 120.83/55.28 thf(11895,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014])). 120.83/55.28 thf(3676,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_zpower__zadd__distrib)). 120.83/55.28 thf(17684,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3676])). 120.83/55.28 thf(3903,axiom,(((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_semiring__norm_I110_J)). 120.83/55.28 thf(18504,plain,(((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3903])). 120.83/55.28 thf(480,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3583_cos__periodic)). 120.83/55.28 thf(6544,plain,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 120.83/55.28 thf(4156,axiom,(((hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096)). 120.83/55.28 thf(19481,plain,(((hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4156])). 120.83/55.28 thf(3242,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) => ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3893_DERIV__even__real__root)). 120.83/55.28 thf(16243,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) => ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3242])). 120.83/55.28 thf(4839,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) != zero_zero_int) => (? [C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D) = one_one_int) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) = B) & (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) & (is_int @ D) & (is_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5118_gcd__coprime__exists__int)). 120.83/55.28 thf(22108,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = zero_zero_int)) => (? [C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D) = one_one_int) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) = B) & (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) & (is_int @ D) & (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4839])). 120.83/55.28 thf(2193,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_comm__mult__strict__left__mono)). 120.83/55.28 thf(12526,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2193])). 120.83/55.28 thf(3346,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ one_one_nat) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3405_natfloor__add__one)). 120.83/55.28 thf(16576,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ one_one_nat) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3346])). 120.83/55.28 thf(2503,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1867_add__nonneg__pos)). 120.83/55.28 thf(13643,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503])). 120.83/55.28 thf(4655,axiom,((zero_zero_int = (hAPP_int_int @ uminus_uminus_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3514_zminus__0)). 120.83/55.28 thf(21439,plain,((zero_zero_int = (hAPP_int_int @ uminus_uminus_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4655])). 120.83/55.28 thf(1328,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.28 thf(9516,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328])). 120.83/55.28 thf(1886,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1567_less__add__iff2)). 120.83/55.28 thf(11504,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886])). 120.83/55.28 thf(2025,axiom,((! [A:$i,B:$i,C:$i]: ((((((hAPP_real_real @ (log @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (C != one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3873_log__mult)). 120.83/55.28 thf(11922,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (log @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) | (C = one_one_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025])). 120.83/55.28 thf(3356,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ one_on1684967323de_int) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2502_mod__by__1)). 120.83/55.28 thf(16604,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ one_on1684967323de_int) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3356])). 120.83/55.28 thf(2719,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1889_add__nonpos__neg)). 120.83/55.28 thf(14404,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2719])). 120.83/55.28 thf(1399,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_mult__nonneg__nonpos)). 120.83/55.28 thf(9754,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399])). 120.83/55.28 thf(4287,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.28 thf(19971,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4287])). 120.83/55.28 thf(4634,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_zcong__zprime__prod__zero)). 120.83/55.28 thf(21348,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4634])). 120.83/55.28 thf(3029,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_mult__strict__left__mono)). 120.83/55.28 thf(15472,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3029])). 120.83/55.28 thf(4202,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_mult__strict__right__mono__neg)). 120.83/55.28 thf(19640,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4202])). 120.83/55.28 thf(110,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ abs_abs_real @ B)))) => (zero_zero_real = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3394_rabs__ratiotest__lemma)). 120.83/55.28 thf(5320,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ abs_abs_real @ B)))) => (zero_zero_real = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 120.83/55.28 thf(399,axiom,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))) = (hAPP_complex_real @ norm_norm_complex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4133_complex__mod__sqrt__Re__mult__cnj)). 120.83/55.28 thf(6283,plain,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))) = (hAPP_complex_real @ norm_norm_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 120.83/55.28 thf(3549,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2916_of__nat__less__0__iff)). 120.83/55.28 thf(17226,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3549])). 120.83/55.28 thf(3301,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D)) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) @ D) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1826_divides__div__not)). 120.83/55.28 thf(16427,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)))) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) @ D) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3301])). 120.83/55.28 thf(3736,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_mult__left__mono)). 120.83/55.28 thf(17903,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3736])). 120.83/55.28 thf(646,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1606_not__less0)). 120.83/55.28 thf(7100,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])). 120.83/55.28 thf(4415,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) <=> ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_eq__number__of__0)). 120.83/55.28 thf(20464,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) & (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4415])). 120.83/55.28 thf(1512,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (div_mod_nat @ E) @ D) = (hAPP_nat_nat @ (div_mod_nat @ C) @ D)) => (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ D) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ E) @ B)) @ D)) <= ((hAPP_nat_nat @ (div_mod_nat @ A) @ D) = (hAPP_nat_nat @ (div_mod_nat @ B) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2406_mod__add__cong)). 120.83/55.28 thf(10134,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (div_mod_nat @ E) @ D) = (hAPP_nat_nat @ (div_mod_nat @ C) @ D)) => (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ D) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ E) @ B)) @ D)) | ~ ((hAPP_nat_nat @ (div_mod_nat @ A) @ D) = (hAPP_nat_nat @ (div_mod_nat @ B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512])). 120.83/55.28 thf(2262,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1657_nat__mult__1)). 120.83/55.28 thf(12753,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262])). 120.83/55.28 thf(3453,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2338_semiring__div__class_Omod__div__equality_H)). 120.83/55.28 thf(16911,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3453])). 120.83/55.28 thf(4659,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_zle__linear)). 120.83/55.28 thf(21450,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4659])). 120.83/55.28 thf(2665,axiom,((! [A:$i,B:$i,C:$i]: (((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5018_normalize__coprime)). 120.83/55.28 thf(14220,plain,((! [A:$i,B:$i,C:$i]: (((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2665])). 120.83/55.28 thf(2590,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1970_add__0__right)). 120.83/55.28 thf(13933,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2590])). 120.83/55.28 thf(3352,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => ((B != zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1815_divides__rev)). 120.83/55.28 thf(16591,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => ((~ (B = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3352])). 120.83/55.28 thf(1380,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1903_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.28 thf(9685,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380])). 120.83/55.28 thf(4294,axiom,((! [A:$i,B:$i]: (((B = (hAPP_nat_int @ semiri1621563631at_int @ A)) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (A = (hAPP_int_nat @ nat @ B)))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3122_int__eq__iff)). 120.83/55.28 thf(19990,plain,((! [A:$i,B:$i]: ((((B = (hAPP_nat_int @ semiri1621563631at_int @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (A = (hAPP_int_nat @ nat @ B)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (A = (hAPP_int_nat @ nat @ B))) => (B = (hAPP_nat_int @ semiri1621563631at_int @ A)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4294])). 120.83/55.28 thf(1679,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1776_le__add__diff)). 120.83/55.28 thf(10743,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679])). 120.83/55.28 thf(2174,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4337_gcd__lcm__complete__lattice__nat_Oinf__bot__right)). 120.83/55.28 thf(12440,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174])). 120.83/55.28 thf(2438,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3335_le__real__sqrt__sumsq)). 120.83/55.28 thf(13410,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438])). 120.83/55.28 thf(2905,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2062_add__strict__right__mono)). 120.83/55.28 thf(15055,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2905])). 120.83/55.28 thf(2098,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2173_double__add__le__zero__iff__single__add__le__zero)). 120.83/55.28 thf(12148,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098])). 120.83/55.28 thf(3538,axiom,((! [A:$i]: ((! [B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ A @ D))) @ B)))))) <=> (hBOOL @ (vanishes @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5150_vanishes__def)). 120.83/55.28 thf(17175,plain,((! [A:$i]: (((! [B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ A @ D))) @ B)))))) => (hBOOL @ (vanishes @ A))) & ((hBOOL @ (vanishes @ A)) => (! [B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ A @ D))) @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3538])). 120.83/55.28 thf(1205,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1793_real__mult__le__cancel__iff1)). 120.83/55.28 thf(9076,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205])). 120.83/55.28 thf(4331,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1390_zero__less__two)). 120.83/55.28 thf(20162,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4331])). 120.83/55.28 thf(2149,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => ((((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ B)) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3285_mod__nat__number__of)). 120.83/55.28 thf(12344,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => ((((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ B)) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149])). 120.83/55.28 thf(4067,axiom,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5149_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J)). 120.83/55.28 thf(19148,plain,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4067])). 120.83/55.28 thf(4176,axiom,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5001_gcd__0__left__int)). 120.83/55.28 thf(19543,plain,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4176])). 120.83/55.28 thf(1496,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_mult__strict__right__mono)). 120.83/55.28 thf(10081,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496])). 120.83/55.28 thf(568,axiom,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4107_Im_Opos__bounded)). 120.83/55.28 thf(6819,plain,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])). 120.83/55.28 thf(3176,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) <= ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D) = (quotient_of @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4669_quotient__of__eq)). 120.83/55.28 thf(15995,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) | ~ ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D) = (quotient_of @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3176])). 120.83/55.28 thf(2161,axiom,(((hAPP_int_complex @ number528085621omplex @ min) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ ii) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3974_power2__i)). 120.83/55.28 thf(12383,plain,(((hAPP_int_complex @ number528085621omplex @ min) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ ii) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161])). 120.83/55.28 thf(4430,axiom,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B) = (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ plus_plus_int) @ A) @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4922_image__add__int__atLeastLessThan)). 120.83/55.28 thf(20516,plain,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B) = (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ plus_plus_int) @ A) @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4430])). 120.83/55.28 thf(3545,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1416_power__increasing__iff)). 120.83/55.28 thf(17214,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3545])). 120.83/55.28 thf(3801,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2606_pos__imp__zdiv__nonneg__iff)). 120.83/55.28 thf(18129,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3801])). 120.83/55.28 thf(4384,axiom,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ pred @ A)) = (hAPP_int_int @ pred @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4041_pred__Bit0)). 120.83/55.28 thf(20332,plain,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ pred @ A)) = (hAPP_int_int @ pred @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4384])). 120.83/55.28 thf(2015,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4159_termination__basic__simps_I5_J)). 120.83/55.28 thf(11898,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015])). 120.83/55.28 thf(4811,axiom,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B) = (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4921_atLeastPlusOneLessThan__greaterThanLessThan__int)). 120.83/55.28 thf(22012,plain,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B) = (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4811])). 120.83/55.28 thf(1428,axiom,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2473_div__by__0)). 120.83/55.28 thf(9864,plain,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428])). 120.83/55.28 thf(4235,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2984_int__less__0__conv)). 120.83/55.28 thf(19755,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4235])). 120.83/55.28 thf(2802,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4708_rat__number__expand_I3_J)). 120.83/55.28 thf(14709,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2802])). 120.83/55.28 thf(4161,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__le__power2)). 120.83/55.28 thf(19494,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4161])). 120.83/55.28 thf(1570,axiom,((! [A:$i]: (((((one_one_rat = (hAPP_rat_rat @ sgn_sgn_rat @ A)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) & ((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) => ((hAPP_rat_rat @ uminus_uminus_rat @ one_one_rat) = (hAPP_rat_rat @ sgn_sgn_rat @ A)))) <= (A != zero_zero_rat)) & (((hAPP_rat_rat @ sgn_sgn_rat @ A) = zero_zero_rat) <= (zero_zero_rat = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4650_sgn__rat__def)). 120.83/55.28 thf(10363,plain,((! [A:$i]: (((((one_one_rat = (hAPP_rat_rat @ sgn_sgn_rat @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) & ((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) => ((hAPP_rat_rat @ uminus_uminus_rat @ one_one_rat) = (hAPP_rat_rat @ sgn_sgn_rat @ A)))) | (A = zero_zero_rat)) & (((hAPP_rat_rat @ sgn_sgn_rat @ A) = zero_zero_rat) | ~ (zero_zero_rat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570])). 120.83/55.28 thf(1299,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4724_zero__le__Fract__iff)). 120.83/55.28 thf(9411,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299])). 120.83/55.28 thf(525,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3456_ln__div)). 120.83/55.28 thf(6690,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 120.83/55.28 thf(329,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.28 thf(6042,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 120.83/55.28 thf(1834,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1765_less__diff__conv)). 120.83/55.28 thf(11318,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834])). 120.83/55.28 thf(1922,axiom,((! [A:$i,B:$i]: (((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3129_mn__eq__m__one)). 120.83/55.28 thf(11620,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922])). 120.83/55.28 thf(4017,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ A) @ (negDivAlg @ B @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2797_negDivAlg__correct)). 120.83/55.28 thf(18893,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ A) @ (negDivAlg @ B @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4017])). 120.83/55.28 thf(1459,axiom,(((hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2927_of__nat__0)). 120.83/55.28 thf(9965,plain,(((hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459])). 120.83/55.28 thf(2840,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ zero_zero_nat) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1302_power__0)). 120.83/55.28 thf(14833,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ zero_zero_nat) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2840])). 120.83/55.28 thf(1742,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) <=> (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1199_mult__less__cancel__right__disj)). 120.83/55.28 thf(10976,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ A))))) & ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ A)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742])). 120.83/55.28 thf(4627,axiom,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3195_numeral__2__eq__2)). 120.83/55.28 thf(21326,plain,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4627])). 120.83/55.28 thf(488,axiom,((! [A:$i]: ((hAPP_complex_complex @ invers1449016382omplex @ (cis @ A)) = (cis @ (hAPP_real_real @ uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4150_cis__inverse)). 120.83/55.28 thf(6566,plain,((! [A:$i]: ((hAPP_complex_complex @ invers1449016382omplex @ (cis @ A)) = (cis @ (hAPP_real_real @ uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 120.83/55.28 thf(607,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1736_real__le__refl)). 120.83/55.28 thf(6954,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 120.83/55.28 thf(2869,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4309_gcd__left__commute__nat)). 120.83/55.28 thf(14932,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2869])). 120.83/55.28 thf(4463,axiom,((! [A:$i,B:$i]: ? [C:$i]: ((is_int @ C) & ! [D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2257_pinf_I10_J)). 120.83/55.28 thf(20651,plain,((? [A:$i]: (is_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4463])). 120.83/55.28 thf(1268,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1327_mult__right__le__imp__le)). 120.83/55.28 thf(9305,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268])). 120.83/55.28 thf(4195,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ zero_zero_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2372_mod__0)). 120.83/55.28 thf(19611,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ zero_zero_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4195])). 120.83/55.28 thf(1247,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1597_le__trans)). 120.83/55.28 thf(9222,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247])). 120.83/55.28 thf(1694,axiom,((! [A:$i,B:$i]: ((B = (hAPP_i769753017umeral @ number1443263063umeral @ A)) <=> ((hAPP_i769753017umeral @ number1443263063umeral @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_number__of__reorient)). 120.83/55.28 thf(10790,plain,((! [A:$i,B:$i]: (((B = (hAPP_i769753017umeral @ number1443263063umeral @ A)) => ((hAPP_i769753017umeral @ number1443263063umeral @ A) = B)) & (((hAPP_i769753017umeral @ number1443263063umeral @ A) = B) => (B = (hAPP_i769753017umeral @ number1443263063umeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694])). 120.83/55.28 thf(2873,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2436_mod__add__self2)). 120.83/55.28 thf(14944,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2873])). 120.83/55.28 thf(3204,axiom,((! [A:$i,B:$i,C:$i]: (((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ C) = A) <=> (B = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ B))) <= (C != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2640_dvd__div__eq__mult)). 120.83/55.28 thf(16092,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ C) = A) => (B = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) & ((B = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ C) = A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ B)) | (C = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3204])). 120.83/55.28 thf(864,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1722_dvd_Oless__imp__not__eq2)). 120.83/55.28 thf(7903,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[864])). 120.83/55.28 thf(2241,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)) @ A) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_power3__eq__cube)). 120.83/55.28 thf(12689,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)) @ A) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241])). 120.83/55.28 thf(1935,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.28 thf(11659,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935])). 120.83/55.28 thf(1549,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_mult__numeral__1__right)). 120.83/55.28 thf(10272,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549])). 120.83/55.28 thf(4886,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i,K:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ K)) => (((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ H) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ I) @ J)) = (xzgcda @ A @ B @ C @ K @ D @ E @ F @ G)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ G) @ B)) = K) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ I) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ J) @ B)) = H)) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ B)) = C)))) <= (is_int @ H)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4202_xzgcda__linear)). 120.83/55.28 thf(22257,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i,K:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ K)) => (((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ H) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ I) @ J)) = (xzgcda @ A @ B @ C @ K @ D @ E @ F @ G)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ G) @ B)) = K) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ I) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ J) @ B)) = H)) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ B)) = C)))) | ~ (is_int @ H)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4886])). 120.83/55.28 thf(1977,axiom,((is_int @ s1)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_s1____)). 120.83/55.28 thf(11790,plain,((is_int @ s1)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977])). 120.83/55.28 thf(3465,axiom,((! [A:$i]: (((zero_zero_real = (hAPP_nat_real @ sin_coeff @ A)) <= (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & (((hAPP_nat_real @ sin_coeff @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3796_sin__coeff__def)). 120.83/55.28 thf(16950,plain,((! [A:$i]: (((zero_zero_real = (hAPP_nat_real @ sin_coeff @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & (((hAPP_nat_real @ sin_coeff @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3465])). 120.83/55.28 thf(2653,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_dvd__triv__right)). 120.83/55.28 thf(14181,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2653])). 120.83/55.28 thf(2256,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2282_mult_Oprod__diff__prod)). 120.83/55.28 thf(12738,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256])). 120.83/55.28 thf(3857,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3540_negative__zle__0)). 120.83/55.28 thf(18328,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3857])). 120.83/55.28 thf(1606,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hBOOL @ (hAPP_complex_bool @ A @ C)) & (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ zero_zero_complex))))) <=> (? [C:$i]: (hBOOL @ (hAPP_complex_bool @ A @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1677_unity__coeff__ex)). 120.83/55.28 thf(10507,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_complex_bool @ A @ C)) & (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ zero_zero_complex))))) => (? [C:$i]: (hBOOL @ (hAPP_complex_bool @ A @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))) & ((? [C:$i]: (hBOOL @ (hAPP_complex_bool @ A @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_complex_bool @ A @ C)) & (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ zero_zero_complex))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606])). 120.83/55.28 thf(1750,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2711_mod__geq)). 120.83/55.28 thf(11008,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750])). 120.83/55.28 thf(3962,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add1__zle__eq)). 120.83/55.28 thf(18691,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3962])). 120.83/55.28 thf(2189,axiom,((one_one_rat != zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_zero__neq__one)). 120.83/55.28 thf(12500,plain,((~ (one_one_rat = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189])). 120.83/55.28 thf(1792,axiom,(((collect_int @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ fEx_int) @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ cOMBB_int_bool_int) @ fequal_int)) @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ plus_plus_int) @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ one_one_int)))) = zOdd)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5029_zOdd__def)). 120.83/55.28 thf(11175,plain,(((collect_int @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ fEx_int) @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ cOMBB_int_bool_int) @ fequal_int)) @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ plus_plus_int) @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ one_one_int)))) = zOdd)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792])). 120.83/55.28 thf(1712,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3209_Suc__mod__eq__add3__mod)). 120.83/55.28 thf(10844,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712])). 120.83/55.28 thf(3448,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_zero__less__mult__pos)). 120.83/55.28 thf(16898,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3448])). 120.83/55.28 thf(2572,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4318_gcd__semilattice__nat_Oinf__mono)). 120.83/55.28 thf(13869,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2572])). 120.83/55.28 thf(357,axiom,((! [A:$i,B:$i]: (((((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) != zero_zero_real) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))) <= ((hAPP_real_real @ cos @ A) != zero_zero_real)) <= ((hAPP_real_real @ cos @ B) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3612_tan__add)). 120.83/55.28 thf(6142,plain,((! [A:$i,B:$i]: (((~ ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) = zero_zero_real)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))) | ((hAPP_real_real @ cos @ A) = zero_zero_real) | ((hAPP_real_real @ cos @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 120.83/55.28 thf(4213,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ B) @ A) = zero_zero_int) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2518_dvd__eq__mod__eq__0)). 120.83/55.28 thf(19681,plain,((! [A:$i,B:$i]: ((((hAPP_int_int @ (div_mod_int @ B) @ A) = zero_zero_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ (div_mod_int @ B) @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4213])). 120.83/55.28 thf(1275,axiom,((one_one_real = (hAPP_nat_real @ semiri132038758t_real @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2971_of__nat__1)). 120.83/55.28 thf(9342,plain,((one_one_real = (hAPP_nat_real @ semiri132038758t_real @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275])). 120.83/55.28 thf(2177,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_nat_nat @ fact_fact_nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3816_fact__reduce__nat)). 120.83/55.28 thf(12458,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_nat_nat @ fact_fact_nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177])). 120.83/55.28 thf(2994,axiom,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.28 thf(15361,plain,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2994])). 120.83/55.28 thf(1810,axiom,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ cnj @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4073_complex__cnj__cnj)). 120.83/55.28 thf(11224,plain,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ cnj @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810])). 120.83/55.28 thf(1137,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_comm__mult__strict__left__mono)). 120.83/55.28 thf(8855,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137])). 120.83/55.28 thf(1014,axiom,((! [A:$i,B:$i]: (((A = zero_zero_rat) & (zero_zero_nat != B)) <=> ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1295_power__eq__0__iff)). 120.83/55.28 thf(8417,plain,((! [A:$i,B:$i]: ((((A = zero_zero_rat) & ~ (zero_zero_nat = B)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B) = zero_zero_rat)) & (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B) = zero_zero_rat) => ((A = zero_zero_rat) & ~ (zero_zero_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])). 120.83/55.28 thf(1843,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3138_diff__Suc__diff__eq2)). 120.83/55.28 thf(11352,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843])). 120.83/55.28 thf(2226,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) <= ((A = one_one_nat) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1497_dvd__power)). 120.83/55.28 thf(12634,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) | ~ ((A = one_one_nat) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226])). 120.83/55.28 thf(862,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3925_real__root__gt__1__iff)). 120.83/55.28 thf(7888,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[862])). 120.83/55.28 thf(2237,axiom,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3241_one__div__nat__number__of)). 120.83/55.28 thf(12674,plain,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237])). 120.83/55.28 thf(1359,axiom,((! [A:$i,B:$i]: (((hAPP_int_complex @ number528085621omplex @ A) = B) <=> ((hAPP_int_complex @ number528085621omplex @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_number__of__reorient)). 120.83/55.28 thf(9621,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359])). 120.83/55.28 thf(2314,axiom,((! [A:$i]: (zero_zero_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4643_Frct__code__post_I1_J)). 120.83/55.28 thf(12949,plain,((! [A:$i]: (zero_zero_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314])). 120.83/55.28 thf(4636,axiom,((! [A:$i,B:$i]: ((((A != zero_zero_int) | (B != zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_sum__squares__gt__zero__iff)). 120.83/55.28 thf(21353,plain,((! [A:$i,B:$i]: ((((~ (A = zero_zero_int) | ~ (B = zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B)))) => (~ (A = zero_zero_int) | ~ (B = zero_zero_int)))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4636])). 120.83/55.28 thf(1556,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ one_on1684967323de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1477_power__strict__decreasing)). 120.83/55.28 thf(10299,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ one_on1684967323de_int)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556])). 120.83/55.28 thf(1343,axiom,((! [A:$i]: ~ ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2903_even__odd__conj)). 120.83/55.28 thf(9573,plain,((! [A:$i]: ~ ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343])). 120.83/55.28 thf(1516,axiom,((! [A:$i,B:$i,C:$i]: (((? [D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) = A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A))) <= ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2774_nat__mod__eq__lemma)). 120.83/55.28 thf(10149,plain,((! [A:$i,B:$i,C:$i]: (? [D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) | ~ ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516])). 120.83/55.28 thf(3949,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) <= (B != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1578_Euler_Oaux1)). 120.83/55.28 thf(18646,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) | (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3949])). 120.83/55.28 thf(2922,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ one_on1645066479umeral))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1476_power__strict__decreasing)). 120.83/55.28 thf(15115,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ one_on1645066479umeral))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2922])). 120.83/55.28 thf(367,axiom,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4396_real__of__int__mult)). 120.83/55.28 thf(6177,plain,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 120.83/55.28 thf(2215,axiom,(((produc713050258nt_int @ uminus_uminus_int) = negateSnd)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4855_negateSnd__def)). 120.83/55.28 thf(12602,plain,(((produc713050258nt_int @ uminus_uminus_int) = negateSnd)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215])). 120.83/55.28 thf(3771,axiom,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3187_transfer__int__nat__numerals_I3_J)). 120.83/55.28 thf(18020,plain,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3771])). 120.83/55.28 thf(3007,axiom,((! [A:$i,B:$i]: (((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3098_of__nat__diff)). 120.83/55.28 thf(15408,plain,((! [A:$i,B:$i]: (((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3007])). 120.83/55.28 thf(3387,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_mult__neg__pos)). 120.83/55.28 thf(16708,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3387])). 120.83/55.28 thf(3573,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3192_realpow__two__diff)). 120.83/55.28 thf(17310,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3573])). 120.83/55.28 thf(1528,axiom,((! [A:$i,B:$i]: ((is_int @ (hAPP_int_int @ A @ B)) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint)). 120.83/55.28 thf(10198,plain,((! [A:$i,B:$i]: ((is_int @ (hAPP_int_int @ A @ B)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528])). 120.83/55.28 thf(2742,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1841_nat__mult__dvd__cancel1)). 120.83/55.28 thf(14468,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2742])). 120.83/55.28 thf(1592,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1276_power__increasing)). 120.83/55.28 thf(10446,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592])). 120.83/55.28 thf(721,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2452_dvd__mod)). 120.83/55.28 thf(7358,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])). 120.83/55.28 thf(3202,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3072_Suc__diff__le)). 120.83/55.28 thf(16086,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3202])). 120.83/55.28 thf(1537,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.28 thf(10234,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537])). 120.83/55.28 thf(2469,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1996_add__le__imp__le__left)). 120.83/55.28 thf(13520,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469])). 120.83/55.28 thf(4928,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ B)) != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ A))) <= ((A != B) & (C = D))) <= (zero_zero_int != E)) <= ((is_int @ A) & (is_int @ E) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_add__scale__eq__noteq)). 120.83/55.28 thf(22397,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ A))) | ~ (~ (A = B) & (C = D)) | (zero_zero_int = E) | ~ ((is_int @ A) & (is_int @ E) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4928])). 120.83/55.28 thf(4564,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2670_neg__zdiv__mult__2)). 120.83/55.28 thf(21114,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4564])). 120.83/55.28 thf(1707,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3026_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.28 thf(10832,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707])). 120.83/55.28 thf(2670,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_mult__nonneg__nonpos)). 120.83/55.28 thf(14235,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2670])). 120.83/55.28 thf(4712,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1467_power__Suc__less)). 120.83/55.28 thf(21662,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4712])). 120.83/55.28 thf(1761,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_power2__le__imp__le)). 120.83/55.28 thf(11043,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761])). 120.83/55.28 thf(2008,axiom,((is_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint)). 120.83/55.28 thf(11880,plain,((is_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008])). 120.83/55.28 thf(2362,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_dvd__power__same)). 120.83/55.28 thf(13120,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362])). 120.83/55.28 thf(1256,axiom,((! [A:$i,B:$i,C:$i]: (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4589_RRset__gcd)). 120.83/55.28 thf(9251,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256])). 120.83/55.28 thf(2815,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_dvd__trans)). 120.83/55.28 thf(14750,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2815])). 120.83/55.28 thf(347,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2297_mult__left_Oadd)). 120.83/55.28 thf(6106,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 120.83/55.28 thf(226,axiom,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) <=> (B = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2782_eq__diff__eq_H)). 120.83/55.28 thf(5696,plain,((! [A:$i,B:$i,C:$i]: (((A = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) => (B = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) & ((B = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) => (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 120.83/55.28 thf(1448,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4194_prime__divprod__pow)). 120.83/55.28 thf(9924,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448])). 120.83/55.28 thf(1119,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_mult__mono)). 120.83/55.28 thf(8797,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119])). 120.83/55.28 thf(2377,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4328_gcd__greatest__iff__nat)). 120.83/55.28 thf(13177,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377])). 120.83/55.28 thf(2634,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2167_add__nonneg__nonneg)). 120.83/55.28 thf(14117,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2634])). 120.83/55.28 thf(4364,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2464_mod__mod__is__mod)). 120.83/55.28 thf(20258,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4364])). 120.83/55.28 thf(2391,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2118_mult__1)). 120.83/55.28 thf(13234,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391])). 120.83/55.28 thf(915,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3337_real__sqrt__two__ge__zero)). 120.83/55.28 thf(8082,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[915])). 120.83/55.28 thf(3612,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.28 thf(17437,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3612])). 120.83/55.28 thf(3547,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.28 thf(17221,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3547])). 120.83/55.28 thf(1616,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1974_add__0__right)). 120.83/55.28 thf(10542,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616])). 120.83/55.28 thf(588,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = zero_zero_real) <=> ((zero_zero_real = A) | (zero_zero_real = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_mult__eq__0__iff)). 120.83/55.28 thf(6883,plain,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = zero_zero_real) => ((zero_zero_real = A) | (zero_zero_real = B))) & (((zero_zero_real = A) | (zero_zero_real = B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 120.83/55.28 thf(543,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))) <= ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2093_diff__eq__diff__less__eq)). 120.83/55.28 thf(6744,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))) | ~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 120.83/55.28 thf(37,axiom,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ A)) = (cis @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4152_cis__def)). 120.83/55.28 thf(5069,plain,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ A)) = (cis @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 120.83/55.28 thf(212,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (bseq_real @ C)) <= (! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_nat_real @ C @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ D)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4948_BseqI2)). 120.83/55.28 thf(5644,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (bseq_real @ C)) | ~ (! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_nat_real @ C @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ D)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 120.83/55.28 thf(3567,axiom,((! [A:$i,B:$i]: (((A = zero_z126310315umeral) | (B = zero_z126310315umeral)) <= ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B) = zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_divisors__zero)). 120.83/55.28 thf(17278,plain,((! [A:$i,B:$i]: ((A = zero_z126310315umeral) | (B = zero_z126310315umeral) | ~ ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B) = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3567])). 120.83/55.28 thf(3405,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) <=> (A = C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1752_eq__diff__iff)). 120.83/55.28 thf(16765,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) => (A = C)) & ((A = C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3405])). 120.83/55.28 thf(3823,axiom,((! [A:$i]: ((? [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))) <=> (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2709_ex__nat)). 120.83/55.28 thf(18193,plain,((! [A:$i]: (((? [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))) => (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B)))))) & ((? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))))) => (? [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3823])). 120.83/55.28 thf(3361,axiom,((! [A:$i]: (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2995_power__0__Suc)). 120.83/55.28 thf(16619,plain,((! [A:$i]: (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3361])). 120.83/55.28 thf(1657,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2962_of__nat__mult)). 120.83/55.28 thf(10673,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657])). 120.83/55.28 thf(3427,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2061_add__strict__right__mono)). 120.83/55.28 thf(16830,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3427])). 120.83/55.28 thf(4750,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.28 thf(21815,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4750])). 120.83/55.28 thf(3794,axiom,((! [A:$i,B:$i]: ((! [C:$i]: (((hBOOL @ (hAPP_int_bool @ B @ C)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))))) <= (is_int @ C))) => (hBOOL @ (hAPP_int_bool @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2218_d22set__induct__old)). 120.83/55.28 thf(18101,plain,((! [A:$i,B:$i]: ((! [C:$i]: ((hBOOL @ (hAPP_int_bool @ B @ C)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)))) | ~ (is_int @ C))) => (hBOOL @ (hAPP_int_bool @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3794])). 120.83/55.28 thf(1659,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((hAPP_int_int @ number_number_of_int @ A) = B) <=> ((hAPP_int_int @ number_number_of_int @ A) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_number__of__reorient)). 120.83/55.28 thf(10679,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659])). 120.83/55.28 thf(2397,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1994_add__le__imp__le__left)). 120.83/55.28 thf(13255,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397])). 120.83/55.28 thf(4649,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3272_neg__number__of__Bit1)). 120.83/55.28 thf(21418,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))))) & ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A)))) => (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4649])). 120.83/55.28 thf(1287,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2197_add__le__less__mono)). 120.83/55.28 thf(9383,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287])). 120.83/55.28 thf(3110,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_one_complex = A)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1493_dvd__power)). 120.83/55.28 thf(15770,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_one_complex = A)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3110])). 120.83/55.28 thf(3482,axiom,((! [A:$i]: ((one_one_nat = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4025_coprime__0_H)). 120.83/55.28 thf(17014,plain,((! [A:$i]: (((one_one_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ zero_zero_nat) @ A)) => (one_one_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3482])). 120.83/55.28 thf(1551,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) <= (zero_z891286103de_int != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2540_div__mult__mult2)). 120.83/55.28 thf(10277,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) | (zero_z891286103de_int = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551])). 120.83/55.28 thf(1010,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1791_real__mult__less__mono2)). 120.83/55.28 thf(8402,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])). 120.83/55.28 thf(4367,axiom,((! [A:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ one_one_nat) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_power__one__right)). 120.83/55.28 thf(20268,plain,((! [A:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ one_one_nat) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4367])). 120.83/55.28 thf(1690,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) | (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2896_EvenOdd_Oeven__product)). 120.83/55.28 thf(10780,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) | (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690])). 120.83/55.28 thf(1624,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2856_Suc__lessD)). 120.83/55.28 thf(10567,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624])). 120.83/55.28 thf(3342,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.28 thf(16566,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3342])). 120.83/55.28 thf(3867,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ A) <=> (hBOOL @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => (((hBOOL @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) <=> ((hBOOL @ A) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1615_conj__le__cong)). 120.83/55.28 thf(18365,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ A) => (hBOOL @ B)) & ((hBOOL @ B) => (hBOOL @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => ((((hBOOL @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => ((hBOOL @ A) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))) & (((hBOOL @ A) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => ((hBOOL @ B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3867])). 120.83/55.28 thf(3383,axiom,((! [A:$i]: (((? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & ((hAPP_nat_int @ semiri1621563631at_int @ B) = A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3251_zero__less__imp__eq__int)). 120.83/55.28 thf(16698,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & ((hAPP_nat_int @ semiri1621563631at_int @ B) = A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3383])). 120.83/55.28 thf(3918,axiom,((zero_z126310315umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zero__power2)). 120.83/55.28 thf(18549,plain,((zero_z126310315umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3918])). 120.83/55.28 thf(710,axiom,(((hAPP_int_int @ number_number_of_int @ pls) != (hAPP_int_int @ number_number_of_int @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_eq__number__of__Pls__Min)). 120.83/55.28 thf(7322,plain,((~ ((hAPP_int_int @ number_number_of_int @ pls) = (hAPP_int_int @ number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])). 120.83/55.28 thf(1124,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1527_nat__dvd__not__less)). 120.83/55.28 thf(8811,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124])). 120.83/55.28 thf(2078,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2195_add__le__less__mono)). 120.83/55.28 thf(12089,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078])). 120.83/55.28 thf(1384,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_dvd__triv__left)). 120.83/55.28 thf(9704,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384])). 120.83/55.28 thf(4924,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4505_zgcd__1__power__distrib)). 120.83/55.28 thf(22384,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) | ~ ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4924])). 120.83/55.28 thf(2767,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_mult__nonneg__nonneg)). 120.83/55.28 thf(14570,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2767])). 120.83/55.28 thf(3526,axiom,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2347_mod__div__equality)). 120.83/55.28 thf(17143,plain,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3526])). 120.83/55.28 thf(4145,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = A) <= (C = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1524_Int2_Oaux1)). 120.83/55.28 thf(19438,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = A) | ~ (C = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4145])). 120.83/55.28 thf(4803,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_rat @ (hAPP_f1900950721nt_rat @ (hAPP_f1270196437nt_rat @ cOMBB_int_rat_int @ A) @ B) @ C) = (hAPP_int_rat @ A @ (hAPP_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Rat__Orat_000tc__Int__Oint_U)). 120.83/55.28 thf(21984,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_rat @ (hAPP_f1900950721nt_rat @ (hAPP_f1270196437nt_rat @ cOMBB_int_rat_int @ A) @ B) @ C) = (hAPP_int_rat @ A @ (hAPP_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4803])). 120.83/55.28 thf(929,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3730_sin__squared__eq)). 120.83/55.28 thf(8118,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[929])). 120.83/55.28 thf(1668,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2399_zmod__simps_I4_J)). 120.83/55.28 thf(10711,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668])). 120.83/55.28 thf(2471,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2000_add__le__imp__le__right)). 120.83/55.28 thf(13525,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2471])). 120.83/55.28 thf(2337,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1913_add__right__imp__eq)). 120.83/55.28 thf(13035,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337])). 120.83/55.28 thf(278,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3667_sin__diff)). 120.83/55.28 thf(5878,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 120.83/55.28 thf(2515,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2907_zero__le__imp__of__nat)). 120.83/55.28 thf(13672,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515])). 120.83/55.28 thf(3884,axiom,((! [A:$i,B:$i,C:$i]: ((((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2585_split__neg__lemma)). 120.83/55.28 thf(18416,plain,((! [A:$i,B:$i,C:$i]: ((((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => (! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3884])). 120.83/55.28 thf(1666,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1663_power2__diff)). 120.83/55.28 thf(10705,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666])). 120.83/55.28 thf(3389,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ E) @ D)) => (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ E) @ B)) @ D)) <= ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2403_mod__mult__cong)). 120.83/55.28 thf(16713,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ E) @ D)) => (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ E) @ B)) @ D)) | ~ ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3389])). 120.83/55.28 thf(2977,axiom,((! [A:$i,B:$i,C:$i]: ((B = C) <= ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1926_add__left__imp__eq)). 120.83/55.28 thf(15293,plain,((! [A:$i,B:$i,C:$i]: ((B = C) | ~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2977])). 120.83/55.28 thf(1547,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3022_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.28 thf(10262,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547])). 120.83/55.28 thf(814,axiom,((! [A:$i,B:$i]: (((natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3702_natfloor__add)). 120.83/55.28 thf(7726,plain,((! [A:$i,B:$i]: (((natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 120.83/55.28 thf(3462,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_power__commutes)). 120.83/55.28 thf(16940,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3462])). 120.83/55.28 thf(4131,axiom,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2678_Euler__part1)). 120.83/55.28 thf(19391,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4131])). 120.83/55.28 thf(2445,axiom,((! [A:$i,B:$i,C:$i]: (((((hAPP_int_int @ (legacy_zgcd @ A) @ C) = B) <=> (? [D:$i,E:$i]: ((is_int @ D) & (is_int @ E) & ((xzgcd @ A @ C) = (hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4530_xzgcd__correct)). 120.83/55.28 thf(13437,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_int_int @ (legacy_zgcd @ A) @ C) = B) => (? [D:$i,E:$i]: ((is_int @ D) & (is_int @ E) & ((xzgcd @ A @ C) = (hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))))) & ((? [D:$i,E:$i]: ((is_int @ D) & (is_int @ E) & ((xzgcd @ A @ C) = (hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))))) => ((hAPP_int_int @ (legacy_zgcd @ A) @ C) = B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2445])). 120.83/55.28 thf(259,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_nat_real @ real_nat @ (natfloor @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3693_real__natfloor__gt__diff__one)). 120.83/55.28 thf(5793,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_nat_real @ real_nat @ (natfloor @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 120.83/55.28 thf(4420,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1837_norR__mem__unique__aux)). 120.83/55.28 thf(20484,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4420])). 120.83/55.28 thf(62,axiom,((! [A:$i]: ((((hAPP_real_real @ arcsin @ (hAPP_real_real @ sin @ A)) = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3740_arcsin__sin)). 120.83/55.28 thf(5173,plain,((! [A:$i]: (((hAPP_real_real @ arcsin @ (hAPP_real_real @ sin @ A)) = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 120.83/55.28 thf(982,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ zero_z891286103de_int) @ A) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2477_div__0)). 120.83/55.28 thf(8315,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ zero_z891286103de_int) @ A) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])). 120.83/55.28 thf(4797,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((((B = A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_zdvd__antisym__nonneg)). 120.83/55.28 thf(21961,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((B = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4797])). 120.83/55.28 thf(3607,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.28 thf(17424,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3607])). 120.83/55.28 thf(686,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.28 thf(7253,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])). 120.83/55.28 thf(1709,axiom,((! [A:$i]: ((one_on1645066479umeral = A) <=> (one_on1645066479umeral = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1953_one__reorient)). 120.83/55.28 thf(10837,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709])). 120.83/55.28 thf(4433,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_f521865025ol_nat @ finite1876863882t_bool @ (setS @ A @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3305_SetS__card)). 120.83/55.28 thf(20534,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_f521865025ol_nat @ finite1876863882t_bool @ (setS @ A @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4433])). 120.83/55.28 thf(3470,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_mult__pos__neg)). 120.83/55.28 thf(16972,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3470])). 120.83/55.28 thf(672,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B) = A) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1771_le__imp__diff__is__add)). 120.83/55.28 thf(7198,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B) = A) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = C)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B) = A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 120.83/55.28 thf(3513,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ B) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2980_of__nat__power)). 120.83/55.28 thf(17104,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ B) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3513])). 120.83/55.28 thf(4173,axiom,((one_one_int != zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_zero__neq__one)). 120.83/55.28 thf(19533,plain,((~ (one_one_int = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4173])). 120.83/55.28 thf(572,axiom,((! [A:$i]: ((hAPP_real_real @ exp_real @ A) = (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3828_abs__exp__cancel)). 120.83/55.28 thf(6830,plain,((! [A:$i]: ((hAPP_real_real @ exp_real @ A) = (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])). 120.83/55.28 thf(1475,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ cos @ B))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ sin @ B))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3727_sin__cos__squared__add2__mult)). 120.83/55.28 thf(10017,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ cos @ B))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ sin @ B))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475])). 120.83/55.28 thf(1197,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_dvd__mult2)). 120.83/55.28 thf(9059,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197])). 120.83/55.28 thf(3627,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((zero_zero_int != (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D)) => (((D = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = one_one_int)) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4965_gcd__coprime__int)). 120.83/55.28 thf(17495,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D))) => (((D = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = one_one_int)) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3627])). 120.83/55.28 thf(3395,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) <= ((hAPP_nat_nat @ suc @ A) != B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2859_Suc__lessI)). 120.83/55.28 thf(16730,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) | ((hAPP_nat_nat @ suc @ A) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3395])). 120.83/55.28 thf(2709,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3474_abs__ln__one__plus__x__minus__x__bound__nonneg)). 120.83/55.28 thf(14377,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2709])). 120.83/55.28 thf(3797,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (z3div @ A) @ B))) & (((hAPP_int_int @ (z3div @ A) @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3950_z3div__def)). 120.83/55.28 thf(18114,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (z3div @ A) @ B))) & (((hAPP_int_int @ (z3div @ A) @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3797])). 120.83/55.28 thf(3172,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4688_divide__rat)). 120.83/55.28 thf(15981,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3172])). 120.83/55.28 thf(3945,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ number_number_of_int @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_add__numeral__0__right)). 120.83/55.28 thf(18635,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ number_number_of_int @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3945])). 120.83/55.28 thf(3492,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3443_ln__less__zero__iff)). 120.83/55.28 thf(17046,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3492])). 120.83/55.28 thf(1880,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (divmod_int @ A @ B))) <= (B != zero_zero_int)) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4192_divmod__int__correct)). 120.83/55.28 thf(11485,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (divmod_int @ A @ B))) | (B = zero_zero_int) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880])). 120.83/55.28 thf(3275,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A))) => ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3201_expand__Suc)). 120.83/55.28 thf(16353,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A))) => ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3275])). 120.83/55.28 thf(668,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1449_power__less__imp__less__exp)). 120.83/55.28 thf(7182,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 120.83/55.28 thf(3780,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3784_nat__even__iff__2__dvd)). 120.83/55.28 thf(18052,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3780])). 120.83/55.28 thf(3634,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C) = B))) <= (zero_zero_int != C)) <= ((is_int @ C) & (is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2642_dvd__div__eq__mult)). 120.83/55.28 thf(17524,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) => (((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C) = B)) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C) = B) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))))) | (zero_zero_int = C) | ~ ((is_int @ C) & (is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3634])). 120.83/55.28 thf(4179,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2059_add__strict__right__mono)). 120.83/55.28 thf(19550,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4179])). 120.83/55.28 thf(2586,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2904_zero__le__imp__of__nat)). 120.83/55.28 thf(13918,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2586])). 120.83/55.28 thf(82,axiom,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4142_Re_Obounded)). 120.83/55.28 thf(5237,plain,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 120.83/55.28 thf(3481,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ one_one_int) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4670_eq__rat_I2_J)). 120.83/55.28 thf(17011,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ one_one_int) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3481])). 120.83/55.28 thf(4721,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_zadd__zless__mono)). 120.83/55.28 thf(21697,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4721])). 120.83/55.28 thf(1158,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ C))) @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ B)) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3749_reals__Archimedean4)). 120.83/55.28 thf(8928,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ C))) @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ B)) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158])). 120.83/55.28 thf(1509,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1983_add__0)). 120.83/55.28 thf(10125,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509])). 120.83/55.28 thf(1295,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (A = C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1484_power__eq__imp__eq__base)). 120.83/55.28 thf(9400,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (A = C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295])). 120.83/55.28 thf(3113,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_mult__strict__right__mono)). 120.83/55.28 thf(15780,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3113])). 120.83/55.28 thf(1482,axiom,((one_on1645066479umeral = (hAPP_n1108039445umeral @ semiri1619134803umeral @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2970_of__nat__1)). 120.83/55.28 thf(10039,plain,((one_on1645066479umeral = (hAPP_n1108039445umeral @ semiri1619134803umeral @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482])). 120.83/55.28 thf(2554,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)) @ D) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_combine__common__factor)). 120.83/55.28 thf(13811,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)) @ D) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2554])). 120.83/55.28 thf(3160,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1610_gr0I)). 120.83/55.28 thf(15926,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3160])). 120.83/55.28 thf(4002,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => ((! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int))))) <= (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2219_int__less__induct)). 120.83/55.28 thf(18837,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => ((! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int))))) | ~ (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4002])). 120.83/55.28 thf(908,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2094_diff__eq__diff__less__eq)). 120.83/55.28 thf(8045,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[908])). 120.83/55.28 thf(715,axiom,((! [A:$i]: (((hAPP_real_real @ sgn_sgn_real @ A) = one_one_real) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3571_real__sgn__pos)). 120.83/55.28 thf(7341,plain,((! [A:$i]: (((hAPP_real_real @ sgn_sgn_real @ A) = one_one_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])). 120.83/55.28 thf(1956,axiom,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4561_plus__code__int__def)). 120.83/55.28 thf(11724,plain,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956])). 120.83/55.28 thf(3348,axiom,((! [A:$i,B:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3741_sin__cos__add)). 120.83/55.28 thf(16581,plain,((! [A:$i,B:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3348])). 120.83/55.28 thf(3306,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (A = (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2691_mod__less)). 120.83/55.28 thf(16449,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (A = (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3306])). 120.83/55.28 thf(2009,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__special_I2_J)). 120.83/55.28 thf(11881,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009])). 120.83/55.28 thf(1281,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1711_dvd__antisym)). 120.83/55.28 thf(9364,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281])). 120.83/55.28 thf(2333,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1617_less__eq__nat_Osimps_I1_J)). 120.83/55.28 thf(13020,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333])). 120.83/55.28 thf(1221,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ A)) <= (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_linorder__neqE__linordered__idom)). 120.83/55.28 thf(9135,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ A)) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221])). 120.83/55.28 thf(3236,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ (hAPP_nat_complex @ semiri2020571505omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2963_of__nat__mult)). 120.83/55.28 thf(16229,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ (hAPP_nat_complex @ semiri2020571505omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3236])). 120.83/55.28 thf(4030,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hAPP_P1175774780nt_int @ product_snd_int_int @ (negDivAlg @ B @ A)) = (hAPP_int_int @ (div_mod_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4234_mod__neg__pos)). 120.83/55.28 thf(18942,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hAPP_P1175774780nt_int @ product_snd_int_int @ (negDivAlg @ B @ A)) = (hAPP_int_int @ (div_mod_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4030])). 120.83/55.28 thf(2385,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4716_Fract__less__zero__iff)). 120.83/55.28 thf(13212,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385])). 120.83/55.28 thf(464,axiom,(((natceiling @ one_one_real) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3393_natceiling__one)). 120.83/55.28 thf(6480,plain,(((natceiling @ one_one_real) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 120.83/55.28 thf(539,axiom,((zero_zero_real != pi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3416_pi__neq__zero)). 120.83/55.28 thf(6732,plain,((~ (zero_zero_real = pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])). 120.83/55.28 thf(2721,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2360_zdiv__zmod__equality)). 120.83/55.28 thf(14409,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2721])). 120.83/55.28 thf(1259,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (log @ A) @ C)) = (hAPP_real_real @ (log @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3872_log__nat__power)). 120.83/55.28 thf(9268,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (log @ A) @ C)) = (hAPP_real_real @ (log @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259])). 120.83/55.28 thf(2729,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ one_one_complex) @ A) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_power__one)). 120.83/55.28 thf(14431,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ one_one_complex) @ A) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2729])). 120.83/55.28 thf(4164,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (legendre @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2768_Euler__Criterion)). 120.83/55.28 thf(19501,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (legendre @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4164])). 120.83/55.28 thf(3290,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2262_minf_I9_J)). 120.83/55.28 thf(16402,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3290])). 120.83/55.28 thf(379,axiom,((! [A:$i,B:$i,C:$i]: (((A = zero_zero_real) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1263_dvd__mult__cancel__left)). 120.83/55.28 thf(6214,plain,((! [A:$i,B:$i,C:$i]: ((((A = zero_zero_real) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) => ((A = zero_zero_real) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 120.83/55.28 thf(2819,axiom,(((hAPP_nat_nat @ suc @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_One__nat__def)). 120.83/55.28 thf(14765,plain,(((hAPP_nat_nat @ suc @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2819])). 120.83/55.28 thf(2383,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2033_add__le__cancel__right)). 120.83/55.28 thf(13202,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383])). 120.83/55.28 thf(2645,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4393_real__of__int__add)). 120.83/55.28 thf(14156,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2645])). 120.83/55.28 thf(4688,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_power3__eq__cube)). 120.83/55.28 thf(21538,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4688])). 120.83/55.28 thf(4509,axiom,((! [A:$i,B:$i]: ((setS @ A @ B) = (image_275383677t_bool @ (multInvPair @ A @ B) @ (hAPP_i1948725293t_bool @ sRStar @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4607_SetS__def)). 120.83/55.28 thf(20830,plain,((! [A:$i,B:$i]: ((setS @ A @ B) = (image_275383677t_bool @ (multInvPair @ A @ B) @ (hAPP_i1948725293t_bool @ sRStar @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4509])). 120.83/55.28 thf(3187,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_arith__simps_I32_J)). 120.83/55.28 thf(16027,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3187])). 120.83/55.28 thf(4388,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_semiring__add__number__of)). 120.83/55.28 thf(20345,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4388])). 120.83/55.28 thf(170,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (rcis @ A @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ sin @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4263_Im__rcis)). 120.83/55.28 thf(5501,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (rcis @ A @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ sin @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 120.83/55.28 thf(2321,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_power__strict__mono)). 120.83/55.28 thf(12971,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321])). 120.83/55.28 thf(3671,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1864_add__nonneg__pos)). 120.83/55.28 thf(17665,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3671])). 120.83/55.28 thf(984,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1454_power__strict__increasing__iff)). 120.83/55.28 thf(8320,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[984])). 120.83/55.28 thf(4344,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_less__int__code_I13_J)). 120.83/55.28 thf(20198,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4344])). 120.83/55.28 thf(4476,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ A) & (is_int @ C)) => (((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)) @ B)))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ C) @ B))) => (((hAPP_int_int @ (inv @ B) @ C) = A) | (A = C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2227_wset__mem__imp__or)). 120.83/55.28 thf(20711,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ A) & (is_int @ C)) => (((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)) @ B)))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ C) @ B))) => (((hAPP_int_int @ (inv @ B) @ C) = A) | (A = C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4476])). 120.83/55.28 thf(474,axiom,((! [A:$i]: (is_int @ (code_int_of @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Code__Numeral_Oint__of)). 120.83/55.28 thf(6522,plain,((! [A:$i]: (is_int @ (code_int_of @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 120.83/55.28 thf(145,axiom,((! [A:$i,B:$i]: (((one_one_real != B) => (((hAPP_real_real @ (log @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (log @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3875_log__inverse)). 120.83/55.28 thf(5425,plain,((! [A:$i,B:$i]: (((~ (one_one_real = B)) => (((hAPP_real_real @ (log @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (log @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 120.83/55.28 thf(3559,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (natfloor @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3385_zero__le__natfloor)). 120.83/55.28 thf(17253,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (natfloor @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3559])). 120.83/55.28 thf(2731,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2298_mult__left_Oadd)). 120.83/55.28 thf(14441,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2731])). 120.83/55.28 thf(4817,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2189_double__add__less__zero__iff__single__add__less__zero)). 120.83/55.28 thf(22030,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4817])). 120.83/55.28 thf(4434,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1381_mult__le__cancel__left__pos)). 120.83/55.28 thf(20537,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4434])). 120.83/55.28 thf(3367,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C) = one_one_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4368_coprime__dvd__mult__iff__nat)). 120.83/55.28 thf(16645,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C) = one_one_nat) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3367])). 120.83/55.28 thf(4472,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1227_not__one__less__zero)). 120.83/55.28 thf(20694,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4472])). 120.83/55.28 thf(3820,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_zmult__1)). 120.83/55.28 thf(18184,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3820])). 120.83/55.28 thf(613,axiom,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4389_real__of__int__diff)). 120.83/55.28 thf(6971,plain,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])). 120.83/55.28 thf(3738,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ A) = (hAPP_int_int @ abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4986_gcd__idem__int)). 120.83/55.28 thf(17907,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ A) = (hAPP_int_int @ abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3738])). 120.83/55.28 thf(3516,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4332_gcd__add2__nat)). 120.83/55.28 thf(17113,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3516])). 120.83/55.28 thf(398,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ B @ E)) @ (hAPP_real_real @ B @ C))))) => (D = zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3885_DERIV__local__max)). 120.83/55.28 thf(6278,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ B @ E)) @ (hAPP_real_real @ B @ C))))) => (D = zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 120.83/55.28 thf(265,axiom,((one_one_complex = (expi @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (of_real_complex @ pi))) @ ii)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3999_expi__two__pi__i)). 120.83/55.28 thf(5814,plain,((one_one_complex = (expi @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (of_real_complex @ pi))) @ ii)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 120.83/55.28 thf(2780,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4916_finite__atLeastLessThan__int)). 120.83/55.28 thf(14617,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2780])). 120.83/55.28 thf(4087,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2229_wset__mem)). 120.83/55.28 thf(19230,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4087])). 120.83/55.28 thf(1688,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_power__mult)). 120.83/55.28 thf(10775,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688])). 120.83/55.28 thf(1235,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => ((archim856651990g_real @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4474_ceiling__eq)). 120.83/55.28 thf(9184,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => ((archim856651990g_real @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235])). 120.83/55.28 thf(3318,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) <= (B != zero_zero_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = A) <= (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4360_gcd__nat_Osimps)). 120.83/55.28 thf(16481,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) | (B = zero_zero_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = A) | ~ (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3318])). 120.83/55.28 thf(435,axiom,(((ratreal @ zero_zero_rat) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4694_Ratreal__number__collapse_I1_J)). 120.83/55.28 thf(6391,plain,(((ratreal @ zero_zero_rat) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 120.83/55.28 thf(950,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((A != B) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1708_dvd_Ole__neq__trans)). 120.83/55.28 thf(8182,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((~ (A = B)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])). 120.83/55.28 thf(1367,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1756_dvd__diffD1)). 120.83/55.28 thf(9644,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367])). 120.83/55.28 thf(3299,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2935_less__imp__of__nat__less)). 120.83/55.28 thf(16424,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3299])). 120.83/55.28 thf(4073,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)) = A)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3123_nat__0__le)). 120.83/55.28 thf(19174,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)) = A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4073])). 120.83/55.28 thf(4155,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit0 @ A) != (hAPP_int_int @ bit1 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_rel__simps_I49_J)). 120.83/55.28 thf(19477,plain,((! [A:$i,B:$i]: ~ ((hAPP_int_int @ bit0 @ A) = (hAPP_int_int @ bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4155])). 120.83/55.28 thf(469,axiom,((! [A:$i]: (((image_nat_int @ semiri1621563631at_int @ (image_int_nat @ nat @ A)) = A) <= (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4618_transfer__nat__int__set__return__embed)). 120.83/55.28 thf(6505,plain,((! [A:$i]: (((image_nat_int @ semiri1621563631at_int @ (image_int_nat @ nat @ A)) = A) | ~ (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 120.83/55.28 thf(3473,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3926_real__root__lt__1__iff)). 120.83/55.28 thf(16982,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3473])). 120.83/55.28 thf(2711,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3930_real__root__less__mono__lemma)). 120.83/55.28 thf(14382,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2711])). 120.83/55.28 thf(1054,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ B)))) = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3210_mod__Suc__eq__mod__add3)). 120.83/55.28 thf(8551,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ B)))) = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054])). 120.83/55.28 thf(4141,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_rel__simps_I9_J)). 120.83/55.28 thf(19423,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit1 @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit1 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4141])). 120.83/55.28 thf(1997,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ fequal_real @ A) @ B)) | (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__RealDef__Oreal_T)). 120.83/55.28 thf(11848,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ fequal_real @ A) @ B)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997])). 120.83/55.28 thf(3270,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4019_coprime__exp)). 120.83/55.28 thf(16336,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3270])). 120.83/55.28 thf(2388,axiom,((! [A:$i]: ((is_int @ A) => (((hAPP_int_int @ abs_abs_int @ A) = one_one_int) <=> ((A = (hAPP_int_int @ number_number_of_int @ min)) | (A = one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3437_abs__eq__1__iff)). 120.83/55.28 thf(13219,plain,((! [A:$i]: ((is_int @ A) => ((((hAPP_int_int @ abs_abs_int @ A) = one_one_int) => ((A = (hAPP_int_int @ number_number_of_int @ min)) | (A = one_one_int))) & (((A = (hAPP_int_int @ number_number_of_int @ min)) | (A = one_one_int)) => ((hAPP_int_int @ abs_abs_int @ A) = one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388])). 120.83/55.28 thf(882,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C) = (quotient_of @ A)) => (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5017_quotient__of__coprime)). 120.83/55.28 thf(7961,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C) = (quotient_of @ A)) => (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[882])). 120.83/55.28 thf(3852,axiom,(((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_semiring__norm_I110_J)). 120.83/55.28 thf(18316,plain,(((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3852])). 120.83/55.28 thf(1219,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_less__number__of)). 120.83/55.28 thf(9127,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219])). 120.83/55.28 thf(602,axiom,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ invers1449016382omplex @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4112_complex__Im__inverse)). 120.83/55.28 thf(6939,plain,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ invers1449016382omplex @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])). 120.83/55.28 thf(4260,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.28 thf(19873,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4260])). 120.83/55.28 thf(3985,axiom,((! [A:$i,B:$i,C:$i]: (((B != zero_zero_nat) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2276_pow__divides__pow__int)). 120.83/55.28 thf(18781,plain,((! [A:$i,B:$i,C:$i]: (((~ (B = zero_zero_nat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3985])). 120.83/55.28 thf(4746,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2664_zdiv__number__of__Bit1)). 120.83/55.28 thf(21798,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4746])). 120.83/55.28 thf(4719,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_rel__simps_I32_J)). 120.83/55.28 thf(21688,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4719])). 120.83/55.28 thf(2531,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1562_le__add__iff1)). 120.83/55.28 thf(13736,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2531])). 120.83/55.28 thf(937,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4667_Fract__1__number__of)). 120.83/55.28 thf(8150,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])). 120.83/55.28 thf(3327,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ one_one_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1474_power__strict__decreasing)). 120.83/55.28 thf(16513,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ one_one_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3327])). 120.83/55.28 thf(807,axiom,((! [A:$i,B:$i]: ((B != zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4361_gcd__non__0__nat)). 120.83/55.28 thf(7695,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 120.83/55.28 thf(1504,axiom,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ A) = one_on1684967323de_int)) & ((A != zero_zero_nat) => (zero_z891286103de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1437_power__0__left)). 120.83/55.28 thf(10103,plain,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ A) = one_on1684967323de_int)) & ((~ (A = zero_zero_nat)) => (zero_z891286103de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504])). 120.83/55.28 thf(519,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_comm__mult__left__mono)). 120.83/55.28 thf(6675,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 120.83/55.28 thf(2526,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2965_of__nat__mult)). 120.83/55.28 thf(13722,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526])). 120.83/55.28 thf(4857,axiom,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2364_mod__self)). 120.83/55.28 thf(22175,plain,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4857])). 120.83/55.28 thf(3075,axiom,((! [A:$i,B:$i]: ((image_int_nat @ nat @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5071_SetInterval_Otransfer__nat__int__set__functions_I2_J)). 120.83/55.28 thf(15651,plain,((! [A:$i,B:$i]: ((image_int_nat @ nat @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3075])). 120.83/55.28 thf(4942,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ one_one_int) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2240_MultInv__prop2)). 120.83/55.28 thf(22448,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ one_one_int) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4942])). 120.83/55.28 thf(1579,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_le__special_I4_J)). 120.83/55.28 thf(10395,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579])). 120.83/55.28 thf(4938,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ min)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1501_one__not__neg__one__mod__m)). 120.83/55.28 thf(22434,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ min)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4938])). 120.83/55.28 thf(2863,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (archim1246769320r_real @ A)) @ B) = (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4420_floor__add)). 120.83/55.28 thf(14905,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (archim1246769320r_real @ A)) @ B) = (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2863])). 120.83/55.28 thf(1568,axiom,(((hAPP_real_real @ sqrt @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3315_real__sqrt__zero)). 120.83/55.28 thf(10358,plain,(((hAPP_real_real @ sqrt @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568])). 120.83/55.28 thf(2491,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3004_power__Suc2)). 120.83/55.28 thf(13596,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2491])). 120.83/55.28 thf(1066,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2943_of__nat__less__iff)). 120.83/55.28 thf(8622,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066])). 120.83/55.28 thf(101,axiom,(((hAPP_int_real @ number267125858f_real @ min) = (hAPP_real_real @ cos @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3569_cos__pi)). 120.83/55.28 thf(5288,plain,(((hAPP_int_real @ number267125858f_real @ min) = (hAPP_real_real @ cos @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 120.83/55.28 thf(1767,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.28 thf(11058,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767])). 120.83/55.28 thf(2183,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.28 thf(12479,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2183])). 120.83/55.28 thf(856,axiom,((! [A:$i]: ((negDivAlg @ (hAPP_int_int @ number_number_of_int @ min) @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2665_negDivAlg__minus1)). 120.83/55.28 thf(7873,plain,((! [A:$i]: ((negDivAlg @ (hAPP_int_int @ number_number_of_int @ min) @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[856])). 120.83/55.28 thf(1752,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.28 thf(11014,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752])). 120.83/55.28 thf(3068,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3440_ln__gt__zero)). 120.83/55.28 thf(15632,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3068])). 120.83/55.28 thf(841,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (tendsto_nat_real @ B @ C @ sequentially)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) <= (? [D:$i]: ! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ B @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5036_LIMSEQ__le__const)). 120.83/55.28 thf(7824,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (tendsto_nat_real @ B @ C @ sequentially)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) | ~ (? [D:$i]: ! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ B @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])). 120.83/55.28 thf(353,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_dvd__mult2)). 120.83/55.28 thf(6127,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 120.83/55.28 thf(2355,axiom,((! [A:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ suc @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2840_of__nat__Suc)). 120.83/55.28 thf(13095,plain,((! [A:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ suc @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355])). 120.83/55.28 thf(4913,axiom,((! [A:$i,B:$i,C:$i]: (((quotient_of @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4658_quotient__of__denom__pos)). 120.83/55.28 thf(22347,plain,((! [A:$i,B:$i,C:$i]: (((quotient_of @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4913])). 120.83/55.28 thf(1805,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3101_of__nat__diff)). 120.83/55.28 thf(11207,plain,((! [A:$i,B:$i]: (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805])). 120.83/55.28 thf(1100,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1639_le__add2)). 120.83/55.28 thf(8747,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100])). 120.83/55.28 thf(4019,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (nat_tsub @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5138_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J)). 120.83/55.28 thf(18897,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (nat_tsub @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4019])). 120.83/55.28 thf(1304,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_mult__strict__right__mono)). 120.83/55.28 thf(9428,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304])). 120.83/55.28 thf(1719,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3030_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.28 thf(10864,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719])). 120.83/55.28 thf(2979,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ finite1395289673t_bool @ B)) => ((! [C:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ C)) <= (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ B)))) => ((! [C:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ B)) => ((hAPP_f957591787ol_nat @ finite_card_int @ C) = A))) => ((hAPP_f521865025ol_nat @ (hAPP_f93439879ol_nat @ big_co1758102091ol_nat @ finite_card_int) @ B) = (hAPP_f521865025ol_nat @ (hAPP_f93439879ol_nat @ big_co1758102091ol_nat @ (cOMBK_1643584600t_bool @ A)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5028_card__setsum__aux)). 120.83/55.28 thf(15299,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ finite1395289673t_bool @ B)) => ((! [C:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ C)) | ~ (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ B)))) => ((! [C:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ B)) => ((hAPP_f957591787ol_nat @ finite_card_int @ C) = A))) => ((hAPP_f521865025ol_nat @ (hAPP_f93439879ol_nat @ big_co1758102091ol_nat @ finite_card_int) @ B) = (hAPP_f521865025ol_nat @ (hAPP_f93439879ol_nat @ big_co1758102091ol_nat @ (cOMBK_1643584600t_bool @ A)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2979])). 120.83/55.28 thf(1045,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.28 thf(8519,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045])). 120.83/55.28 thf(2400,axiom,((~ (hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4167_prime__Suc0)). 120.83/55.28 thf(13270,plain,((~ (hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400])). 120.83/55.28 thf(2023,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3737_cos__double)). 120.83/55.28 thf(11917,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023])). 120.83/55.28 thf(3544,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2361_zdiv__zmod__equality2)). 120.83/55.28 thf(17211,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3544])). 120.83/55.28 thf(3813,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4511_zgcd__zmult__eq__self2)). 120.83/55.28 thf(18161,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3813])). 120.83/55.28 thf(1828,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_right__distrib__number__of)). 120.83/55.28 thf(11288,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828])). 120.83/55.28 thf(3198,axiom,((! [A:$i,B:$i,C:$i]: ((A = C) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1935_add__right__cancel)). 120.83/55.28 thf(16071,plain,((! [A:$i,B:$i,C:$i]: (((A = C) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))) & (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) => (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3198])). 120.83/55.28 thf(109,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ ln @ B) = A) <= (B = (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3821_exp__ln__eq)). 120.83/55.28 thf(5316,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ ln @ B) = A) | ~ (B = (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 120.83/55.28 thf(3766,axiom,((! [A:$i]: ((is_int @ A) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ one_one_int)) <= (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2805_two__times__odd__div__two__plus__one)). 120.83/55.28 thf(18001,plain,((! [A:$i]: ((is_int @ A) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ one_one_int)) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3766])). 120.83/55.28 thf(750,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3058_Suc__le__lessD)). 120.83/55.28 thf(7484,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])). 120.83/55.28 thf(3423,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2570_div__mult__swap)). 120.83/55.28 thf(16817,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3423])). 120.83/55.28 thf(445,axiom,((! [A:$i,B:$i]: ((B = A) <=> (((hAPP_complex_real @ re @ B) = (hAPP_complex_real @ re @ A)) & ((hAPP_complex_real @ im @ B) = (hAPP_complex_real @ im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4116_complex__eq__iff)). 120.83/55.28 thf(6416,plain,((! [A:$i,B:$i]: (((B = A) => (((hAPP_complex_real @ re @ B) = (hAPP_complex_real @ re @ A)) & ((hAPP_complex_real @ im @ B) = (hAPP_complex_real @ im @ A)))) & ((((hAPP_complex_real @ re @ B) = (hAPP_complex_real @ re @ A)) & ((hAPP_complex_real @ im @ B) = (hAPP_complex_real @ im @ A))) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 120.83/55.28 thf(4827,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_power2__sum)). 120.83/55.28 thf(22076,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4827])). 120.83/55.28 thf(4740,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ B)) => (! [D:$i]: (((! [E:$i]: (((! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (D != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E))))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C)))) <= (is_int @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))))) <= (is_int @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5092_bset_I8_J)). 120.83/55.28 thf(21766,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ B)) => (! [D:$i]: (((! [E:$i]: (! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E))))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) | ~ (is_int @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))))) | ~ (is_int @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4740])). 120.83/55.28 thf(880,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2211_less__iff__diff__less__0)). 120.83/55.28 thf(7949,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[880])). 120.83/55.28 thf(4704,axiom,((! [A:$i,B:$i]: (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => ((B = A) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_power2__eq__imp__eq)). 120.83/55.28 thf(21627,plain,((! [A:$i,B:$i]: (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => ((B = A) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4704])). 120.83/55.28 thf(2305,axiom,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_mult__zero__right)). 120.83/55.28 thf(12921,plain,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305])). 120.83/55.28 thf(1425,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2758_Suc__n__div__2__gt__zero)). 120.83/55.28 thf(9855,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425])). 120.83/55.28 thf(4152,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_mult__nonpos__nonneg)). 120.83/55.28 thf(19468,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4152])). 120.83/55.28 thf(2289,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3615_arccos__bounded)). 120.83/55.28 thf(12865,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289])). 120.83/55.28 thf(4875,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4483_zgcd__zdvd1)). 120.83/55.28 thf(22225,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4875])). 120.83/55.28 thf(577,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) <=> ((hAPP_real_real @ exp_real @ (hAPP_real_real @ ln @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3847_exp__ln__iff)). 120.83/55.28 thf(6851,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ exp_real @ (hAPP_real_real @ ln @ A)) = A)) & (((hAPP_real_real @ exp_real @ (hAPP_real_real @ ln @ A)) = A) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])). 120.83/55.28 thf(4661,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2604_nonneg1__imp__zdiv__pos__iff)). 120.83/55.28 thf(21454,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4661])). 120.83/55.28 thf(2941,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2510_mod__mult__self2)). 120.83/55.28 thf(15175,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2941])). 120.83/55.28 thf(4641,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)))) <= ((zero_zero_int != B) | (zero_zero_int != A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5004_div__gcd__coprime__int)). 120.83/55.28 thf(21383,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)))) | ~ (~ (zero_zero_int = B) | ~ (zero_zero_int = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4641])). 120.83/55.28 thf(1246,axiom,((! [A:$i]: ((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)))) & (is_int @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4478_reals__Archimedean__6c__int)). 120.83/55.28 thf(9218,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)))) & (is_int @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246])). 120.83/55.28 thf(3350,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1356_mult__le__less__imp__less)). 120.83/55.28 thf(16587,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3350])). 120.83/55.28 thf(2253,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2951_of__nat__le__iff)). 120.83/55.28 thf(12725,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253])). 120.83/55.28 thf(2360,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2086_diff__self)). 120.83/55.28 thf(13115,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360])). 120.83/55.28 thf(2902,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2075_add__less__cancel__right)). 120.83/55.28 thf(15034,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2902])). 120.83/55.28 thf(3642,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) <= (zero_zero_int != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3434_dvd__imp__le__int)). 120.83/55.28 thf(17556,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | (zero_zero_int = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3642])). 120.83/55.28 thf(3145,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ fFalse) @ A) @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T)). 120.83/55.28 thf(15885,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ fFalse) @ A) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3145])). 120.83/55.28 thf(4545,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)) <=> (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2831_of__nat__eq__iff)). 120.83/55.28 thf(21016,plain,((! [A:$i,B:$i]: ((((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)) => (B = A)) & ((B = A) => ((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4545])). 120.83/55.28 thf(4809,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.28 thf(21999,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4809])). 120.83/55.28 thf(230,axiom,((! [A:$i]: (((hAPP_real_real @ ln @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ ln @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3852_ln__inverse)). 120.83/55.28 thf(5713,plain,((! [A:$i]: (((hAPP_real_real @ ln @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ ln @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 120.83/55.28 thf(61,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((? [E:$i]: (! [F:$i]: (((hAPP_real_real @ B @ (hAPP_real_real @ A @ F)) = F) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ F) @ (hAPP_real_real @ B @ C))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ F) @ (hAPP_real_real @ B @ C)))) @ E)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E)))) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E))))) <= (! [E:$i]: ((E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5180_isCont__inv__fun__inv)). 120.83/55.28 thf(5163,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (! [F:$i]: (((hAPP_real_real @ B @ (hAPP_real_real @ A @ F)) = F) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ F) @ (hAPP_real_real @ B @ C))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ F) @ (hAPP_real_real @ B @ C)))) @ E)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)))) | ~ (! [E:$i]: ((E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 120.83/55.28 thf(3658,axiom,((! [A:$i]: ((zero_zero_real = A) <=> (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zero__eq__power2)). 120.83/55.28 thf(17609,plain,((! [A:$i]: (((zero_zero_real = A) => (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (zero_zero_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3658])). 120.83/55.28 thf(220,axiom,((! [A:$i,B:$i]: ((A = (hAPP_real_real @ ln @ B)) <= ((hAPP_real_real @ exp_real @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3820_ln__unique)). 120.83/55.28 thf(5674,plain,((! [A:$i,B:$i]: ((A = (hAPP_real_real @ ln @ B)) | ~ ((hAPP_real_real @ exp_real @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 120.83/55.28 thf(2878,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_real_real @ sqrt @ B) = (hAPP_real_real @ sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3311_real__sqrt__eq__iff)). 120.83/55.28 thf(14959,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_real_real @ sqrt @ B) = (hAPP_real_real @ sqrt @ A))) & (((hAPP_real_real @ sqrt @ B) = (hAPP_real_real @ sqrt @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2878])). 120.83/55.28 thf(1814,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4685_minus__rat__cancel)). 120.83/55.28 thf(11239,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814])). 120.83/55.28 thf(2835,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_mult__strict__left__mono)). 120.83/55.28 thf(14818,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2835])). 120.83/55.28 thf(4518,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2892_even__difference)). 120.83/55.28 thf(20862,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) => (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4518])). 120.83/55.28 thf(2170,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ D)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))) <=> ((D = B) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_crossproduct__eq)). 120.83/55.28 thf(12421,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ D)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))) => ((D = B) | (A = C))) & (((D = B) | (A = C)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ D)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170])). 120.83/55.28 thf(4645,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.28 thf(21403,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4645])). 120.83/55.28 thf(60,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_dvd__triv__right)). 120.83/55.28 thf(5161,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 120.83/55.28 thf(2985,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2155_add__increasing)). 120.83/55.28 thf(15331,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2985])). 120.83/55.28 thf(4273,axiom,((! [A:$i,B:$i]: ((((zero_zero_int = B) & (zero_zero_int = A)) <=> (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4975_gcd__zero__int)). 120.83/55.28 thf(19919,plain,((! [A:$i,B:$i]: (((((zero_zero_int = B) & (zero_zero_int = A)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) & ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) => ((zero_zero_int = B) & (zero_zero_int = A)))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4273])). 120.83/55.28 thf(1327,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = A) <=> (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_add__0__iff)). 120.83/55.28 thf(9509,plain,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = A) => (B = zero_zero_real)) & ((B = zero_zero_real) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327])). 120.83/55.28 thf(620,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3701_real__of__nat__div3)). 120.83/55.28 thf(6996,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 120.83/55.28 thf(636,axiom,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) = (hAPP_real_real @ tan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3610_tan__periodic)). 120.83/55.28 thf(7068,plain,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) = (hAPP_real_real @ tan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])). 120.83/55.28 thf(2047,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2390_mod__mult__mult1)). 120.83/55.28 thf(11994,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047])). 120.83/55.28 thf(2502,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3632_sin__arccos)). 120.83/55.28 thf(13640,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2502])). 120.83/55.28 thf(1133,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3429_ln__less__cancel__iff)). 120.83/55.28 thf(8838,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133])). 120.83/55.28 thf(3404,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__special_I3_J)). 120.83/55.28 thf(16762,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3404])). 120.83/55.28 thf(3064,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3071_Suc__eq__plus1__left)). 120.83/55.28 thf(15611,plain,((! [A:$i]: ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3064])). 120.83/55.28 thf(209,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ exp_real @ one_one_real))) @ (hAPP_real_real @ ln @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_real_real @ ln @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3860_log__base__10__eq1)). 120.83/55.28 thf(5636,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ exp_real @ one_one_real))) @ (hAPP_real_real @ ln @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_real_real @ ln @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 120.83/55.28 thf(2209,axiom,((! [A:$i]: ((~ (! [B:$i]: (A != (hAPP_nat_nat @ suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3309_nat_Oexhaust)). 120.83/55.28 thf(12585,plain,((! [A:$i]: (~ (! [B:$i]: ~ (A = (hAPP_nat_nat @ suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209])). 120.83/55.28 thf(3239,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4410_powr__less__mono)). 120.83/55.28 thf(16236,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3239])). 120.83/55.28 thf(3330,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1300_power__0)). 120.83/55.28 thf(16520,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3330])). 120.83/55.28 thf(1766,axiom,((one_on1645066479umeral != zero_z126310315umeral)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_zero__neq__one)). 120.83/55.28 thf(11055,plain,((~ (one_on1645066479umeral = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766])). 120.83/55.28 thf(2073,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2050_add__strict__mono)). 120.83/55.28 thf(12077,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073])). 120.83/55.28 thf(3469,axiom,((! [A:$i,B:$i,C:$i]: (((zero_z126310315umeral != C) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)))) & ((C = zero_z126310315umeral) => (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2551_div__mult__mult1__if)). 120.83/55.28 thf(16965,plain,((! [A:$i,B:$i,C:$i]: (((~ (zero_z126310315umeral = C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)))) & ((C = zero_z126310315umeral) => (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3469])). 120.83/55.28 thf(4256,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2579_div__add)). 120.83/55.28 thf(19863,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4256])). 120.83/55.28 thf(1262,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3871_log__le__cancel__iff)). 120.83/55.28 thf(9278,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262])). 120.83/55.28 thf(1306,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1745_diff__diff__left)). 120.83/55.28 thf(9433,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306])). 120.83/55.28 thf(2690,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ H) @ zero_zero_int)) => ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ F)) = (xzgcda @ A @ B @ C @ H @ D @ E @ F @ G))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ H) @ zero_zero_int))) => ((xzgcda @ A @ B @ C @ H @ D @ E @ F @ G) = (xzgcda @ A @ B @ H @ (hAPP_int_int @ (div_mod_int @ C) @ H) @ E @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ H)) @ E)) @ G @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ H)) @ G)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4200_xzgcda_Osimps)). 120.83/55.28 thf(14301,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ H) @ zero_zero_int)) => ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ F)) = (xzgcda @ A @ B @ C @ H @ D @ E @ F @ G))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ H) @ zero_zero_int))) => ((xzgcda @ A @ B @ C @ H @ D @ E @ F @ G) = (xzgcda @ A @ B @ H @ (hAPP_int_int @ (div_mod_int @ C) @ H) @ E @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ H)) @ E)) @ G @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ H)) @ G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2690])). 120.83/55.28 thf(2582,axiom,((zero_z126310315umeral = (hAPP_i769753017umeral @ number1443263063umeral @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3141_zero__code__numeral__code)). 120.83/55.28 thf(13901,plain,((zero_z126310315umeral = (hAPP_i769753017umeral @ number1443263063umeral @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2582])). 120.83/55.28 thf(4632,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_add__Bit0__Bit1)). 120.83/55.28 thf(21343,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4632])). 120.83/55.28 thf(888,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.28 thf(7980,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[888])). 120.83/55.28 thf(4560,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3783_even__dvd)). 120.83/55.28 thf(21096,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4560])). 120.83/55.28 thf(3454,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_dvd__mult__right)). 120.83/55.28 thf(16915,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3454])). 120.83/55.28 thf(1677,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4692_normalize__eq)). 120.83/55.28 thf(10737,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677])). 120.83/55.28 thf(1901,axiom,((! [A:$i]: (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.28 thf(11549,plain,((! [A:$i]: (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901])). 120.83/55.28 thf(585,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3504_ln__one__minus__pos__lower__bound)). 120.83/55.28 thf(6877,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])). 120.83/55.28 thf(2773,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3817_Ln_Oaux1)). 120.83/55.28 thf(14591,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2773])). 120.83/55.28 thf(4276,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((zero_zero_int != D) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ B)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))) <= (zero_zero_int != C))) <= ((is_int @ D) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2638_dvd__div__div__eq__mult)). 120.83/55.28 thf(19932,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (zero_zero_int = D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ B)) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))) | (zero_zero_int = C))) | ~ ((is_int @ D) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4276])). 120.83/55.28 thf(1986,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3002_Nat__Transfer_Otransfer__int__nat__functions_I2_J)). 120.83/55.28 thf(11816,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986])). 120.83/55.28 thf(2344,axiom,((! [A:$i,B:$i]: ((((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_semiring__mult__number__of)). 120.83/55.28 thf(13056,plain,((! [A:$i,B:$i]: (((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344])). 120.83/55.28 thf(69,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4377_ln__powr__bound)). 120.83/55.28 thf(5192,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 120.83/55.28 thf(4744,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2946_of__nat__less__iff)). 120.83/55.28 thf(21781,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4744])). 120.83/55.28 thf(1564,axiom,((! [A:$i,B:$i,C:$i]: (((A = B) <=> ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1288_power__inject__exp)). 120.83/55.28 thf(10341,plain,((! [A:$i,B:$i,C:$i]: ((((A = B) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) & (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) => (A = B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564])). 120.83/55.28 thf(2460,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4447_lemma__floor2)). 120.83/55.28 thf(13488,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460])). 120.83/55.28 thf(4297,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__imp__0__less)). 120.83/55.28 thf(20011,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4297])). 120.83/55.28 thf(1319,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_comm__mult__strict__left__mono)). 120.83/55.28 thf(9481,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319])). 120.83/55.28 thf(3101,axiom,((! [A:$i]: ((A = zero_z126310315umeral) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ zero_z126310315umeral) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_dvd__0__left)). 120.83/55.28 thf(15735,plain,((! [A:$i]: ((A = zero_z126310315umeral) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ zero_z126310315umeral) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3101])). 120.83/55.28 thf(1377,axiom,((! [A:$i,B:$i]: (((zero_zero_real != A) | (zero_zero_real != B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sum__power2__gt__zero__iff)). 120.83/55.28 thf(9672,plain,((! [A:$i,B:$i]: (((~ (zero_zero_real = A) | ~ (zero_zero_real = B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (~ (zero_zero_real = A) | ~ (zero_zero_real = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377])). 120.83/55.28 thf(4671,axiom,(((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zero__power2)). 120.83/55.28 thf(21482,plain,(((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4671])). 120.83/55.28 thf(4836,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2524_Divides_Otransfer__nat__int__function__closures_I1_J)). 120.83/55.28 thf(22101,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4836])). 120.83/55.28 thf(2688,axiom,((! [A:$i]: ((((hAPP_rat_rat @ abs_abs_rat @ A) = A) <= (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))) & (((hAPP_rat_rat @ abs_abs_rat @ A) = (hAPP_rat_rat @ uminus_uminus_rat @ A)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4649_abs__rat__def)). 120.83/55.28 thf(14292,plain,((! [A:$i]: ((((hAPP_rat_rat @ abs_abs_rat @ A) = A) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat))) & (((hAPP_rat_rat @ abs_abs_rat @ A) = (hAPP_rat_rat @ uminus_uminus_rat @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2688])). 120.83/55.28 thf(3744,axiom,((! [A:$i]: ((! [B:$i,C:$i]: (((A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((B != zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) != one_one_int)))) <= ((is_int @ B) & (is_int @ C)))) => (zero_zero_rat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5025_Rat__cases__nonzero)). 120.83/55.28 thf(17924,plain,((! [A:$i]: ((! [B:$i,C:$i]: (((A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((~ (B = zero_zero_int)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int))))) | ~ ((is_int @ B) & (is_int @ C)))) => (zero_zero_rat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3744])). 120.83/55.28 thf(4595,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2433_mod__add__self2)). 120.83/55.28 thf(21224,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4595])). 120.83/55.28 thf(4302,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) = (hAPP_nat_nat @ suc @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3247_inv__is__inv__aux)). 120.83/55.28 thf(20031,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) = (hAPP_nat_nat @ suc @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4302])). 120.83/55.28 thf(2058,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2175_zero__le__double__add__iff__zero__le__single__add)). 120.83/55.28 thf(12026,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058])). 120.83/55.28 thf(3699,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) <=> ((A = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_zless__add1__eq)). 120.83/55.28 thf(17766,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) => ((A = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) & (((A = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3699])). 120.83/55.28 thf(3531,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1238_power__mono)). 120.83/55.28 thf(17158,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3531])). 120.83/55.28 thf(1871,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) <=> ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3530_negative__eq__positive)). 120.83/55.28 thf(11449,plain,((! [A:$i,B:$i]: ((((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => ((B = zero_zero_nat) & (A = zero_zero_nat))) & (((B = zero_zero_nat) & (A = zero_zero_nat)) => ((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871])). 120.83/55.28 thf(663,axiom,(((hAPP_int_complex @ number528085621omplex @ pls) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_semiring__numeral__0__eq__0)). 120.83/55.28 thf(7168,plain,(((hAPP_int_complex @ number528085621omplex @ pls) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])). 120.83/55.28 thf(3374,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3025_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.28 thf(16668,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3374])). 120.83/55.28 thf(4303,axiom,((! [A:$i]: ((is_int @ A) => ((? [B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ B))) = A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3557_negD)). 120.83/55.28 thf(20034,plain,((! [A:$i]: ((is_int @ A) => (? [B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ B))) = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4303])). 120.83/55.28 thf(4666,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (inv @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2761_WilsonRuss_Oinv__def)). 120.83/55.28 thf(21467,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (inv @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4666])). 120.83/55.28 thf(385,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ cos) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5161_isCont__cos)). 120.83/55.28 thf(6236,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ cos) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 120.83/55.28 thf(3477,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_mult__mono)). 120.83/55.28 thf(16994,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3477])). 120.83/55.28 thf(1562,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1255_zero__less__power)). 120.83/55.28 thf(10336,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562])). 120.83/55.28 thf(1931,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (A = (hAPP_real_real @ sqrt @ B))) <= (B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3340_real__sqrt__unique)). 120.83/55.28 thf(11645,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (A = (hAPP_real_real @ sqrt @ B))) | ~ (B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931])). 120.83/55.28 thf(2447,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ ln @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_real_real @ ln @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3697_ln__realpow)). 120.83/55.28 thf(13452,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ ln @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_real_real @ ln @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2447])). 120.83/55.28 thf(1588,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1275_power__increasing)). 120.83/55.28 thf(10427,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588])). 120.83/55.28 thf(1317,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_power2__eq__square)). 120.83/55.28 thf(9476,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317])). 120.83/55.28 thf(2627,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))) <= (zero_zero_real != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3941_DERIV__odd__real__root)). 120.83/55.28 thf(14089,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))) | (zero_zero_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2627])). 120.83/55.28 thf(2648,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4446_int__less__real__le)). 120.83/55.28 thf(14168,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ (hAPP_int_real @ real_int @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2648])). 120.83/55.28 thf(241,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_mult__right__mono__neg)). 120.83/55.28 thf(5740,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 120.83/55.28 thf(878,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_mult__pos__neg2)). 120.83/55.28 thf(7944,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])). 120.83/55.28 thf(1199,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3118_power__gt1)). 120.83/55.28 thf(9064,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199])). 120.83/55.28 thf(2308,axiom,((! [A:$i]: ((((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3266_one__mod__nat__number__of)). 120.83/55.28 thf(12929,plain,((! [A:$i]: ((((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308])). 120.83/55.28 thf(3396,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_mult__nonpos__nonneg)). 120.83/55.28 thf(16733,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3396])). 120.83/55.28 thf(3640,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1888_add__nonpos__neg)). 120.83/55.28 thf(17549,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3640])). 120.83/55.28 thf(592,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3830_divide__real__def)). 120.83/55.28 thf(6909,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])). 120.83/55.28 thf(3138,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3809_fact__dvd)). 120.83/55.28 thf(15863,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3138])). 120.83/55.28 thf(3191,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.28 thf(16039,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3191])). 120.83/55.28 thf(1266,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ sqrt) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5163_isCont__real__sqrt)). 120.83/55.28 thf(9292,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ sqrt) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266])). 120.83/55.28 thf(2597,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1907_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.28 thf(13965,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2597])). 120.83/55.28 thf(917,axiom,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_int_complex @ ring_11397209091omplex @ A)) = (hAPP_int_complex @ ring_11397209091omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4580_complex__cnj__of__int)). 120.83/55.28 thf(8086,plain,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_int_complex @ ring_11397209091omplex @ A)) = (hAPP_int_complex @ ring_11397209091omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[917])). 120.83/55.28 thf(2987,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2873_le__SucI)). 120.83/55.28 thf(15335,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2987])). 120.83/55.28 thf(394,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_mult__nonpos__nonneg)). 120.83/55.28 thf(6268,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 120.83/55.28 thf(1992,axiom,((! [A:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) <= (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3781_even__nat__div__two__times__two)). 120.83/55.28 thf(11834,plain,((! [A:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992])). 120.83/55.28 thf(164,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ ln @ B)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ A)) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4476_ln__powr__bound2)). 120.83/55.28 thf(5486,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ ln @ B)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ A)) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 120.83/55.28 thf(4467,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4979_gcd__assoc__int)). 120.83/55.28 thf(20662,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4467])). 120.83/55.28 thf(4188,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => ((hBOOL @ (hAPP_int_bool @ B @ D)) <=> (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))))))) => ((? [D:$i]: ! [E:$i]: ((is_int @ E) => (((hBOOL @ (hAPP_int_bool @ B @ E)) <=> (hBOOL @ (hAPP_int_bool @ A @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))))) => ((? [D:$i]: (hBOOL @ (hAPP_int_bool @ B @ D))) => (? [D:$i]: ((hBOOL @ (hAPP_int_bool @ A @ D)) & (is_int @ D)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4007_plusinfinity)). 120.83/55.28 thf(19575,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => (((hBOOL @ (hAPP_int_bool @ B @ D)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))))) & ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C)))) => (hBOOL @ (hAPP_int_bool @ B @ D)))))) => ((? [D:$i]: ! [E:$i]: ((is_int @ E) => ((((hBOOL @ (hAPP_int_bool @ B @ E)) => (hBOOL @ (hAPP_int_bool @ A @ E))) & ((hBOOL @ (hAPP_int_bool @ A @ E)) => (hBOOL @ (hAPP_int_bool @ B @ E)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))))) => ((? [D:$i]: (hBOOL @ (hAPP_int_bool @ B @ D))) => (? [D:$i]: ((hBOOL @ (hAPP_int_bool @ A @ D)) & (is_int @ D)))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4188])). 120.83/55.28 thf(2094,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1611_plus__nat_Oadd__0)). 120.83/55.28 thf(12141,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094])). 120.83/55.28 thf(4793,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2611_neg__mod__conj)). 120.83/55.28 thf(21948,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4793])). 120.83/55.28 thf(1477,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3345_real__sqrt__sum__squares__ge2)). 120.83/55.28 thf(10022,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477])). 120.83/55.28 thf(2356,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2695_mod__mult__distrib)). 120.83/55.28 thf(13098,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356])). 120.83/55.28 thf(1633,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ one_on1645066479umeral))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1405_power__decreasing)). 120.83/55.28 thf(10599,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ one_on1645066479umeral))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633])). 120.83/55.28 thf(640,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (! [D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ E))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2815_less__mono__imp__le__mono)). 120.83/55.28 thf(7079,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (! [D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ E))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])). 120.83/55.28 thf(3681,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ C) => ((hAPP_int_nat @ nat @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ C) @ A) @ B)))) & ((~ (hBOOL @ C)) => ((hAPP_int_nat @ nat @ B) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ C) @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2683_nat__if__cong)). 120.83/55.28 thf(17710,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ C) => ((hAPP_int_nat @ nat @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ C) @ A) @ B)))) & ((~ (hBOOL @ C)) => ((hAPP_int_nat @ nat @ B) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ C) @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3681])). 120.83/55.28 thf(2117,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_on1684967323de_int)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ one_on1684967323de_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3160_power__Suc__less__one)). 120.83/55.28 thf(12225,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_on1684967323de_int)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ one_on1684967323de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117])). 120.83/55.28 thf(3392,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.28 thf(16720,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3392])). 120.83/55.28 thf(2901,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ D))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_mult__mono)). 120.83/55.28 thf(15032,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ D)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2901])). 120.83/55.28 thf(1050,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.28 thf(8539,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050])). 120.83/55.28 thf(4866,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_zless__imp__add1__zle)). 120.83/55.28 thf(22197,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4866])). 120.83/55.28 thf(4001,axiom,((! [A:$i]: (((zero_zero_int = A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ zero_zero_int) @ A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_dvd__0__left)). 120.83/55.28 thf(18834,plain,((! [A:$i]: ((zero_zero_int = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4001])). 120.83/55.28 thf(756,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.28 thf(7499,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])). 120.83/55.28 thf(431,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1518_dvd__diff)). 120.83/55.28 thf(6381,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 120.83/55.28 thf(3503,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ one_on1645066479umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A))) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3155_realpow__Suc__le__self)). 120.83/55.28 thf(17081,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ one_on1645066479umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A))) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3503])). 120.83/55.28 thf(1126,axiom,(((hAPP_n522471361de_int @ semiri1424489471de_int @ zero_zero_nat) = zero_z891286103de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2923_of__nat__0)). 120.83/55.28 thf(8816,plain,(((hAPP_n522471361de_int @ semiri1424489471de_int @ zero_zero_nat) = zero_z891286103de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126])). 120.83/55.28 thf(3854,axiom,(((hAPP_int_int @ fact_fact_int @ zero_zero_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4276_fact__0__int)). 120.83/55.28 thf(18321,plain,(((hAPP_int_int @ fact_fact_int @ zero_zero_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3854])). 120.83/55.28 thf(1617,axiom,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ B @ C)) & ! [D:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ B @ D))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C))))) <= (hBOOL @ (hAPP_nat_bool @ B @ A))) <= (~ (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2245_ex__least__nat__le)). 120.83/55.28 thf(10545,plain,((! [A:$i,B:$i]: (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ B @ C)) & ! [D:$i]: (~ (hBOOL @ (hAPP_nat_bool @ B @ D)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ B @ A)) | (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617])). 120.83/55.28 thf(243,axiom,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (ratreal @ A)) = (ratreal @ (hAPP_rat_rat @ uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4703_real__uminus__code)). 120.83/55.28 thf(5745,plain,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (ratreal @ A)) = (ratreal @ (hAPP_rat_rat @ uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 120.83/55.28 thf(3443,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1851_nat__le__add__iff2)). 120.83/55.28 thf(16877,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3443])). 120.83/55.28 thf(1789,axiom,((! [A:$i,B:$i]: ((! [C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) <=> (C = one_one_nat))) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4350_coprime__nat)). 120.83/55.28 thf(11146,plain,((! [A:$i,B:$i]: (((! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) => (C = one_one_nat)) & ((C = one_one_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat) => (! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) => (C = one_one_nat)) & ((C = one_one_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789])). 120.83/55.28 thf(4531,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__nat__number__of)). 120.83/55.28 thf(20926,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ B))))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4531])). 120.83/55.28 thf(4136,axiom,(((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2750_transfer__nat__int__numerals_I3_J)). 120.83/55.28 thf(19410,plain,(((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4136])). 120.83/55.28 thf(4228,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ A)) = (hAPP_int_int @ fact_fact_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5084_fact__altdef__int)). 120.83/55.28 thf(19732,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ A)) = (hAPP_int_int @ fact_fact_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4228])). 120.83/55.28 thf(1213,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_dvd__mult2)). 120.83/55.28 thf(9096,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213])). 120.83/55.28 thf(492,axiom,((! [A:$i]: ? [B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ C)) @ (expi @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4052_complex__expi__Ex)). 120.83/55.28 thf(6583,plain,((! [A:$i]: ? [B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ C)) @ (expi @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 120.83/55.28 thf(3099,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3908_real__root__mult__exp)). 120.83/55.28 thf(15730,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3099])). 120.83/55.28 thf(815,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3621_tan__less__zero)). 120.83/55.28 thf(7729,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ A)) @ zero_zero_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 120.83/55.28 thf(4024,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_mult__numeral__1__right)). 120.83/55.28 thf(18925,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4024])). 120.83/55.28 thf(4605,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3274_neg__number__of__Bit0)). 120.83/55.28 thf(21253,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))))) & ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A)))) => (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4605])). 120.83/55.28 thf(3972,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => (((! [D:$i]: ((is_int @ D) => ((! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => ((D != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))))) <= (is_int @ E))) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) <= (A = D))))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5095_bset_I3_J)). 120.83/55.28 thf(18728,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => (! [D:$i]: ((is_int @ D) => ((! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))))) | ~ (is_int @ E))) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) | ~ (A = D)))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3972])). 120.83/55.28 thf(2482,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) <=> (? [C:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2706_mod__eq__0__iff)). 120.83/55.28 thf(13552,plain,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) => (? [C:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))) & ((? [C:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482])). 120.83/55.28 thf(4169,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1342_mult__less__imp__less__right)). 120.83/55.28 thf(19518,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4169])). 120.83/55.28 thf(1913,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i345030060t_bool @ (hAPP_f791698359t_bool @ (hAPP_f847817363t_bool @ cOMBB_562416518ol_int @ A) @ B) @ C) = (hAPP_f428220345t_bool @ A @ (hAPP_i345030060t_bool @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__fun_Itc__Int__Oint_Mtc__HOL__026)). 120.83/55.28 thf(11588,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i345030060t_bool @ (hAPP_f791698359t_bool @ (hAPP_f847817363t_bool @ cOMBB_562416518ol_int @ A) @ B) @ C) = (hAPP_f428220345t_bool @ A @ (hAPP_i345030060t_bool @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913])). 120.83/55.28 thf(4325,axiom,((! [A:$i,B:$i]: ((! [C:$i]: ((is_int @ C) => ((C = one_one_int) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5019_coprime__int)). 120.83/55.28 thf(20107,plain,((! [A:$i,B:$i]: (((! [C:$i]: ((is_int @ C) => (((C = one_one_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => (C = one_one_int))))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = one_one_int)) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = one_one_int) => (! [C:$i]: ((is_int @ C) => (((C = one_one_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => (C = one_one_int))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4325])). 120.83/55.28 thf(33,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((C = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4218_div__eq)). 120.83/55.28 thf(5056,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((C = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 120.83/55.28 thf(1141,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.28 thf(8866,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141])). 120.83/55.28 thf(2430,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ zero_zero_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_mult__pos__neg2)). 120.83/55.28 thf(13378,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ zero_zero_nat))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2430])). 120.83/55.28 thf(2717,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_power__strict__mono)). 120.83/55.28 thf(14396,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2717])). 120.83/55.28 thf(2761,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1890_add__nonpos__neg)). 120.83/55.28 thf(14553,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2761])). 120.83/55.28 thf(3141,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_zero__le__square)). 120.83/55.28 thf(15870,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3141])). 120.83/55.28 thf(1755,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3308_real__sqrt__sum__squares__mult__ge__zero)). 120.83/55.28 thf(11024,plain,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755])). 120.83/55.28 thf(3264,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_power__strict__mono)). 120.83/55.28 thf(16319,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3264])). 120.83/55.28 thf(2746,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1456_power__strict__increasing__iff)). 120.83/55.28 thf(14488,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2746])). 120.83/55.28 thf(4033,axiom,((! [A:$i,B:$i]: ? [C:$i]: (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))) & (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2263_minf_I9_J)). 120.83/55.28 thf(18955,plain,((? [A:$i]: (is_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4033])). 120.83/55.28 thf(3900,axiom,((! [A:$i]: (min != (hAPP_int_int @ bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_rel__simps_I45_J)). 120.83/55.28 thf(18496,plain,((! [A:$i]: ~ (min = (hAPP_int_int @ bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3900])). 120.83/55.28 thf(3250,axiom,((! [A:$i]: ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3813_fact__plus__one__nat)). 120.83/55.28 thf(16268,plain,((! [A:$i]: ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3250])). 120.83/55.28 thf(4535,axiom,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Numeral1__eq1__nat)). 120.83/55.28 thf(20941,plain,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4535])). 120.83/55.28 thf(1386,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2852_nat_Osimps_I2_J)). 120.83/55.29 thf(9708,plain,((! [A:$i]: ~ ((hAPP_nat_nat @ suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386])). 120.83/55.29 thf(3319,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim1246769320r_real @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4468_less__floor__eq)). 120.83/55.29 thf(16488,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim1246769320r_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim1246769320r_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3319])). 120.83/55.29 thf(4937,axiom,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2322_zOddI)). 120.83/55.29 thf(22429,plain,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4937])). 120.83/55.29 thf(2151,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_mult__strict__right__mono__neg)). 120.83/55.29 thf(12356,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151])). 120.83/55.29 thf(4513,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3555_neg__odd__power)). 120.83/55.29 thf(20845,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4513])). 120.83/55.29 thf(4693,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((A = B) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2076_right__minus__eq)). 120.83/55.29 thf(21560,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((A = B) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = zero_zero_int)) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = zero_zero_int) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4693])). 120.83/55.29 thf(2053,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_rat)) <=> ((zero_zero_rat = B) & (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_sum__power2__le__zero__iff)). 120.83/55.29 thf(12009,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_rat)) => ((zero_zero_rat = B) & (A = zero_zero_rat))) & (((zero_zero_rat = B) & (A = zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053])). 120.83/55.29 thf(3332,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1884_add__neg__nonpos)). 120.83/55.29 thf(16530,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3332])). 120.83/55.29 thf(2163,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1712_dvd_Oantisym)). 120.83/55.29 thf(12388,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163])). 120.83/55.29 thf(3691,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3197_add__2__eq__Suc)). 120.83/55.29 thf(17739,plain,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3691])). 120.83/55.29 thf(943,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((A = C) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1480_power__eq__imp__eq__base)). 120.83/55.29 thf(8165,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((A = C) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])). 120.83/55.29 thf(2265,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))) <= (A != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3131_one__less__k)). 120.83/55.29 thf(12770,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) | (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265])). 120.83/55.29 thf(1293,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_dvd__add)). 120.83/55.29 thf(9396,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293])). 120.83/55.29 thf(3231,axiom,((! [A:$i,B:$i]: ((hBOOL @ (vanishes @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ B @ D))) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5151_vanishesD)). 120.83/55.29 thf(16211,plain,((! [A:$i,B:$i]: ((hBOOL @ (vanishes @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ B @ D))) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3231])). 120.83/55.29 thf(4461,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_le__special_I3_J)). 120.83/55.29 thf(20643,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4461])). 120.83/55.29 thf(4402,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ A @ C)))) <=> (? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ C)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ B))) & (is_int @ C)))) <= (! [C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))) <=> (hBOOL @ (hAPP_int_bool @ A @ C))) <= ((is_int @ D) & (is_int @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5101_periodic__finite__ex)). 120.83/55.29 thf(20409,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((((? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ A @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ C)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ B))) & (is_int @ C)))) & ((? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ C)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ B))) & (is_int @ C))) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ A @ C)))))) | ~ (! [C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))) => (hBOOL @ (hAPP_int_bool @ A @ C))) & ((hBOOL @ (hAPP_int_bool @ A @ C)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))))) | ~ ((is_int @ D) & (is_int @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4402])). 120.83/55.29 thf(4590,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__eq__number__of__int__code)). 120.83/55.29 thf(21203,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4590])). 120.83/55.29 thf(4129,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ (comple219730294t_bool @ (setS @ A @ B)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4809_Union__SetS__setprod__prop1)). 120.83/55.29 thf(19387,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ (comple219730294t_bool @ (setS @ A @ B)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4129])). 120.83/55.29 thf(2610,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_f429935748t_bool @ (hAPP_i872162435t_bool @ A @ C) @ B) = (hAPP_i1948725293t_bool @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_013)). 120.83/55.29 thf(14023,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_f429935748t_bool @ (hAPP_i872162435t_bool @ A @ C) @ B) = (hAPP_i1948725293t_bool @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2610])). 120.83/55.29 thf(1086,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2489_odd__mult__odd__prop)). 120.83/55.29 thf(8699,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086])). 120.83/55.29 thf(4109,axiom,((! [A:$i,B:$i]: ((((hAPP_P1175774780nt_int @ product_fst_int_int @ (negDivAlg @ B @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4225_div__neg__pos)). 120.83/55.29 thf(19318,plain,((! [A:$i,B:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (negDivAlg @ B @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4109])). 120.83/55.29 thf(2785,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_not__sum__power2__lt__zero)). 120.83/55.29 thf(14644,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2785])). 120.83/55.29 thf(1112,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_mult__left__mono__neg)). 120.83/55.29 thf(8779,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112])). 120.83/55.29 thf(4678,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_less__0__number__of)). 120.83/55.29 thf(21503,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4678])). 120.83/55.29 thf(4081,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.29 thf(19209,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4081])). 120.83/55.29 thf(2656,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.29 thf(14188,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2656])). 120.83/55.29 thf(2270,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2074_add__less__cancel__right)). 120.83/55.29 thf(12785,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270])). 120.83/55.29 thf(94,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4118_complex__Re__le__cmod)). 120.83/55.29 thf(5269,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 120.83/55.29 thf(4600,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ (hAPP_int_int @ uminus_uminus_int @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3519_zcong__zminus)). 120.83/55.29 thf(21239,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ (hAPP_int_int @ uminus_uminus_int @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ (hAPP_int_int @ uminus_uminus_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4600])). 120.83/55.29 thf(4735,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_less__special_I4_J)). 120.83/55.29 thf(21752,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4735])). 120.83/55.29 thf(2852,axiom,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (cis @ A)) @ (cis @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4148_cis__mult)). 120.83/55.29 thf(14871,plain,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (cis @ A)) @ (cis @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2852])). 120.83/55.29 thf(1991,axiom,((! [A:$i,B:$i]: (((B != zero_zero_int) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2545_div__mult__self2__is__id)). 120.83/55.29 thf(11831,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_int)) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991])). 120.83/55.29 thf(2326,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2363_zmult__div__cancel)). 120.83/55.29 thf(13003,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326])). 120.83/55.29 thf(402,axiom,((! [A:$i]: ((archim1246769320r_real @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4020_floor__real__of__nat)). 120.83/55.29 thf(6291,plain,((! [A:$i]: ((archim1246769320r_real @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 120.83/55.29 thf(2588,axiom,((! [A:$i]: ((one_one_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2755_mod2__gr__0)). 120.83/55.29 thf(13923,plain,((! [A:$i]: (((one_one_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (one_one_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2588])). 120.83/55.29 thf(2673,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2036_add__less__imp__less__left)). 120.83/55.29 thf(14245,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2673])). 120.83/55.29 thf(1292,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1556_dvd__imp__le)). 120.83/55.29 thf(9394,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292])). 120.83/55.29 thf(2420,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2577_div__add)). 120.83/55.29 thf(13346,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2420])). 120.83/55.29 thf(961,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) => ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) <=> ((B = D) & (A = C))) <= (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4355_coprime__crossproduct__nat)). 120.83/55.29 thf(8224,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) => (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) => ((B = D) & (A = C))) & (((B = D) & (A = C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)))) | ~ (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[961])). 120.83/55.29 thf(3770,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3149_zero__less__int__conv)). 120.83/55.29 thf(18015,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3770])). 120.83/55.29 thf(2069,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2212_less__iff__diff__less__0)). 120.83/55.29 thf(12062,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069])). 120.83/55.29 thf(2924,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2515_dvd__imp__mod__0)). 120.83/55.29 thf(15119,plain,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2924])). 120.83/55.29 thf(2235,axiom,((! [A:$i,B:$i]: (((zero_zero_real = A) & (zero_zero_nat != B)) <=> (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1291_power__eq__0__iff)). 120.83/55.29 thf(12661,plain,((! [A:$i,B:$i]: ((((zero_zero_real = A) & ~ (zero_zero_nat = B)) => (zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) => ((zero_zero_real = A) & ~ (zero_zero_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235])). 120.83/55.29 thf(4611,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1638_zspecial__product)). 120.83/55.29 thf(21274,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4611])). 120.83/55.29 thf(4317,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_neg @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3270_neg__def)). 120.83/55.29 thf(20078,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ nat_neg @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4317])). 120.83/55.29 thf(1819,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_less__special_I1_J)). 120.83/55.29 thf(11250,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819])). 120.83/55.29 thf(1604,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) <= (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4362_coprime__exp__nat)). 120.83/55.29 thf(10501,plain,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) | ~ (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604])). 120.83/55.29 thf(3062,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_power__one)). 120.83/55.29 thf(15605,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3062])). 120.83/55.29 thf(3969,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ (hAPP_i1948725293t_bool @ sRStar @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2763_StandardRes__SRStar__prop4)). 120.83/55.29 thf(18717,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ (hAPP_i1948725293t_bool @ sRStar @ B))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3969])). 120.83/55.29 thf(706,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_power__strict__mono)). 120.83/55.29 thf(7311,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])). 120.83/55.29 thf(3541,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3185_div__Suc)). 120.83/55.29 thf(17197,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3541])). 120.83/55.29 thf(3636,axiom,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_zero__is__num__zero)). 120.83/55.29 thf(17534,plain,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3636])). 120.83/55.29 thf(4764,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ E)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_zcong__zmult__prop2)). 120.83/55.29 thf(21856,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ E))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4764])). 120.83/55.29 thf(1542,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_mult__pos__pos)). 120.83/55.29 thf(10248,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542])). 120.83/55.29 thf(4347,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4652_normalize__negative)). 120.83/55.29 thf(20209,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4347])). 120.83/55.29 thf(2942,axiom,((! [A:$i,B:$i,C:$i]: ((zero_z126310315umeral != C) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2622_div__mult__self1)). 120.83/55.29 thf(15178,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_z126310315umeral = C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2942])). 120.83/55.29 thf(2918,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2964_of__nat__mult)). 120.83/55.29 thf(15104,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2918])). 120.83/55.29 thf(24,axiom,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ re @ B)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4136_complex__mult__def)). 120.83/55.29 thf(5024,plain,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ re @ B)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 120.83/55.29 thf(1627,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3427_ln__less__self)). 120.83/55.29 thf(10584,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627])). 120.83/55.29 thf(122,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2356_div__mod__equality)). 120.83/55.29 thf(5352,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 120.83/55.29 thf(2664,axiom,((! [A:$i,B:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B) = A) <=> (B = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_add__0__iff)). 120.83/55.29 thf(14213,plain,((! [A:$i,B:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B) = A) => (B = zero_zero_complex)) & ((B = zero_zero_complex) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2664])). 120.83/55.29 thf(118,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ (hAPP_f248847589l_real @ cOMBC_real_nat_real @ power_power_real) @ A) @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4781_DERIV__pow)). 120.83/55.29 thf(5342,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ (hAPP_f248847589l_real @ cOMBC_real_nat_real @ power_power_real) @ A) @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 120.83/55.29 thf(4556,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ B) @ A)) @ A)) @ one_one_int) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2241_MultInv__prop2a)). 120.83/55.29 thf(21079,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ B) @ A)) @ A)) @ one_one_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4556])). 120.83/55.29 thf(4469,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.29 thf(20679,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4469])). 120.83/55.29 thf(729,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B) = A) <= (zero_zero_nat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2542_div__mult__self1__is__id)). 120.83/55.29 thf(7390,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B) = A) | (zero_zero_nat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])). 120.83/55.29 thf(3523,axiom,((! [A:$i]: ((is_int @ A) => (A = (quickcheck_int_of @ (hAPP_i1732201573de_int @ quickcheck_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4557_int__of__of__int)). 120.83/55.29 thf(17132,plain,((! [A:$i]: ((is_int @ A) => (A = (quickcheck_int_of @ (hAPP_i1732201573de_int @ quickcheck_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3523])). 120.83/55.29 thf(4286,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.29 thf(19968,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4286])). 120.83/55.29 thf(2783,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1350_mult__right__less__imp__less)). 120.83/55.29 thf(14630,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2783])). 120.83/55.29 thf(1456,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3767_real__of__nat__fact__ge__zero)). 120.83/55.29 thf(9960,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456])). 120.83/55.29 thf(3889,axiom,((! [A:$i,B:$i]: ((((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) <=> ((one_one_int = A) & (one_one_int = B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_pos__zmult__eq__1__iff)). 120.83/55.29 thf(18437,plain,((! [A:$i,B:$i]: ((((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) => ((one_one_int = A) & (one_one_int = B))) & (((one_one_int = A) & (one_one_int = B)) => (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3889])). 120.83/55.29 thf(4572,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.29 thf(21143,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4572])). 120.83/55.29 thf(3915,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B)) @ (rsetR @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4596_Bnor__in__RsetR)). 120.83/55.29 thf(18539,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B)) @ (rsetR @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3915])). 120.83/55.29 thf(4468,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((A != zero_zero_int) | (B != zero_zero_int)) => (? [C:$i,D:$i]: (((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)) @ D) = A) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)) @ C)) & (is_int @ D) & (is_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4539_make__zrelprime)). 120.83/55.29 thf(20665,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((~ (A = zero_zero_int) | ~ (B = zero_zero_int)) => (? [C:$i,D:$i]: (((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)) @ D) = A) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)) @ C)) & (is_int @ D) & (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4468])). 120.83/55.29 thf(2379,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3791_lemma__odd__mod__4__div__2)). 120.83/55.29 thf(13191,plain,((! [A:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2379])). 120.83/55.29 thf(3977,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zadd__left__mono)). 120.83/55.29 thf(18754,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3977])). 120.83/55.29 thf(1863,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (nat_tsub @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2820_Nat__Transfer_Otransfer__int__nat__functions_I3_J)). 120.83/55.29 thf(11426,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (nat_tsub @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863])). 120.83/55.29 thf(250,axiom,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = (hAPP_complex_complex @ invers1449016382omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4110_complex__inverse__def)). 120.83/55.29 thf(5765,plain,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = (hAPP_complex_complex @ invers1449016382omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 120.83/55.29 thf(1641,axiom,((! [A:$i,B:$i]: (((? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4207_bezout__prime)). 120.83/55.29 thf(10619,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641])). 120.83/55.29 thf(3488,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2019_add__right__mono)). 120.83/55.29 thf(17036,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3488])). 120.83/55.29 thf(1196,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1727_dvd_Oless__trans)). 120.83/55.29 thf(9056,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))) | ~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196])). 120.83/55.29 thf(1729,axiom,((! [A:$i,B:$i]: ((A = B) <= ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2827_Suc__inject)). 120.83/55.29 thf(10903,plain,((! [A:$i,B:$i]: ((A = B) | ~ ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729])). 120.83/55.29 thf(2411,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3020_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.29 thf(13313,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2411])). 120.83/55.29 thf(4022,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2413_zmod__simps_I2_J)). 120.83/55.29 thf(18920,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4022])). 120.83/55.29 thf(2512,axiom,(((hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2976_transfer__int__nat__numerals_I1_J)). 120.83/55.29 thf(13664,plain,(((hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2512])). 120.83/55.29 thf(788,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3424_pi__gt__zero)). 120.83/55.29 thf(7620,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])). 120.83/55.29 thf(3338,axiom,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1391_zero__less__two)). 120.83/55.29 thf(16552,plain,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3338])). 120.83/55.29 thf(192,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4131_complex__Re__mult)). 120.83/55.29 thf(5585,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 120.83/55.29 thf(3158,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_power2__less__imp__less)). 120.83/55.29 thf(15922,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3158])). 120.83/55.29 thf(4781,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_zero__less__mult__pos)). 120.83/55.29 thf(21916,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4781])). 120.83/55.29 thf(3593,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_power__even__eq)). 120.83/55.29 thf(17381,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3593])). 120.83/55.29 thf(2744,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_mult__less__cancel__left__pos)). 120.83/55.29 thf(14474,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2744])). 120.83/55.29 thf(1039,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ D)) @ (hAPP_nat_real @ C @ (hAPP_nat_nat @ suc @ D))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ A)) @ (hAPP_nat_real @ C @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3374_lemma__f__mono__add)). 120.83/55.29 thf(8500,plain,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ D)) @ (hAPP_nat_real @ C @ (hAPP_nat_nat @ suc @ D))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ A)) @ (hAPP_nat_real @ C @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039])). 120.83/55.29 thf(2181,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_mult__strict__right__mono)). 120.83/55.29 thf(12475,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181])). 120.83/55.29 thf(4451,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P62333565t_bool @ B @ A)) <=> (hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_mem__def)). 120.83/55.29 thf(20594,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_P62333565t_bool @ B @ A)) => (hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ A) @ B))) & ((hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ A) @ B)) => (hBOOL @ (hAPP_P62333565t_bool @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4451])). 120.83/55.29 thf(2042,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4440_real__of__int__ge__zero__cancel__iff)). 120.83/55.29 thf(11976,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042])). 120.83/55.29 thf(4146,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.29 thf(19443,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4146])). 120.83/55.29 thf(4915,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.29 thf(22353,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4915])). 120.83/55.29 thf(809,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_zero__less__power__nat__eq)). 120.83/55.29 thf(7701,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])). 120.83/55.29 thf(4154,axiom,((! [A:$i,B:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2131_add__diff__cancel)). 120.83/55.29 thf(19473,plain,((! [A:$i,B:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4154])). 120.83/55.29 thf(4066,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2738_transfer__nat__int__relations_I2_J)). 120.83/55.29 thf(19145,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4066])). 120.83/55.29 thf(328,axiom,((zero_zero_complex != ii)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3975_complex__i__not__zero)). 120.83/55.29 thf(6039,plain,((~ (zero_zero_complex = ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 120.83/55.29 thf(2551,axiom,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1512_number__of__diff)). 120.83/55.29 thf(13803,plain,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551])). 120.83/55.29 thf(478,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2370_mod__by__0)). 120.83/55.29 thf(6538,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 120.83/55.29 thf(5,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ uminus473333897omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3528_complex__diff__def)). 120.83/55.29 thf(4956,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ uminus473333897omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 120.83/55.29 thf(3175,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3087_exp__mono__lt)). 120.83/55.29 thf(15990,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3175])). 120.83/55.29 thf(2838,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)))) <= (C != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2277_pow__divides__eq__nat)). 120.83/55.29 thf(14825,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) | (C = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2838])). 120.83/55.29 thf(4619,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((zero_zero_int != C) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2620_div__mult__self1)). 120.83/55.29 thf(21307,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((~ (zero_zero_int = C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4619])). 120.83/55.29 thf(1981,axiom,((! [A:$i]: (zero_zero_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4642_Frct__code__post_I2_J)). 120.83/55.29 thf(11798,plain,((! [A:$i]: (zero_zero_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981])). 120.83/55.29 thf(1499,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ sgn_sgn_real @ A) = (hAPP_int_real @ number267125858f_real @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3574_real__sgn__neg)). 120.83/55.29 thf(10089,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ sgn_sgn_real @ A) = (hAPP_int_real @ number267125858f_real @ min))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499])). 120.83/55.29 thf(1182,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2150_add__increasing2)). 120.83/55.29 thf(8996,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182])). 120.83/55.29 thf(280,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_complex_real @ norm_norm_complex @ (rcis @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4259_complex__mod__rcis)). 120.83/55.29 thf(5883,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_complex_real @ norm_norm_complex @ (rcis @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 120.83/55.29 thf(4561,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_semiring__add__number__of)). 120.83/55.29 thf(21101,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4561])). 120.83/55.29 thf(1350,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3942_DERIV__real__root)). 120.83/55.29 thf(9597,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ B) @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350])). 120.83/55.29 thf(2284,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3343_real__sqrt__pow2__gt__zero)). 120.83/55.29 thf(12832,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284])). 120.83/55.29 thf(1745,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4158_termination__basic__simps_I2_J)). 120.83/55.29 thf(10997,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745])). 120.83/55.29 thf(918,axiom,(((hAPP_int_real @ real_int @ one_one_int) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4395_real__of__one)). 120.83/55.29 thf(8089,plain,(((hAPP_int_real @ real_int @ one_one_int) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])). 120.83/55.29 thf(2960,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2044_add__less__imp__less__right)). 120.83/55.29 thf(15231,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2960])). 120.83/55.29 thf(481,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3695_sin__expansion__lemma)). 120.83/55.29 thf(6547,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 120.83/55.29 thf(1746,axiom,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2845_int__Suc0__eq__1)). 120.83/55.29 thf(10999,plain,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746])). 120.83/55.29 thf(396,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ A))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_dvd__trans)). 120.83/55.29 thf(6274,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ A)) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 120.83/55.29 thf(3975,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4982_gcd__greatest__int)). 120.83/55.29 thf(18750,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3975])). 120.83/55.29 thf(3717,axiom,((! [A:$i]: ((? [B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3785_even__mult__two__ex)). 120.83/55.29 thf(17824,plain,((! [A:$i]: (((? [B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (? [B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3717])). 120.83/55.29 thf(2678,axiom,((! [A:$i,B:$i,C:$i]: ((C = B) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1921_add__imp__eq)). 120.83/55.29 thf(14260,plain,((! [A:$i,B:$i,C:$i]: ((C = B) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2678])). 120.83/55.29 thf(2558,axiom,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_power__one)). 120.83/55.29 thf(13821,plain,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2558])). 120.83/55.29 thf(4216,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))) <= (hBOOL @ (hAPP_int_bool @ B @ D))))) => ((! [D:$i]: ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (hBOOL @ (hAPP_int_bool @ B @ D)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1690_decr__mult__lemma)). 120.83/55.29 thf(19693,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D))))) => (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4216])). 120.83/55.29 thf(1338,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_mult__mono_H)). 120.83/55.29 thf(9561,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338])). 120.83/55.29 thf(3727,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_mult__mono_H)). 120.83/55.29 thf(17857,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3727])). 120.83/55.29 thf(1487,axiom,(((hAPP_int_rat @ number_number_of_rat @ pls) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_number__of__Pls)). 120.83/55.29 thf(10053,plain,(((hAPP_int_rat @ number_number_of_rat @ pls) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487])). 120.83/55.29 thf(4449,axiom,(((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__power2)). 120.83/55.29 thf(20583,plain,(((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4449])). 120.83/55.29 thf(1468,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ D) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2557_div__mult__div__if__dvd)). 120.83/55.29 thf(9988,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ D) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468])). 120.83/55.29 thf(2021,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1487_one__less__power)). 120.83/55.29 thf(11913,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021])). 120.83/55.29 thf(248,axiom,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ A) != ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3977_complex__i__not__number__of)). 120.83/55.29 thf(5759,plain,((! [A:$i]: ~ ((hAPP_int_complex @ number528085621omplex @ A) = ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 120.83/55.29 thf(2335,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.29 thf(13030,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335])). 120.83/55.29 thf(1933,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ fact @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4567_fact__le)). 120.83/55.29 thf(11652,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ fact @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933])). 120.83/55.29 thf(2703,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3404_less__one__imp__sqr__less__one)). 120.83/55.29 thf(14351,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2703])). 120.83/55.29 thf(4870,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f351634443t_bool @ (hAPP_f1576199059t_bool @ cOMBB_95956018ol_int @ A) @ B) @ C) = (hAPP_f429384717t_bool @ A @ (hAPP_i627165055t_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__RealDef__Oreal_J_000tc__fun_)). 120.83/55.29 thf(22207,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f351634443t_bool @ (hAPP_f1576199059t_bool @ cOMBB_95956018ol_int @ A) @ B) @ C) = (hAPP_f429384717t_bool @ A @ (hAPP_i627165055t_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4870])). 120.83/55.29 thf(840,axiom,((one_on1684967323de_int = (hAPP_i1732201573de_int @ quickcheck_of_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4568_one__code__int__def)). 120.83/55.29 thf(7822,plain,((one_on1684967323de_int = (hAPP_i1732201573de_int @ quickcheck_of_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])). 120.83/55.29 thf(804,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1351_mult__right__less__imp__less)). 120.83/55.29 thf(7683,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 120.83/55.29 thf(4372,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3010_power__Suc2)). 120.83/55.29 thf(20281,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4372])). 120.83/55.29 thf(4429,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_rel__simps_I30_J)). 120.83/55.29 thf(20511,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ min))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4429])). 120.83/55.29 thf(4754,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3269_not__neg__int)). 120.83/55.29 thf(21825,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4754])). 120.83/55.29 thf(700,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1235_power__mono)). 120.83/55.29 thf(7294,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])). 120.83/55.29 thf(3185,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_power__commutes)). 120.83/55.29 thf(16022,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3185])). 120.83/55.29 thf(3358,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3015_power__Suc)). 120.83/55.29 thf(16609,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3358])). 120.83/55.29 thf(1122,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ prime @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) <= (B != A))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4166_distinct__prime__coprime)). 120.83/55.29 thf(8806,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ prime @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) | (B = A))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122])). 120.83/55.29 thf(3760,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3510_negative__zle)). 120.83/55.29 thf(17983,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3760])). 120.83/55.29 thf(2806,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.29 thf(14722,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2806])). 120.83/55.29 thf(1073,axiom,((! [A:$i,B:$i]: (((A = zero_zero_real) & (zero_zero_real = B)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1786_real__two__squares__add__zero__iff)). 120.83/55.29 thf(8647,plain,((! [A:$i,B:$i]: ((((A = zero_zero_real) & (zero_zero_real = B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real) => ((A = zero_zero_real) & (zero_zero_real = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073])). 120.83/55.29 thf(536,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ fTrue) @ A) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__RealDef__Oreal_T)). 120.83/55.29 thf(6723,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ fTrue) @ A) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])). 120.83/55.29 thf(3655,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4228_div__pos__neg)). 120.83/55.29 thf(17598,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3655])). 120.83/55.29 thf(2496,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3647_not__real__of__nat__less__zero)). 120.83/55.29 thf(13619,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496])). 120.83/55.29 thf(2649,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_power__strict__mono)). 120.83/55.29 thf(14173,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2649])). 120.83/55.29 thf(718,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1853_nat__diff__add__eq1)). 120.83/55.29 thf(7349,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])). 120.83/55.29 thf(3552,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_mult__nonpos__nonneg)). 120.83/55.29 thf(17234,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3552])). 120.83/55.29 thf(544,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.29 thf(6749,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])). 120.83/55.29 thf(2507,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2694_mod__mult__distrib2)). 120.83/55.29 thf(13651,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2507])). 120.83/55.29 thf(4521,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3244_odd__plus__one__div__two)). 120.83/55.29 thf(20881,plain,((! [A:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4521])). 120.83/55.29 thf(3446,axiom,((! [A:$i,B:$i]: (((B != zero_zero_int) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ (hAPP_int_real @ real_int @ B))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4466_real__of__int__div__aux)). 120.83/55.29 thf(16890,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_int)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ (hAPP_int_real @ real_int @ B))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3446])). 120.83/55.29 thf(2371,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))) @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3184_Suc__times__mod__eq)). 120.83/55.29 thf(13151,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))) @ B) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371])). 120.83/55.29 thf(4766,axiom,(((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zero__power2)). 120.83/55.29 thf(21861,plain,(((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4766])). 120.83/55.29 thf(1671,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ abs_abs_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3398_abs__add__one__gt__zero)). 120.83/55.29 thf(10719,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ abs_abs_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671])). 120.83/55.29 thf(2168,axiom,((! [A:$i,B:$i,C:$i]: ((zero_z891286103de_int != C) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ B)) => (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ C) = A) <=> ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2641_dvd__div__eq__mult)). 120.83/55.29 thf(12407,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_z891286103de_int = C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ B)) => ((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ C) = A) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C) = B)) & (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C) = B) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ C) = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168])). 120.83/55.29 thf(1872,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2186_add__pos__pos)). 120.83/55.29 thf(11458,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872])). 120.83/55.29 thf(3225,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ C) @ A)) => (? [F:$i,G:$i,H:$i]: ((is_int @ H) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ F) @ E) = (hAPP_int_int @ abs_abs_int @ A)) & ((hAPP_int_int @ abs_abs_int @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ H) @ E)) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ G) @ E) = (hAPP_int_int @ abs_abs_int @ B)) & (is_int @ G) & (is_int @ F)))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ E))) <= ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4538_int__triple__relprime__power__divisors)). 120.83/55.29 thf(16176,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ C) @ A)) => (? [F:$i,G:$i,H:$i]: ((is_int @ H) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ F) @ E) = (hAPP_int_int @ abs_abs_int @ A)) & ((hAPP_int_int @ abs_abs_int @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ H) @ E)) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ G) @ E) = (hAPP_int_int @ abs_abs_int @ B)) & (is_int @ G) & (is_int @ F)))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ E)) | ~ ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3225])). 120.83/55.29 thf(957,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ zero_z126310315umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_mult__pos__neg2)). 120.83/55.29 thf(8214,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[957])). 120.83/55.29 thf(3623,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ phi @ B))) @ one_one_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4482_Euler__Fermat)). 120.83/55.29 thf(17481,plain,((! [A:$i,B:$i]: ((((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ phi @ B))) @ one_one_int) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3623])). 120.83/55.29 thf(612,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ real_nat @ A))) @ pi)) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3735_cos__2npi)). 120.83/55.29 thf(6968,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ real_nat @ A))) @ pi)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 120.83/55.29 thf(3565,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2284_mult_Ozero__left)). 120.83/55.29 thf(17270,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3565])). 120.83/55.29 thf(1046,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ fact @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4552_divides__fact)). 120.83/55.29 thf(8522,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ fact @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046])). 120.83/55.29 thf(1777,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1946_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.29 thf(11111,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777])). 120.83/55.29 thf(3474,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2983_of__nat__power)). 120.83/55.29 thf(16985,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3474])). 120.83/55.29 thf(2165,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4018_coprime__exp__imp)). 120.83/55.29 thf(12394,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165])). 120.83/55.29 thf(411,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.29 thf(6315,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 120.83/55.29 thf(2300,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat) = (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3070_Suc__eq__plus1)). 120.83/55.29 thf(12901,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat) = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300])). 120.83/55.29 thf(2542,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3844_one__less__exp__iff)). 120.83/55.29 thf(13776,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542])). 120.83/55.29 thf(4877,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_le__imp__power__dvd)). 120.83/55.29 thf(22229,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4877])). 120.83/55.29 thf(53,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_complex @ number528085621omplex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) <=> (((hAPP_int_real @ number267125858f_real @ C) = A) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3959_Complex__eq__number__of)). 120.83/55.29 thf(5130,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_complex @ number528085621omplex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) => (((hAPP_int_real @ number267125858f_real @ C) = A) & (B = zero_zero_real))) & ((((hAPP_int_real @ number267125858f_real @ C) = A) & (B = zero_zero_real)) => ((hAPP_int_complex @ number528085621omplex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 120.83/55.29 thf(854,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) @ D) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1845_left__add__mult__distrib)). 120.83/55.29 thf(7867,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) @ D) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])). 120.83/55.29 thf(3412,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1598_eq__imp__le)). 120.83/55.29 thf(16789,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3412])). 120.83/55.29 thf(1985,axiom,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3307_real__lbound__gt__zero)). 120.83/55.29 thf(11812,plain,((! [A:$i,B:$i]: (? [C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985])). 120.83/55.29 thf(1442,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (~ ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4315_gcd__semilattice__nat_Ole__infE)). 120.83/55.29 thf(9909,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442])). 120.83/55.29 thf(955,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3466_pi__half__le__two)). 120.83/55.29 thf(8208,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])). 120.83/55.29 thf(3872,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_bin__less__0__simps_I2_J)). 120.83/55.29 thf(18385,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3872])). 120.83/55.29 thf(2867,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) <=> (A = B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1286_power__inject__exp)). 120.83/55.29 thf(14923,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) => (A = B)) & ((A = B) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2867])). 120.83/55.29 thf(3775,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_power2__ge__self)). 120.83/55.29 thf(18030,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3775])). 120.83/55.29 thf(3086,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ A) != B) => (~ (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (B != (hAPP_nat_nat @ suc @ C)))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3303_lessE)). 120.83/55.29 thf(15680,plain,((! [A:$i,B:$i]: (((~ ((hAPP_nat_nat @ suc @ A) = B)) => (~ (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (~ (B = (hAPP_nat_nat @ suc @ C))))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3086])). 120.83/55.29 thf(4895,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit0 @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_rel__simps_I4_J)). 120.83/55.29 thf(22287,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit0 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit0 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4895])). 120.83/55.29 thf(3528,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3065_Suc__mult__less__cancel1)). 120.83/55.29 thf(17149,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3528])). 120.83/55.29 thf(2210,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2168_add__nonneg__nonneg)). 120.83/55.29 thf(12589,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210])). 120.83/55.29 thf(4902,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4988_gcd__abs2__int)). 120.83/55.29 thf(22321,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4902])). 120.83/55.29 thf(1524,axiom,((! [A:$i,B:$i,C:$i]: ((~ (? [D:$i]: ((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)) & ~ (hBOOL @ (hAPP_nat_bool @ A @ D))) | (~ (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))) <=> (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1780_nat__diff__split__asm)). 120.83/55.29 thf(10174,plain,((! [A:$i,B:$i,C:$i]: (((~ (? [D:$i]: ((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)) & ~ (hBOOL @ (hAPP_nat_bool @ A @ D))) | (~ (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => (~ (? [D:$i]: ((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)) & ~ (hBOOL @ (hAPP_nat_bool @ A @ D))) | (~ (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524])). 120.83/55.29 thf(2217,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1924_add__left__imp__eq)). 120.83/55.29 thf(12606,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217])). 120.83/55.29 thf(516,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = A) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D)) = B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3948_polar__ex1)). 120.83/55.29 thf(6662,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = A) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D)) = B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 120.83/55.29 thf(3821,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_mult__zero__right)). 120.83/55.29 thf(18187,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3821])). 120.83/55.29 thf(315,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D != C) & (A != B)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ A)) != (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_crossproduct__noteq)). 120.83/55.29 thf(5989,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (D = C) & ~ (A = B)) => (~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))))) & ((~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) => (~ (D = C) & ~ (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 120.83/55.29 thf(2100,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2487_zcong__zmod__aux)). 120.83/55.29 thf(12161,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100])). 120.83/55.29 thf(415,axiom,((! [A:$i]: ((hAPP_real_real @ (log @ (hAPP_real_real @ exp_real @ one_one_real)) @ A) = (hAPP_real_real @ ln @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3869_log__ln)). 120.83/55.29 thf(6332,plain,((! [A:$i]: ((hAPP_real_real @ (log @ (hAPP_real_real @ exp_real @ one_one_real)) @ A) = (hAPP_real_real @ ln @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 120.83/55.29 thf(473,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ cos @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3570_cos__periodic__pi)). 120.83/55.29 thf(6519,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ cos @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 120.83/55.29 thf(4686,axiom,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_power2__eq__square)). 120.83/55.29 thf(21530,plain,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4686])). 120.83/55.29 thf(2347,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1891_add__nonpos__neg)). 120.83/55.29 thf(13067,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347])). 120.83/55.29 thf(3016,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3362_real__gt__half__sum)). 120.83/55.29 thf(15441,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3016])). 120.83/55.29 thf(2402,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.29 thf(13275,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402])). 120.83/55.29 thf(1924,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_real @ sequentially)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5033_LIMSEQ__realpow__zero)). 120.83/55.29 thf(11628,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_real @ sequentially)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924])). 120.83/55.29 thf(48,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D))) => (D = (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4219_mod__eq)). 120.83/55.29 thf(5108,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D))) => (D = (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 120.83/55.29 thf(510,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim856651990g_real @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4471_ceiling__less__eq)). 120.83/55.29 thf(6643,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim856651990g_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim856651990g_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 120.83/55.29 thf(4428,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (nat_tsub @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2803_Nat__Transfer_Otransfer__nat__int__functions_I3_J)). 120.83/55.29 thf(20508,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (nat_tsub @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4428])). 120.83/55.29 thf(2250,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1364_mult__less__le__imp__less)). 120.83/55.29 thf(12713,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250])). 120.83/55.29 thf(4609,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3171_Suc3__eq__add__3)). 120.83/55.29 thf(21268,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4609])). 120.83/55.29 thf(798,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.29 thf(7665,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])). 120.83/55.29 thf(4898,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_semiring__mult__2__right)). 120.83/55.29 thf(22304,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4898])). 120.83/55.29 thf(157,axiom,((! [A:$i,B:$i]: ((zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2516_dvd__eq__mod__eq__0)). 120.83/55.29 thf(5461,plain,((! [A:$i,B:$i]: (((zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 120.83/55.29 thf(3961,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_P2110489235nt_int @ A @ C) @ B) = (hAPP_P1175774780nt_int @ (hAPP_i61245889nt_int @ (hAPP_f578362681nt_int @ cOMBC_1417754532nt_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oin)). 120.83/55.29 thf(18688,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_P2110489235nt_int @ A @ C) @ B) = (hAPP_P1175774780nt_int @ (hAPP_i61245889nt_int @ (hAPP_f578362681nt_int @ cOMBC_1417754532nt_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3961])). 120.83/55.29 thf(2839,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_one__neq__zero)). 120.83/55.29 thf(14830,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2839])). 120.83/55.29 thf(1760,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ zero_zero_nat) = one_on1684967323de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.29 thf(11040,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ zero_zero_nat) = one_on1684967323de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760])). 120.83/55.29 thf(2259,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2722_div__mult__self1__is__m)). 120.83/55.29 thf(12745,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259])). 120.83/55.29 thf(1433,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.29 thf(9877,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433])). 120.83/55.29 thf(1108,axiom,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4920_card__atLeastLessThan__int)). 120.83/55.29 thf(8770,plain,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108])). 120.83/55.29 thf(1135,axiom,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4222_euclid)). 120.83/55.29 thf(8849,plain,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135])). 120.83/55.29 thf(3529,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4320_gcd__semilattice__nat_Ole__infI)). 120.83/55.29 thf(17154,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3529])). 120.83/55.29 thf(845,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_power2__less__imp__less)). 120.83/55.29 thf(7835,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])). 120.83/55.29 thf(3420,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1920_add__imp__eq)). 120.83/55.29 thf(16809,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3420])). 120.83/55.29 thf(894,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_dvd__add)). 120.83/55.29 thf(7997,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[894])). 120.83/55.29 thf(1362,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3076_Divides_Otransfer__int__nat__functions_I1_J)). 120.83/55.29 thf(9629,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362])). 120.83/55.29 thf(658,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_dvd__mult__right)). 120.83/55.29 thf(7156,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])). 120.83/55.29 thf(4888,axiom,((! [A:$i]: (zero_zero_int != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_odd__nonzero)). 120.83/55.29 thf(22268,plain,((! [A:$i]: ~ (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4888])). 120.83/55.29 thf(4594,axiom,((! [A:$i]: (((~ (! [B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int) != A) <= (is_int @ B)))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2671_zOddE)). 120.83/55.29 thf(21220,plain,((! [A:$i]: (~ (! [B:$i]: (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int) = A) | ~ (is_int @ B))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4594])). 120.83/55.29 thf(930,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__special_I2_J)). 120.83/55.29 thf(8121,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[930])). 120.83/55.29 thf(4409,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_int @ number_number_of_int @ min)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2752_EvenOdd_Oneg__one__odd__power)). 120.83/55.29 thf(20445,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_int @ number_number_of_int @ min)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4409])). 120.83/55.29 thf(3331,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1670_mult__less__cancel2)). 120.83/55.29 thf(16523,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3331])). 120.83/55.29 thf(387,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real))) & (A = (hAPP_real_real @ exp_real @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3858_lemma__exp__total)). 120.83/55.29 thf(6240,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real))) & (A = (hAPP_real_real @ exp_real @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 120.83/55.29 thf(823,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3931_real__root__mult__lemma)). 120.83/55.29 thf(7754,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 120.83/55.29 thf(4639,axiom,((! [A:$i,B:$i]: (((? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ C)) = B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3003_zle__iff__zadd)). 120.83/55.29 thf(21367,plain,((! [A:$i,B:$i]: ((((? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ C)) = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ C)) = B)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4639])). 120.83/55.29 thf(3678,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) <=> ((hAPP_int_int @ (standardRes @ B) @ A) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2593_StandardRes__prop3)). 120.83/55.29 thf(17694,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (~ ((hAPP_int_int @ (standardRes @ B) @ A) = zero_zero_int))) & ((~ ((hAPP_int_int @ (standardRes @ B) @ A) = zero_zero_int)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3678])). 120.83/55.29 thf(3126,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> (? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3770_even__nat__equiv__def2)). 120.83/55.29 thf(15819,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B) = A))) & ((? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B) = A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3126])). 120.83/55.29 thf(3725,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1439_power__strict__increasing)). 120.83/55.29 thf(17852,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3725])). 120.83/55.29 thf(391,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3590_cos__ge__zero)). 120.83/55.29 thf(6253,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 120.83/55.29 thf(1812,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A)))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_le__number__of__eq__not__less)). 120.83/55.29 thf(11232,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) => (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812])). 120.83/55.29 thf(3390,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1450_power__less__imp__less__exp)). 120.83/55.29 thf(16716,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3390])). 120.83/55.29 thf(2240,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) <=> (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1938_add__left__cancel)). 120.83/55.29 thf(12682,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (B = C)) & ((B = C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240])). 120.83/55.29 thf(4847,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_combine__common__factor)). 120.83/55.29 thf(22144,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4847])). 120.83/55.29 thf(3734,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4501_zgcd__geq__zero)). 120.83/55.29 thf(17894,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3734])). 120.83/55.29 thf(123,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ A))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_dvd__add)). 120.83/55.29 thf(5355,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ A))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 120.83/55.29 thf(4479,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 120.83/55.29 thf(20719,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4479])). 120.83/55.29 thf(1410,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3075_zdiv__int)). 120.83/55.29 thf(9800,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410])). 120.83/55.29 thf(2043,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4335_gcd__lcm__complete__lattice__nat_Oinf__bot__left)). 120.83/55.29 thf(11981,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043])). 120.83/55.29 thf(89,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (hAPP_complex_real @ re @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4125_complex__Re__number__of)). 120.83/55.29 thf(5256,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (hAPP_complex_real @ re @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 120.83/55.29 thf(1874,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_mult__right__mono)). 120.83/55.29 thf(11463,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874])). 120.83/55.29 thf(76,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2100_mult_Ocomm__neutral)). 120.83/55.29 thf(5214,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 120.83/55.29 thf(3938,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2053_add__strict__left__mono)). 120.83/55.29 thf(18617,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3938])). 120.83/55.29 thf(199,axiom,((! [A:$i]: (is_int @ (archim791455193or_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_000tc__Rat__Orat)). 120.83/55.29 thf(5605,plain,((! [A:$i]: (is_int @ (archim791455193or_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 120.83/55.29 thf(3510,axiom,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1217_not__one__le__zero)). 120.83/55.29 thf(17097,plain,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3510])). 120.83/55.29 thf(3822,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.29 thf(18190,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3822])). 120.83/55.29 thf(1356,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) <= (zero_zero_nat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4374_bezout__nat)). 120.83/55.29 thf(9612,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) | (zero_zero_nat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356])). 120.83/55.29 thf(4323,axiom,((! [A:$i]: (((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_int @ number_number_of_int @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3220_of__nat__number__of__lemma)). 120.83/55.29 thf(20098,plain,((! [A:$i]: (((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_int @ number_number_of_int @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4323])). 120.83/55.29 thf(1005,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.29 thf(8389,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])). 120.83/55.29 thf(1152,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ one_one_complex)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.29 thf(8902,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ one_one_complex)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152])). 120.83/55.29 thf(2899,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_mult__pos__neg)). 120.83/55.29 thf(15028,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2899])). 120.83/55.29 thf(4205,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ A))) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2813_of__nat__double)). 120.83/55.29 thf(19658,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ A))) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4205])). 120.83/55.29 thf(4370,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5020_transfer__nat__int__gcd_I1_J)). 120.83/55.29 thf(20276,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4370])). 120.83/55.29 thf(1714,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.29 thf(10850,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714])). 120.83/55.29 thf(2020,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1341_mult__left__less__imp__less)). 120.83/55.29 thf(11911,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020])). 120.83/55.29 thf(2660,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_dvd__power__le)). 120.83/55.29 thf(14205,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2660])). 120.83/55.29 thf(1827,axiom,((! [A:$i]: (((hAPP_real_real @ sqrt @ A) != zero_zero_real) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3327_real__sqrt__not__eq__zero)). 120.83/55.29 thf(11285,plain,((! [A:$i]: (~ ((hAPP_real_real @ sqrt @ A) = zero_zero_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827])). 120.83/55.29 thf(4391,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ C) @ B) = (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (hAPP_f428220345t_bool @ cOMBC_int_int_bool @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U)). 120.83/55.29 thf(20364,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ C) @ B) = (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (hAPP_f428220345t_bool @ cOMBC_int_int_bool @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4391])). 120.83/55.29 thf(4752,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) | (A = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_zless__linear)). 120.83/55.29 thf(21820,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) | (A = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4752])). 120.83/55.29 thf(1608,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1376_mult__strict__mono)). 120.83/55.29 thf(10516,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608])). 120.83/55.29 thf(1919,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = A) <=> (zero_zero_nat = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_add__0__iff)). 120.83/55.29 thf(11609,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = A) => (zero_zero_nat = B)) & ((zero_zero_nat = B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919])). 120.83/55.29 thf(1888,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((zero_zero_rat != E) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ B)) != (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ A))) <= ((D = C) & (B != A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_add__scale__eq__noteq)). 120.83/55.29 thf(11512,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (zero_zero_rat = E)) => (~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ A))) | ~ ((D = C) & ~ (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888])). 120.83/55.29 thf(4658,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1665_zdiff__power2)). 120.83/55.29 thf(21447,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4658])). 120.83/55.29 thf(3493,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_comm__mult__strict__left__mono)). 120.83/55.29 thf(17049,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3493])). 120.83/55.29 thf(980,axiom,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3779_even__num__iff)). 120.83/55.29 thf(8310,plain,((! [A:$i]: ((((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])). 120.83/55.29 thf(834,axiom,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1298_power__0)). 120.83/55.29 thf(7803,plain,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 120.83/55.29 thf(1227,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2117_mult__1)). 120.83/55.29 thf(9155,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227])). 120.83/55.29 thf(2593,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1641_le__iff__add)). 120.83/55.29 thf(13942,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) & ((? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2593])). 120.83/55.29 thf(1907,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4701_real__plus__code)). 120.83/55.29 thf(11564,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907])). 120.83/55.29 thf(3940,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096)). 120.83/55.29 thf(18624,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3940])). 120.83/55.29 thf(3793,axiom,((! [A:$i]: ((((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_int) <= (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A))) & ((zero_zero_nat != (hAPP_int_nat @ number_number_of_nat @ A)) => (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_power__0__left__number__of)). 120.83/55.29 thf(18094,plain,((! [A:$i]: ((((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_int) | ~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A))) & ((~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A))) => (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3793])). 120.83/55.29 thf(3321,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1388_mult__right__le__one__le)). 120.83/55.29 thf(16495,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3321])). 120.83/55.29 thf(3786,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_s)). 120.83/55.29 thf(18069,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3786])). 120.83/55.29 thf(4085,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1555_less__bin__lemma)). 120.83/55.29 thf(19223,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4085])). 120.83/55.29 thf(3619,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.29 thf(17466,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3619])). 120.83/55.29 thf(498,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1528_inf__period_I3_J)). 120.83/55.29 thf(6599,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 120.83/55.29 thf(3349,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4229_div__neg__neg)). 120.83/55.29 thf(16584,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3349])). 120.83/55.29 thf(2175,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A) = zero_zero_real) <=> ((zero_zero_real = A) & (zero_zero_real = B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2162_add__nonneg__eq__0__iff)). 120.83/55.29 thf(12443,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A) = zero_zero_real) => ((zero_zero_real = A) & (zero_zero_real = B))) & (((zero_zero_real = A) & (zero_zero_real = B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A) = zero_zero_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175])). 120.83/55.29 thf(135,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ invers1449016382omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3972_complex__divide__def)). 120.83/55.29 thf(5397,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ invers1449016382omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 120.83/55.29 thf(3868,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ A @ (hAPP_int_int @ B @ C)) = (hAPP_int_bool @ (hAPP_f429935748t_bool @ (hAPP_f1512942609t_bool @ cOMBB_int_bool_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Int__Oint_U)). 120.83/55.29 thf(18375,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ A @ (hAPP_int_int @ B @ C)) = (hAPP_int_bool @ (hAPP_f429935748t_bool @ (hAPP_f1512942609t_bool @ cOMBB_int_bool_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3868])). 120.83/55.29 thf(111,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1697_real__le__eq__diff)). 120.83/55.29 thf(5323,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 120.83/55.29 thf(3307,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2954_of__nat__add)). 120.83/55.29 thf(16452,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3307])). 120.83/55.29 thf(162,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => ((natfloor @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3397_natfloor__neg)). 120.83/55.29 thf(5480,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => ((natfloor @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 120.83/55.29 thf(963,axiom,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_n1699378549t_bool @ ord_less_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4741_less__eq__Suc__le__raw)). 120.83/55.29 thf(8235,plain,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_n1699378549t_bool @ ord_less_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[963])). 120.83/55.29 thf(4345,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2425_mod__add__right__eq)). 120.83/55.29 thf(20203,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4345])). 120.83/55.29 thf(2222,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2848_Suc__neq__Zero)). 120.83/55.29 thf(12621,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222])). 120.83/55.29 thf(3042,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_n1108039445umeral @ semiri1619134803umeral @ A) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2829_of__nat__eq__iff)). 120.83/55.29 thf(15509,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_n1108039445umeral @ semiri1619134803umeral @ A) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) & (((hAPP_n1108039445umeral @ semiri1619134803umeral @ A) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3042])). 120.83/55.29 thf(3505,axiom,(((hAPP_nat_complex @ semiri2020571505omplex @ zero_zero_nat) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2924_of__nat__0)). 120.83/55.29 thf(17085,plain,(((hAPP_nat_complex @ semiri2020571505omplex @ zero_zero_nat) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3505])). 120.83/55.29 thf(601,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3617_tan__monotone_H)). 120.83/55.29 thf(6936,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 120.83/55.29 thf(1531,axiom,((! [A:$i,B:$i]: (((quotient_of @ B) = (quotient_of @ A)) <=> (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4655_quotient__of__inject__eq)). 120.83/55.29 thf(10206,plain,((! [A:$i,B:$i]: ((((quotient_of @ B) = (quotient_of @ A)) => (A = B)) & ((A = B) => ((quotient_of @ B) = (quotient_of @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531])). 120.83/55.29 thf(4274,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2809_of__nat__double)). 120.83/55.29 thf(19927,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4274])). 120.83/55.29 thf(4031,axiom,((! [A:$i]: ((((hAPP_int_int @ fact_fact_int @ A) = zero_zero_int) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_int_nat @ nat @ A))) = (hAPP_int_int @ fact_fact_int @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4271_fact__int__def)). 120.83/55.29 thf(18945,plain,((! [A:$i]: ((((hAPP_int_int @ fact_fact_int @ A) = zero_zero_int) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_int_nat @ nat @ A))) = (hAPP_int_int @ fact_fact_int @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4031])). 120.83/55.29 thf(851,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3094_even__plus__odd__prop2)). 120.83/55.29 thf(7857,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[851])). 120.83/55.29 thf(597,axiom,((zero_zero_real = (hAPP_real_real @ tan @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3599_tan__pi)). 120.83/55.29 thf(6923,plain,((zero_zero_real = (hAPP_real_real @ tan @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])). 120.83/55.29 thf(738,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1878_add__strict__increasing2)). 120.83/55.29 thf(7436,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])). 120.83/55.29 thf(1651,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zEven)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2899_even__minus__even)). 120.83/55.29 thf(10650,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651])). 120.83/55.29 thf(4277,axiom,((! [A:$i]: ((zero_zero_rat = A) <=> (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__eq__power2)). 120.83/55.29 thf(19937,plain,((! [A:$i]: (((zero_zero_rat = A) => (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (zero_zero_rat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4277])). 120.83/55.29 thf(4486,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1239_zero__le__power)). 120.83/55.29 thf(20740,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4486])). 120.83/55.29 thf(1783,axiom,((one_one_rat = (hAPP_nat_rat @ semiri151668891at_rat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2967_of__nat__1)). 120.83/55.29 thf(11132,plain,((one_one_rat = (hAPP_nat_rat @ semiri151668891at_rat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783])). 120.83/55.29 thf(4922,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_zcong__zmult__prop1)). 120.83/55.29 thf(22374,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ E))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4922])). 120.83/55.29 thf(4041,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4292_Bnor__mem__zle__swap)). 120.83/55.29 thf(18982,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4041])). 120.83/55.29 thf(631,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2283_mult_Ozero__left)). 120.83/55.29 thf(7047,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 120.83/55.29 thf(2046,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) => ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4354_coprime__mult__nat)). 120.83/55.29 thf(11991,plain,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) => ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046])). 120.83/55.29 thf(773,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4369_coprime__dvd__mult__nat)). 120.83/55.29 thf(7560,plain,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])). 120.83/55.29 thf(299,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3672_real__of__nat__div4)). 120.83/55.29 thf(5942,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 120.83/55.29 thf(1003,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.29 thf(8384,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003])). 120.83/55.29 thf(3337,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ A @ C)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ zero_z891286103de_int))))) <=> (? [C:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ A @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1678_unity__coeff__ex)). 120.83/55.29 thf(16545,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ A @ C)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ zero_z891286103de_int))))) => (? [C:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ A @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))) & ((? [C:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ A @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ A @ C)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ zero_z891286103de_int))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3337])). 120.83/55.29 thf(2920,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3407_real__sqrt__ge__abs2)). 120.83/55.29 thf(15110,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2920])). 120.83/55.29 thf(2776,axiom,((! [A:$i,B:$i]: ((B != zero_z891286103de_int) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2544_div__mult__self1__is__id)). 120.83/55.29 thf(14597,plain,((! [A:$i,B:$i]: ((~ (B = zero_z891286103de_int)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2776])). 120.83/55.29 thf(4101,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_power2__eq__square)). 120.83/55.29 thf(19282,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4101])). 120.83/55.29 thf(2866,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) <=> ((zero_zero_nat = B) | (A = (hAPP_nat_nat @ suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3080_nat__power__eq__Suc__0__iff)). 120.83/55.29 thf(14913,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) => ((zero_zero_nat = B) | (A = (hAPP_nat_nat @ suc @ zero_zero_nat)))) & (((zero_zero_nat = B) | (A = (hAPP_nat_nat @ suc @ zero_zero_nat))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2866])). 120.83/55.29 thf(1082,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3093_even__plus__odd__prop1)). 120.83/55.29 thf(8674,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082])). 120.83/55.29 thf(1620,axiom,((! [A:$i,B:$i,C:$i]: ((C = A) <= ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1908_add__right__imp__eq)). 120.83/55.29 thf(10555,plain,((! [A:$i,B:$i,C:$i]: ((C = A) | ~ ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620])). 120.83/55.29 thf(4008,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | (zero_zero_int = B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1270_dvd__mult__cancel__right)). 120.83/55.29 thf(18856,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | (zero_zero_int = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | (zero_zero_int = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4008])). 120.83/55.29 thf(1462,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1992_add__le__imp__le__left)). 120.83/55.29 thf(9973,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462])). 120.83/55.29 thf(2324,axiom,((! [A:$i,B:$i]: ((! [C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ A)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ B)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ B))) => (C = D)))) <=> (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4054_ResSet__def)). 120.83/55.29 thf(12988,plain,((! [A:$i,B:$i]: (((! [C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ A)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ B)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ B))) => (C = D)))) => (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ A) @ B))) & ((hBOOL @ (hAPP_f448129468l_bool @ (resSet @ A) @ B)) => (! [C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ A)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ B)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ B))) => (C = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2324])). 120.83/55.29 thf(2875,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) <= (zero_zero_int != C)) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2537_div__mult__mult2)). 120.83/55.29 thf(14949,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) | (zero_zero_int = C) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2875])). 120.83/55.29 thf(4506,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_zcong__trans)). 120.83/55.29 thf(20822,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4506])). 120.83/55.29 thf(4035,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1245_less__1__mult)). 120.83/55.29 thf(18964,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4035])). 120.83/55.29 thf(4064,axiom,((one_one_int != zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_int__0__neq__1)). 120.83/55.29 thf(19140,plain,((~ (one_one_int = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4064])). 120.83/55.29 thf(1665,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = one_one_nat) <= ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4371_invertible__coprime__nat)). 120.83/55.29 thf(10702,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = one_one_nat) | ~ ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665])). 120.83/55.29 thf(3657,axiom,((! [A:$i]: ((is_int @ A) => ((pls = A) <=> (pls = (hAPP_int_int @ bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_rel__simps_I44_J)). 120.83/55.29 thf(17603,plain,((! [A:$i]: ((is_int @ A) => (((pls = A) => (pls = (hAPP_int_int @ bit0 @ A))) & ((pls = (hAPP_int_int @ bit0 @ A)) => (pls = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3657])). 120.83/55.29 thf(3710,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1233_power__mono)). 120.83/55.29 thf(17807,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3710])). 120.83/55.29 thf(4147,axiom,((! [A:$i]: (((? [B:$i]: (A = (hAPP_nat_int @ semiri1621563631at_int @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3261_zero__le__imp__eq__int)). 120.83/55.29 thf(19446,plain,((! [A:$i]: (? [B:$i]: (A = (hAPP_nat_int @ semiri1621563631at_int @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4147])). 120.83/55.29 thf(931,axiom,((! [A:$i,B:$i]: (is_int @ (hAPP_P1175774780nt_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oint)). 120.83/55.29 thf(8126,plain,((! [A:$i,B:$i]: (is_int @ (hAPP_P1175774780nt_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[931])). 120.83/55.29 thf(2340,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4339_gcd__0__nat)). 120.83/55.29 thf(13044,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340])). 120.83/55.29 thf(3366,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2027_add__le__cancel__left)). 120.83/55.29 thf(16640,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3366])). 120.83/55.29 thf(4346,axiom,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ uminus_uminus_int @ A)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3513_minus__Bit0)). 120.83/55.29 thf(20206,plain,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ uminus_uminus_int @ A)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4346])). 120.83/55.29 thf(3910,axiom,(((hAPP_int_int @ bit1 @ pls) = (hAPP_int_int @ succ @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3291_succ__Pls)). 120.83/55.29 thf(18528,plain,(((hAPP_int_int @ bit1 @ pls) = (hAPP_int_int @ succ @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3910])). 120.83/55.29 thf(906,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2026_add__le__cancel__left)). 120.83/55.29 thf(8037,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])). 120.83/55.29 thf(3670,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5007_divides__mult__int)). 120.83/55.29 thf(17662,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3670])). 120.83/55.29 thf(167,axiom,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3738_sin__3over2__pi)). 120.83/55.29 thf(5493,plain,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 120.83/55.29 thf(1097,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.29 thf(8738,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097])). 120.83/55.29 thf(2947,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3032_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.29 thf(15193,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2947])). 120.83/55.29 thf(2911,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_number__of__mult)). 120.83/55.29 thf(15073,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2911])). 120.83/55.29 thf(1661,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((? [J:$i,K:$i]: ((is_int @ J) & (is_int @ K) & ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ I) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ J) @ K)) = (xzgcda @ A @ B @ G @ H @ C @ D @ E @ F)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ H))) <= (I = (hAPP_int_int @ (legacy_zgcd @ G) @ H))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4535_xzgcd__correct__aux1)). 120.83/55.29 thf(10682,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (? [J:$i,K:$i]: ((is_int @ J) & (is_int @ K) & ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ I) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ J) @ K)) = (xzgcda @ A @ B @ G @ H @ C @ D @ E @ F))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ H)) | ~ (I = (hAPP_int_int @ (legacy_zgcd @ G) @ H))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661])). 120.83/55.29 thf(40,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3962_complex__add)). 120.83/55.29 thf(5077,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 120.83/55.29 thf(3514,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1963_add_Ocomm__neutral)). 120.83/55.29 thf(17107,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3514])). 120.83/55.29 thf(994,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1628_trans__less__add2)). 120.83/55.29 thf(8352,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])). 120.83/55.29 thf(1373,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1842_diff__commute)). 120.83/55.29 thf(9661,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373])). 120.83/55.29 thf(4078,axiom,((! [A:$i]: ((hAPP_int_int @ bit1 @ A) != pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_rel__simps_I46_J)). 120.83/55.29 thf(19197,plain,((! [A:$i]: ~ ((hAPP_int_int @ bit1 @ A) = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4078])). 120.83/55.29 thf(941,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ one_on1684967323de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1471_power__Suc__less)). 120.83/55.29 thf(8161,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ one_on1684967323de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[941])). 120.83/55.29 thf(204,axiom,((! [A:$i]: ((rcis @ one_one_real @ A) = (cis @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4260_cis__rcis__eq)). 120.83/55.29 thf(5617,plain,((! [A:$i]: ((rcis @ one_one_real @ A) = (cis @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 120.83/55.29 thf(4499,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_mult__right__mono)). 120.83/55.29 thf(20790,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4499])). 120.83/55.29 thf(1882,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_mult__nonpos__nonneg)). 120.83/55.29 thf(11495,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882])). 120.83/55.29 thf(648,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2055_add__strict__left__mono)). 120.83/55.29 thf(7112,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])). 120.83/55.29 thf(1786,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1774_add__diff__assoc)). 120.83/55.29 thf(11139,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786])). 120.83/55.29 thf(9,axiom,((! [A:$i,B:$i]: (((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = ii) <=> ((A = zero_zero_real) & (one_one_real = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3981_Complex__eq__i)). 120.83/55.29 thf(4967,plain,((! [A:$i,B:$i]: ((((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = ii) => ((A = zero_zero_real) & (one_one_real = B))) & (((A = zero_zero_real) & (one_one_real = B)) => ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = ii))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 120.83/55.29 thf(4537,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5068_SetInterval_Otransfer__nat__int__set__function__closures)). 120.83/55.29 thf(20946,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4537])). 120.83/55.29 thf(3899,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ B @ C)) => ((! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ B @ D)))))) => ((! [D:$i]: ((is_int @ D) => (((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ B @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ C))))) => (hBOOL @ (hAPP_int_bool @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4005_int__induct)). 120.83/55.29 thf(18479,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ B @ C)) => ((! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D)))))) => ((! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ C))))) => (hBOOL @ (hAPP_int_bool @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3899])). 120.83/55.29 thf(1387,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3917_real__root__le__0__iff)). 120.83/55.29 thf(9712,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387])). 120.83/55.29 thf(3610,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_rel__simps_I3_J)). 120.83/55.29 thf(17432,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3610])). 120.83/55.29 thf(4492,axiom,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_one__add__one__is__two)). 120.83/55.29 thf(20755,plain,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4492])). 120.83/55.29 thf(817,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1455_power__strict__increasing__iff)). 120.83/55.29 thf(7733,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 120.83/55.29 thf(680,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_int_complex @ number528085621omplex @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ C))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_int_complex @ number528085621omplex @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1550_left__diff__distrib__number__of)). 120.83/55.29 thf(7236,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_int_complex @ number528085621omplex @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ C))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_int_complex @ number528085621omplex @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])). 120.83/55.29 thf(3818,axiom,((! [A:$i]: ((hAPP_int_int @ bit1 @ A) != pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_rel__simps_I39_J)). 120.83/55.29 thf(18175,plain,((! [A:$i]: ~ ((hAPP_int_int @ bit1 @ A) = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3818])). 120.83/55.29 thf(1895,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (natfloor @ B)) @ A) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3724_natfloor__div__nat)). 120.83/55.29 thf(11533,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (natfloor @ B)) @ A) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895])). 120.83/55.29 thf(2455,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3773_odd__nat__mod__two__eq__one)). 120.83/55.29 thf(13474,plain,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455])). 120.83/55.29 thf(3162,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ one_on1684967323de_int) @ A) = one_on1684967323de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_power__one)). 120.83/55.29 thf(15954,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ one_on1684967323de_int) @ A) = one_on1684967323de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3162])). 120.83/55.29 thf(4603,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1396_power__less__imp__less__base)). 120.83/55.29 thf(21249,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4603])). 120.83/55.29 thf(3685,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1324_mult__right__le__imp__le)). 120.83/55.29 thf(17723,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3685])). 120.83/55.29 thf(617,axiom,((! [A:$i,B:$i]: (((A = B) <=> ((hAPP_i1732201573de_int @ quickcheck_of_int @ B) = (hAPP_i1732201573de_int @ quickcheck_of_int @ A))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4554_Quickcheck__Narrowing_Oof__int__inject)). 120.83/55.29 thf(6983,plain,((! [A:$i,B:$i]: ((((A = B) => ((hAPP_i1732201573de_int @ quickcheck_of_int @ B) = (hAPP_i1732201573de_int @ quickcheck_of_int @ A))) & (((hAPP_i1732201573de_int @ quickcheck_of_int @ B) = (hAPP_i1732201573de_int @ quickcheck_of_int @ A)) => (A = B))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 120.83/55.29 thf(3672,axiom,((min = (hAPP_int_int @ uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3532_Int_OMin__def)). 120.83/55.29 thf(17667,plain,((min = (hAPP_int_int @ uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3672])). 120.83/55.29 thf(3983,axiom,((! [A:$i]: ((hAPP_int_int @ ring_1_of_int_int @ A) = (hAPP_int_int @ number_number_of_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4583_int__number__of__def)). 120.83/55.29 thf(18773,plain,((! [A:$i]: ((hAPP_int_int @ ring_1_of_int_int @ A) = (hAPP_int_int @ number_number_of_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3983])). 120.83/55.29 thf(3490,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ one_on1645066479umeral)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.29 thf(17040,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ one_on1645066479umeral)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3490])). 120.83/55.29 thf(4127,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1330_mult__less__imp__less__left)). 120.83/55.29 thf(19382,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4127])). 120.83/55.29 thf(341,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3670_sin__periodic__pi)). 120.83/55.29 thf(6081,plain,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 120.83/55.29 thf(3144,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2590_dvd__eq__mod__eq__0__number__of)). 120.83/55.29 thf(15878,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat)) & (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3144])). 120.83/55.29 thf(2612,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.29 thf(14034,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2612])). 120.83/55.29 thf(2883,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_power__le__dvd)). 120.83/55.29 thf(14981,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2883])). 120.83/55.29 thf(14,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4083_complex__cnj)). 120.83/55.29 thf(4988,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 120.83/55.29 thf(148,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (archim1246769320r_real @ A)) @ B) = (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4426_floor__subtract)). 120.83/55.29 thf(5433,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (archim1246769320r_real @ A)) @ B) = (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 120.83/55.29 thf(1007,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1635_less__imp__le__nat)). 120.83/55.29 thf(8394,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])). 120.83/55.29 thf(92,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4413_powr__divide2)). 120.83/55.29 thf(5264,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 120.83/55.29 thf(3282,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ A) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2431_mod__add__self1)). 120.83/55.29 thf(16379,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ A) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3282])). 120.83/55.29 thf(3881,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5006_coprime__dvd__mult__iff__int)). 120.83/55.29 thf(18407,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3881])). 120.83/55.29 thf(3195,axiom,((! [A:$i,B:$i,C:$i]: (((C = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = zero_zero_nat)) & ((zero_zero_nat != C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2550_div__mult__mult1__if)). 120.83/55.29 thf(16050,plain,((! [A:$i,B:$i,C:$i]: (((C = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = zero_zero_nat)) & ((~ (zero_zero_nat = C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3195])). 120.83/55.29 thf(2907,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.29 thf(15060,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2907])). 120.83/55.29 thf(1166,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1971_add__0__right)). 120.83/55.29 thf(8956,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166])). 120.83/55.29 thf(3108,axiom,((! [A:$i]: ((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ tan @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3629_lemma__tan__total)). 120.83/55.29 thf(15763,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ tan @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3108])). 120.83/55.29 thf(2958,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.29 thf(15225,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2958])). 120.83/55.29 thf(831,axiom,((! [A:$i]: ((quotient_of @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4664_quotient__of__number_I3_J)). 120.83/55.29 thf(7792,plain,((! [A:$i]: ((quotient_of @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 120.83/55.29 thf(3039,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2384_mod__mult__left__eq)). 120.83/55.29 thf(15500,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3039])). 120.83/55.29 thf(829,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1297_power__0)). 120.83/55.29 thf(7786,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])). 120.83/55.29 thf(1868,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3364_lemma__real__divide__sqrt__less)). 120.83/55.29 thf(11441,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868])). 120.83/55.29 thf(2054,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2264_minf_I9_J)). 120.83/55.29 thf(12018,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054])). 120.83/55.29 thf(216,axiom,(((ratreal @ one_one_rat) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4698_Ratreal__number__collapse_I2_J)). 120.83/55.29 thf(5663,plain,(((ratreal @ one_one_rat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 120.83/55.29 thf(1648,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2690_div__le__dividend)). 120.83/55.29 thf(10641,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648])). 120.83/55.29 thf(2306,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_power3__eq__cube)). 120.83/55.29 thf(12924,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306])). 120.83/55.29 thf(2369,axiom,((! [A:$i,B:$i]: ((((zero_zero_int = B) => ((pdivmod @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ (hAPP_int_int @ abs_abs_int @ A)))) & (((pdivmod @ A @ B) = (posDivAlg @ (hAPP_int_int @ abs_abs_int @ A) @ (hAPP_int_int @ abs_abs_int @ B))) <= (B != zero_zero_int))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3944_pdivmod__posDivAlg)). 120.83/55.29 thf(13138,plain,((! [A:$i,B:$i]: ((((zero_zero_int = B) => ((pdivmod @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ (hAPP_int_int @ abs_abs_int @ A)))) & (((pdivmod @ A @ B) = (posDivAlg @ (hAPP_int_int @ abs_abs_int @ A) @ (hAPP_int_int @ abs_abs_int @ B))) | (B = zero_zero_int))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369])). 120.83/55.29 thf(4425,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2597_div__neg__neg__trivial)). 120.83/55.29 thf(20499,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4425])). 120.83/55.29 thf(903,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1840_nat__mult__le__cancel1)). 120.83/55.29 thf(8029,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[903])). 120.83/55.29 thf(3078,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ min)) = (hAPP_int_int @ uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3546_zdiv__minus1__right)). 120.83/55.29 thf(15659,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ min)) = (hAPP_int_int @ uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3078])). 120.83/55.29 thf(1769,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.29 thf(11064,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769])). 120.83/55.29 thf(4306,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1499__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096)). 120.83/55.29 thf(20042,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4306])). 120.83/55.29 thf(4296,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_int) <=> ((zero_zero_int = A) & (zero_zero_int = B))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_sum__power2__eq__zero__iff)). 120.83/55.29 thf(20003,plain,((! [A:$i,B:$i]: (((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_int) => ((zero_zero_int = A) & (zero_zero_int = B))) & (((zero_zero_int = A) & (zero_zero_int = B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_int))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4296])). 120.83/55.29 thf(3096,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) <=> ((zero_zero_rat = B) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1269_dvd__mult__cancel__right)). 120.83/55.29 thf(15716,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => ((zero_zero_rat = B) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ C)))) & (((zero_zero_rat = B) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3096])). 120.83/55.29 thf(282,axiom,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_real @ norm_norm_complex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4076_complex__mod__cnj)). 120.83/55.29 thf(5888,plain,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_real @ norm_norm_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 120.83/55.29 thf(2975,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (C = zero_zero_nat)) | ? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ D)))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ B)))) <=> (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3212_split__div_H)). 120.83/55.29 thf(15274,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (C = zero_zero_nat)) | ? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ D)))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ B)))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) => (((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) & (C = zero_zero_nat)) | ? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ D)))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2975])). 120.83/55.29 thf(176,axiom,((zero_zero_real = (hAPP_complex_real @ re @ zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4121_Re_Ozero)). 120.83/55.29 thf(5526,plain,((zero_zero_real = (hAPP_complex_real @ re @ zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 120.83/55.29 thf(2605,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4186_prime__power__dvd__cancel__right)). 120.83/55.29 thf(13987,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2605])). 120.83/55.29 thf(1435,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2942_of__nat__less__iff)). 120.83/55.29 thf(9882,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435])). 120.83/55.29 thf(4300,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (! [E:$i]: ((is_int @ E) => ((! [F:$i]: (((! [G:$i]: ((is_int @ G) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F) != E) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B))))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D)))) <= (is_int @ F))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D)) @ A))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5103_bset_I10_J)). 120.83/55.29 thf(20021,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (! [E:$i]: ((is_int @ E) => ((! [F:$i]: (! [G:$i]: ((is_int @ G) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F) = E) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) | ~ (is_int @ F))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D)) @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4300])). 120.83/55.29 thf(3459,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2729_transfer__nat__int__relations_I3_J)). 120.83/55.29 thf(16929,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3459])). 120.83/55.29 thf(2798,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ C))) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_i769753017umeral @ number1443263063umeral @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_left__distrib__number__of)). 120.83/55.29 thf(14697,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ C))) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_i769753017umeral @ number1443263063umeral @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2798])). 120.83/55.29 thf(1321,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_zero__less__mult__pos2)). 120.83/55.29 thf(9490,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321])). 120.83/55.29 thf(2443,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.29 thf(13425,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443])). 120.83/55.29 thf(25,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4092_Im)). 120.83/55.29 thf(5027,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 120.83/55.29 thf(3789,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (multInv @ A) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2756_MultInv__def)). 120.83/55.29 thf(18075,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (multInv @ A) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3789])). 120.83/55.29 thf(4858,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1251_zero__less__power)). 120.83/55.29 thf(22178,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4858])). 120.83/55.29 thf(3415,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5067_finite__atLeastAtMost__int)). 120.83/55.29 thf(16798,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3415])). 120.83/55.29 thf(3536,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1374_mult__strict__mono)). 120.83/55.29 thf(17171,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3536])). 120.83/55.29 thf(4843,axiom,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_semiring__norm_I110_J)). 120.83/55.29 thf(22127,plain,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4843])). 120.83/55.29 thf(683,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4338_gcd__0__left__nat)). 120.83/55.29 thf(7245,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])). 120.83/55.29 thf(1630,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2014_add__left__mono)). 120.83/55.29 thf(10591,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630])). 120.83/55.29 thf(1209,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_le__imp__power__dvd)). 120.83/55.29 thf(9088,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209])). 120.83/55.29 thf(4769,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ pls) @ A) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__Pls)). 120.83/55.29 thf(21867,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ pls) @ A) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4769])). 120.83/55.29 thf(4883,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (? [C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) @ B)) & (is_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3476_best__division__abs)). 120.83/55.29 thf(22249,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (? [C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) @ B)) & (is_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4883])). 120.83/55.29 thf(3522,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2387_mod__mult__eq)). 120.83/55.29 thf(17129,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3522])). 120.83/55.29 thf(1419,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.29 thf(9832,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419])). 120.83/55.29 thf(3846,axiom,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_int_bool @ A @ D)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)))))) & ((! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E))) => (hBOOL @ (hAPP_int_bool @ A @ D))) <= ((is_int @ D) & (is_int @ E)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & ((hBOOL @ (hAPP_int_bool @ A @ zero_zero_int)) <= (zero_zero_int = C))) <=> (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)))) <= ((is_int @ C) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2654_split__zdiv)). 120.83/55.29 thf(18273,plain,((! [A:$i,B:$i,C:$i]: ((((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_int_bool @ A @ D)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)))))) & (! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E))) => (hBOOL @ (hAPP_int_bool @ A @ D))) | ~ ((is_int @ D) & (is_int @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & ((hBOOL @ (hAPP_int_bool @ A @ zero_zero_int)) | ~ (zero_zero_int = C))) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)))) & ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_int_bool @ A @ D)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)))))) & (! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E))) => (hBOOL @ (hAPP_int_bool @ A @ D))) | ~ ((is_int @ D) & (is_int @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & ((hBOOL @ (hAPP_int_bool @ A @ zero_zero_int)) | ~ (zero_zero_int = C))))) | ~ ((is_int @ C) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3846])). 120.83/55.29 thf(4768,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ C)) @ C)) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ C)) @ B)) @ D))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2239_aux______4)). 120.83/55.29 thf(21865,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ C)) @ C)) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ C)) @ B)) @ D)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4768])). 120.83/55.29 thf(4610,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => (one_one_int = (hAPP_int_int @ abs_abs_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5016_coprime__common__divisor__int)). 120.83/55.29 thf(21271,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => (one_one_int = (hAPP_int_int @ abs_abs_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4610])). 120.83/55.29 thf(3792,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ C))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & ((((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B))))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3280_nat__number__of__add__left)). 120.83/55.29 thf(18084,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ C))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & ((((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B))))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3792])). 120.83/55.29 thf(3193,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2939_less__imp__of__nat__less)). 120.83/55.29 thf(16045,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3193])). 120.83/55.29 thf(2505,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1282_one__le__power)). 120.83/55.29 thf(13647,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505])). 120.83/55.29 thf(4120,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_zprime__zdvd__power)). 120.83/55.29 thf(19359,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4120])). 120.83/55.29 thf(1067,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_le__imp__power__dvd)). 120.83/55.29 thf(8627,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067])). 120.83/55.29 thf(2415,axiom,((one_one_real = (hAPP_nat_real @ real_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3653_real__of__nat__1)). 120.83/55.29 thf(13325,plain,((one_one_real = (hAPP_nat_real @ real_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2415])). 120.83/55.29 thf(3730,axiom,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ one_one_int) @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4489_zgcd__1__left)). 120.83/55.29 thf(17879,plain,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ one_one_int) @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3730])). 120.83/55.29 thf(1160,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ A) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1723_dvd_Oless__imp__triv)). 120.83/55.29 thf(8934,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ A) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160])). 120.83/55.29 thf(1139,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1530_inf__period_I3_J)). 120.83/55.29 thf(8860,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A))))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139])). 120.83/55.29 thf(3864,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4523_zgcd__zcong__zgcd)). 120.83/55.29 thf(18348,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C)) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3864])). 120.83/55.29 thf(2212,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult__number__of__left)). 120.83/55.29 thf(12593,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212])). 120.83/55.29 thf(3796,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ A)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2667_zprime__zOdd__eq__grt__2)). 120.83/55.29 thf(18111,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ A)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3796])). 120.83/55.29 thf(2012,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3162_power__Suc__less__one)). 120.83/55.29 thf(11891,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012])). 120.83/55.29 thf(4244,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int = A) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ abs_abs_int @ A)) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3433_zabs__less__one__iff)). 120.83/55.29 thf(19808,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_int = A) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ abs_abs_int @ A)) @ one_one_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ abs_abs_int @ A)) @ one_one_int)) => (zero_zero_int = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4244])). 120.83/55.29 thf(2726,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.29 thf(14423,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2726])). 120.83/55.29 thf(4069,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1315_zcong__eq__zdvd__prop)). 120.83/55.29 thf(19152,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4069])). 120.83/55.29 thf(2621,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2193_zero__less__double__add__iff__zero__less__single__add)). 120.83/55.29 thf(14061,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2621])). 120.83/55.29 thf(890,axiom,((one_one_complex = (hAPP_complex_complex @ cnj @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4069_complex__cnj__one)). 120.83/55.29 thf(7986,plain,((one_one_complex = (hAPP_complex_complex @ cnj @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])). 120.83/55.29 thf(4079,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3202_div2__Suc__Suc)). 120.83/55.29 thf(19201,plain,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4079])). 120.83/55.29 thf(443,axiom,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4108_Im_Ononneg__bounded)). 120.83/55.29 thf(6410,plain,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 120.83/55.29 thf(1117,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5190_nat__minus__add__max)). 120.83/55.29 thf(8791,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117])). 120.83/55.29 thf(1173,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3027_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.29 thf(8972,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173])). 120.83/55.29 thf(2681,axiom,((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1220_not__one__le__zero)). 120.83/55.29 thf(14267,plain,((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2681])). 120.83/55.29 thf(3027,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3471_arctan__ubound)). 120.83/55.29 thf(15468,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3027])). 120.83/55.29 thf(4543,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.29 thf(21007,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4543])). 120.83/55.29 thf(3617,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_rel__simps_I28_J)). 120.83/55.29 thf(17453,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ min))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3617])). 120.83/55.29 thf(1421,axiom,((! [A:$i,B:$i]: ((A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) <=> (zero_zero_rat = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_add__0__iff)). 120.83/55.29 thf(9837,plain,((! [A:$i,B:$i]: (((A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) => (zero_zero_rat = B)) & ((zero_zero_rat = B) => (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421])). 120.83/55.29 thf(3742,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I31_J)). 120.83/55.29 thf(17916,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3742])). 120.83/55.29 thf(301,axiom,((! [A:$i]: ((zero_zero_real = (hAPP_real_real @ sin @ A)) <= (one_one_real = (hAPP_real_real @ cos @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3662_cos__one__sin__zero)). 120.83/55.29 thf(5946,plain,((! [A:$i]: ((zero_zero_real = (hAPP_real_real @ sin @ A)) | ~ (one_one_real = (hAPP_real_real @ cos @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 120.83/55.29 thf(406,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.29 thf(6300,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 120.83/55.29 thf(1941,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1355_mult__le__less__imp__less)). 120.83/55.29 thf(11676,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941])). 120.83/55.29 thf(4664,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2148_add__increasing2)). 120.83/55.29 thf(21462,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4664])). 120.83/55.29 thf(2135,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2039_add__less__imp__less__left)). 120.83/55.29 thf(12296,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135])). 120.83/55.29 thf(4625,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_zero__le__power2)). 120.83/55.29 thf(21322,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4625])). 120.83/55.29 thf(1852,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_power__commutes)). 120.83/55.29 thf(11389,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852])). 120.83/55.29 thf(912,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4359_gcd__diff1__nat)). 120.83/55.29 thf(8065,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])). 120.83/55.29 thf(2934,axiom,(((hAPP_nat_nat @ fact_fact_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3803_fact__1__nat)). 120.83/55.29 thf(15150,plain,(((hAPP_nat_nat @ fact_fact_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2934])). 120.83/55.29 thf(1947,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = one_one_nat) => (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4356_coprime__lmult__nat)). 120.83/55.29 thf(11691,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = one_one_nat) => (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947])). 120.83/55.29 thf(4542,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (div_mod_int @ B) @ C))) <=> (((zero_zero_int = C) => (hBOOL @ (hAPP_int_bool @ A @ B))) & ((! [D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ A @ E)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)))) <= ((is_int @ D) & (is_int @ E)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & ((! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => ((hBOOL @ (hAPP_int_bool @ A @ E)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2660_split__zmod)). 120.83/55.29 thf(20978,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ B)) => (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => (((zero_zero_int = C) => (hBOOL @ (hAPP_int_bool @ A @ B))) & (! [D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ A @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E))) | ~ ((is_int @ D) & (is_int @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & (! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => ((hBOOL @ (hAPP_int_bool @ A @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))))) & ((((zero_zero_int = C) => (hBOOL @ (hAPP_int_bool @ A @ B))) & (! [D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ A @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E))) | ~ ((is_int @ D) & (is_int @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) & (! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => ((hBOOL @ (hAPP_int_bool @ A @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) & (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)))) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (div_mod_int @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4542])). 120.83/55.29 thf(3599,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2066_add__less__cancel__left)). 120.83/55.29 thf(17398,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3599])). 120.83/55.29 thf(3380,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1410_power__le__imp__le__exp)). 120.83/55.29 thf(16693,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3380])). 120.83/55.29 thf(1701,axiom,((! [A:$i,B:$i]: ((B != zero_z126310315umeral) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ one_on1645066479umeral) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2634_div__add__self2)). 120.83/55.29 thf(10816,plain,((! [A:$i,B:$i]: ((~ (B = zero_z126310315umeral)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ one_on1645066479umeral) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701])). 120.83/55.29 thf(802,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2362_zmod__zdiv__equality_H)). 120.83/55.29 thf(7677,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 120.83/55.29 thf(58,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (div_mod_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4553_mod__code__int__def)). 120.83/55.29 thf(5156,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (div_mod_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 120.83/55.29 thf(1311,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4321_gcd__greatest__nat)). 120.83/55.29 thf(9457,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311])). 120.83/55.29 thf(2223,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (B = A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2857_less__SucE)). 120.83/55.29 thf(12625,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (B = A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223])). 120.83/55.29 thf(4528,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5005_coprime__dvd__mult__int)). 120.83/55.29 thf(20917,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4528])). 120.83/55.29 thf(1952,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1620_mult__0__right)). 120.83/55.29 thf(11709,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952])). 120.83/55.29 thf(819,axiom,((! [A:$i,B:$i,C:$i]: ((C = B) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1715_dvd_Oord__eq__less__trans)). 120.83/55.29 thf(7739,plain,((! [A:$i,B:$i,C:$i]: ((C = B) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[819])). 120.83/55.29 thf(4946,axiom,((! [A:$i,B:$i]: ((((B != zero_zero_int) | (zero_zero_int != A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4995_gcd__pos__int)). 120.83/55.29 thf(22456,plain,((! [A:$i,B:$i]: ((((~ (B = zero_zero_int) | ~ (zero_zero_int = A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) => (~ (B = zero_zero_int) | ~ (zero_zero_int = A)))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4946])). 120.83/55.29 thf(1071,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2057_add__strict__left__mono)). 120.83/55.29 thf(8642,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071])). 120.83/55.29 thf(4899,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2178_add__neg__neg)). 120.83/55.29 thf(22307,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4899])). 120.83/55.29 thf(2622,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1949_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.29 thf(14066,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2622])). 120.83/55.29 thf(485,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (natfloor @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3687_le__natfloor__eq)). 120.83/55.29 thf(6559,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (natfloor @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (natfloor @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 120.83/55.29 thf(3628,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2119_mult__1__left)). 120.83/55.29 thf(17498,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3628])). 120.83/55.29 thf(2246,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ prime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4175_prime__dvd__power)). 120.83/55.29 thf(12703,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246])). 120.83/55.29 thf(1979,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ one_one_complex)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ one_one_complex)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A)) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1824_real__squared__diff__one__factored)). 120.83/55.29 thf(11793,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ one_one_complex)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ one_one_complex)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A)) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979])). 120.83/55.29 thf(1870,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1513_number__of__diff)). 120.83/55.29 thf(11446,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870])). 120.83/55.29 thf(1573,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ arccos @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3861_DERIV__arccos)). 120.83/55.29 thf(10378,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ arccos @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573])). 120.83/55.29 thf(2479,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_semiring__mult__2)). 120.83/55.29 thf(13543,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2479])). 120.83/55.29 thf(1104,axiom,((! [A:$i]: ((A != zero_z126310315umeral) => (one_on1645066479umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2555_div__self)). 120.83/55.29 thf(8759,plain,((! [A:$i]: ((~ (A = zero_z126310315umeral)) => (one_on1645066479umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104])). 120.83/55.29 thf(3302,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | (zero_zero_nat = B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1812_nat__mult__dvd__cancel__disj_H)). 120.83/55.29 thf(16431,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | (zero_zero_nat = B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | (zero_zero_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3302])). 120.83/55.29 thf(2040,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1468_power__Suc__less)). 120.83/55.29 thf(11971,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040])). 120.83/55.29 thf(4053,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_mult__right__mono__neg)). 120.83/55.29 thf(19056,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4053])). 120.83/55.29 thf(2493,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5193_max__Suc__Suc)). 120.83/55.29 thf(13604,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2493])). 120.83/55.29 thf(2713,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4299_gcd__dvd1__nat)). 120.83/55.29 thf(14387,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2713])). 120.83/55.29 thf(2208,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2869_Suc__n__not__le__n)). 120.83/55.29 thf(12582,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208])). 120.83/55.29 thf(1031,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.29 thf(8479,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])). 120.83/55.29 thf(3581,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_mult__2__right)). 120.83/55.29 thf(17342,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3581])). 120.83/55.29 thf(3057,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1766_less__diff__iff)). 120.83/55.29 thf(15569,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3057])). 120.83/55.29 thf(125,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ D)) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))))) => (((hAPP_real_real @ A @ B) = (hAPP_real_real @ A @ C)) <= (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ zero_zero_real)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5178_DERIV__isconst__end)). 120.83/55.29 thf(5360,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ D)) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))))) => (((hAPP_real_real @ A @ B) = (hAPP_real_real @ A @ C)) | ~ (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ zero_zero_real)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 120.83/55.29 thf(2255,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2296_mult_Oadd__left)). 120.83/55.29 thf(12735,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255])). 120.83/55.29 thf(2062,axiom,((! [A:$i,B:$i]: ((B != A) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1586_linorder__neqE__nat)). 120.83/55.29 thf(12041,plain,((! [A:$i,B:$i]: ((~ (B = A)) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062])). 120.83/55.29 thf(4253,axiom,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2458_zmod__self)). 120.83/55.29 thf(19845,plain,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4253])). 120.83/55.29 thf(2669,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ min) = (hAPP_int_int @ succ @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3296_diff__bin__simps_I2_J)). 120.83/55.29 thf(14232,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ min) = (hAPP_int_int @ succ @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2669])). 120.83/55.29 thf(534,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => ((hAPP_real_real @ arccos @ (hAPP_real_real @ cos @ A)) = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3603_arccos__cos)). 120.83/55.29 thf(6717,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => ((hAPP_real_real @ arccos @ (hAPP_real_real @ cos @ A)) = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 120.83/55.29 thf(1676,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2388_mod__mult__eq)). 120.83/55.29 thf(10734,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676])). 120.83/55.29 thf(1474,axiom,((! [A:$i,B:$i,C:$i]: ((zero_zero_nat != C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2621_div__mult__self1)). 120.83/55.29 thf(10014,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_zero_nat = C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474])). 120.83/55.29 thf(90,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_dvd__power__same)). 120.83/55.29 thf(5259,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 120.83/55.29 thf(4321,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ nat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2734_zero__less__nat__eq)). 120.83/55.29 thf(20091,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4321])). 120.83/55.29 thf(3135,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2158_add__increasing)). 120.83/55.29 thf(15856,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3135])). 120.83/55.29 thf(3129,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.29 thf(15834,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3129])). 120.83/55.29 thf(3502,axiom,((! [A:$i,B:$i,C:$i]: ((((C = A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3107_power__inject__base)). 120.83/55.29 thf(17078,plain,((! [A:$i,B:$i,C:$i]: ((C = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3502])). 120.83/55.29 thf(2689,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ one_on1645066479umeral) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_one__dvd)). 120.83/55.29 thf(14299,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ one_on1645066479umeral) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2689])). 120.83/55.29 thf(4218,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = A) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4196_prime__odd)). 120.83/55.29 thf(19700,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = A) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4218])). 120.83/55.29 thf(486,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4407_powr__mono)). 120.83/55.29 thf(6562,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 120.83/55.29 thf(1048,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2849_Zero__neq__Suc)). 120.83/55.29 thf(8532,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048])). 120.83/55.29 thf(2180,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.29 thf(12472,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180])). 120.83/55.29 thf(3148,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.29 thf(15893,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3148])). 120.83/55.29 thf(3205,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2203_add__less__le__mono)). 120.83/55.29 thf(16099,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3205])). 120.83/55.29 thf(3922,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2468_zdvd__zmod__imp__zdvd)). 120.83/55.29 thf(18560,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3922])). 120.83/55.29 thf(3410,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1877_add__strict__increasing2)). 120.83/55.29 thf(16785,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3410])). 120.83/55.29 thf(1926,axiom,((is_int @ min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OMin)). 120.83/55.29 thf(11632,plain,((is_int @ min)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926])). 120.83/55.29 thf(1432,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1599_nat__le__linear)). 120.83/55.29 thf(9875,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432])). 120.83/55.29 thf(4223,axiom,((hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4191_two__is__prime)). 120.83/55.29 thf(19717,plain,((hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4223])). 120.83/55.29 thf(909,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2072_add__less__cancel__right)). 120.83/55.29 thf(8050,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[909])). 120.83/55.29 thf(748,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_semiring__mult__2__right)). 120.83/55.29 thf(7473,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 120.83/55.29 thf(2144,axiom,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (natfloor @ (hAPP_int_real @ number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3387_natfloor__number__of__eq)). 120.83/55.29 thf(12330,plain,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (natfloor @ (hAPP_int_real @ number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144])). 120.83/55.29 thf(3213,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2693_mod__less__eq__dividend)). 120.83/55.29 thf(16131,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3213])). 120.83/55.29 thf(295,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ cos @ A))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3568_abs__cos__le__one)). 120.83/55.29 thf(5929,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ cos @ A))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 120.83/55.29 thf(1492,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((zero_zero_int != B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4450_real__of__int__div)). 120.83/55.29 thf(10070,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((~ (zero_zero_int = B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492])). 120.83/55.29 thf(4380,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I34_J)). 120.83/55.29 thf(20317,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4380])). 120.83/55.29 thf(1815,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3580_cos__two__less__zero)). 120.83/55.29 thf(11242,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815])). 120.83/55.29 thf(240,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_mult__mono_H)). 120.83/55.29 thf(5738,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 120.83/55.29 thf(3180,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_zero__less__mult__pos)). 120.83/55.29 thf(16007,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3180])). 120.83/55.29 thf(2525,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ pls)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_add__numeral__0)). 120.83/55.29 thf(13719,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ pls)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525])). 120.83/55.29 thf(1879,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim1246769320r_real @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4469_floor__le__eq)). 120.83/55.29 thf(11480,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim1246769320r_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim1246769320r_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879])). 120.83/55.29 thf(1808,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = A) => ((zero_zero_nat = A) | (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1673_mult__eq__self__implies__10)). 120.83/55.29 thf(11218,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = A) => ((zero_zero_nat = A) | (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808])). 120.83/55.29 thf(3400,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2936_less__imp__of__nat__less)). 120.83/55.29 thf(16744,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3400])). 120.83/55.29 thf(3633,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) & (A = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ B)))) <=> ((hAPP_int_int @ number_number_of_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3168_int__eq__iff__number__of)). 120.83/55.29 thf(17513,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) & (A = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_int @ number_number_of_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A))) & (((hAPP_int_int @ number_number_of_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) & (A = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3633])). 120.83/55.29 thf(3450,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1917_add__imp__eq)). 120.83/55.29 thf(16902,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3450])). 120.83/55.29 thf(1440,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.29 thf(9897,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440])). 120.83/55.29 thf(511,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (natfloor @ A))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3674_real__natfloor__le)). 120.83/55.29 thf(6648,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (natfloor @ A))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])). 120.83/55.29 thf(3600,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.29 thf(17403,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3600])). 120.83/55.29 thf(4177,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1257_less__add__one)). 120.83/55.29 thf(19546,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4177])). 120.83/55.29 thf(4905,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ B) @ zero_zero_int)) @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4520_zgcd__code)). 120.83/55.29 thf(22329,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ B) @ zero_zero_int)) @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4905])). 120.83/55.29 thf(1763,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_mult__pos__neg2)). 120.83/55.29 thf(11047,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763])). 120.83/55.29 thf(4532,axiom,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3151_transfer__int__nat__numerals_I4_J)). 120.83/55.29 thf(20934,plain,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4532])). 120.83/55.29 thf(4643,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4195_prime__ge__2)). 120.83/55.29 thf(21390,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4643])). 120.83/55.29 thf(153,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ abs_abs_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5168_isCont__abs)). 120.83/55.29 thf(5448,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ abs_abs_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 120.83/55.29 thf(3432,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => (B = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2566_dvd__div__mult__self)). 120.83/55.29 thf(16841,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => (B = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3432])). 120.83/55.29 thf(523,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ ln @ B)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4460_ln__powr)). 120.83/55.29 thf(6685,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ ln @ B)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 120.83/55.29 thf(1822,axiom,((! [A:$i]: ? [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3952_reals__Archimedean2)). 120.83/55.29 thf(11265,plain,((! [A:$i]: ? [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822])). 120.83/55.29 thf(4685,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_zdvd__reduce)). 120.83/55.29 thf(21525,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4685])). 120.83/55.29 thf(968,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1593_nat__add__assoc)). 120.83/55.29 thf(8261,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[968])). 120.83/55.29 thf(78,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2077_right__minus__eq)). 120.83/55.29 thf(5220,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 120.83/55.29 thf(4790,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1221_zero__less__one)). 120.83/55.29 thf(21940,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4790])). 120.83/55.29 thf(1461,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5192_max__0L)). 120.83/55.29 thf(9970,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461])). 120.83/55.29 thf(4437,axiom,((! [A:$i,B:$i]: (((B != zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2632_div__add__self2)). 120.83/55.29 thf(20547,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4437])). 120.83/55.29 thf(546,axiom,((! [A:$i,B:$i]: ((archim856651990g_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_int_real @ real_int @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (archim856651990g_real @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4429_ceiling__subtract)). 120.83/55.29 thf(6755,plain,((! [A:$i,B:$i]: ((archim856651990g_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_int_real @ real_int @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (archim856651990g_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 120.83/55.29 thf(555,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1564_le__add__iff2)). 120.83/55.29 thf(6777,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])). 120.83/55.29 thf(541,axiom,(((natfloor @ one_one_real) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3388_natfloor__one)). 120.83/55.29 thf(6740,plain,(((natfloor @ one_one_real) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 120.83/55.29 thf(2196,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zEven))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3091_IntNatAux_Oodd__plus__odd)). 120.83/55.29 thf(12536,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zEven))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196])). 120.83/55.29 thf(4074,axiom,(((produc1298267108nt_int @ (hAPP_f1760145644nt_int @ (hAPP_f808647893nt_int @ cOMBC_736024425nt_int @ (hAPP_f836602773nt_int @ (hAPP_f888249301nt_int @ cOMBB_1875755114nt_int @ cOMBB_int_int_int) @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ plus_plus_int) @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ power_power_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ power_power_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = twoSqu1907779896sum2sq)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4838_sum2sq__def)). 120.83/55.29 thf(19177,plain,(((produc1298267108nt_int @ (hAPP_f1760145644nt_int @ (hAPP_f808647893nt_int @ cOMBC_736024425nt_int @ (hAPP_f836602773nt_int @ (hAPP_f888249301nt_int @ cOMBB_1875755114nt_int @ cOMBB_int_int_int) @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ plus_plus_int) @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ power_power_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ power_power_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = twoSqu1907779896sum2sq)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4074])). 120.83/55.29 thf(130,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ pi) @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3669_sin__periodic__pi2)). 120.83/55.29 thf(5384,plain,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ pi) @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 120.83/55.29 thf(4501,axiom,((zero_zero_int = pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Pls__def)). 120.83/55.29 thf(20794,plain,((zero_zero_int = pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4501])). 120.83/55.29 thf(126,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A))) @ one_one_real)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4458_real__of__int__ceiling__diff__one__le)). 120.83/55.29 thf(5370,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A))) @ one_one_real)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 120.83/55.29 thf(1841,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_power__even__eq)). 120.83/55.29 thf(11346,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841])). 120.83/55.29 thf(623,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (rcis @ A @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ cos @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4262_Re__rcis)). 120.83/55.29 thf(7004,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (rcis @ A @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ cos @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 120.83/55.29 thf(3118,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1413_power__le__imp__le__exp)). 120.83/55.29 thf(15799,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3118])). 120.83/55.29 thf(3933,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) => ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4486_zgcd__zgcd__zmult)). 120.83/55.29 thf(18604,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ C)) => ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3933])). 120.83/55.29 thf(604,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (A = (hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3703_sin__arcsin)). 120.83/55.29 thf(6947,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (A = (hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])). 120.83/55.29 thf(2853,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ fact_fact_nat @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3812_dvd__fact__nat)). 120.83/55.29 thf(14874,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ fact_fact_nat @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2853])). 120.83/55.29 thf(875,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4317_dvd__gcd__D1__nat)). 120.83/55.29 thf(7936,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[875])). 120.83/55.29 thf(1785,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_power2__eq__square__number__of)). 120.83/55.29 thf(11136,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785])). 120.83/55.29 thf(2200,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) <=> (B = A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3897_real__root__eq__iff)). 120.83/55.29 thf(12554,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) => (B = A)) & ((B = A) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200])). 120.83/55.29 thf(3394,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim1246769320r_real @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4416_floor__less__eq)). 120.83/55.29 thf(16725,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim1246769320r_real @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (archim1246769320r_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3394])). 120.83/55.29 thf(3836,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3222_int__even__iff__2__dvd)). 120.83/55.29 thf(18241,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3836])). 120.83/55.29 thf(866,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1972_add__0__right)). 120.83/55.29 thf(7909,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])). 120.83/55.29 thf(4584,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_unique__quotient__lemma__neg)). 120.83/55.29 thf(21181,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4584])). 120.83/55.29 thf(3496,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ zero_z891286103de_int) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_mult__zero__right)). 120.83/55.29 thf(17058,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ zero_z891286103de_int) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3496])). 120.83/55.29 thf(4003,axiom,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_nat @ number_number_of_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2714_nat__number__of__def)). 120.83/55.29 thf(18842,plain,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_nat @ number_number_of_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4003])). 120.83/55.29 thf(104,axiom,((! [A:$i]: ((natceiling @ A) = (hAPP_int_nat @ nat @ (archim856651990g_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4364_natceiling__def)). 120.83/55.29 thf(5296,plain,((! [A:$i]: ((natceiling @ A) = (hAPP_int_nat @ nat @ (archim856651990g_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 120.83/55.29 thf(2060,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5170_isCont__root__neg)). 120.83/55.29 thf(12036,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060])). 120.83/55.29 thf(3466,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1778_diff__diff__right)). 120.83/55.29 thf(16957,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3466])). 120.83/55.29 thf(4783,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_mult__mono)). 120.83/55.29 thf(21924,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4783])). 120.83/55.29 thf(881,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) <=> (? [B:$i]: (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3769_odd__nat__equiv__def2)). 120.83/55.29 thf(7954,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (? [B:$i]: (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B))))) & ((? [B:$i]: (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ B)))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])). 120.83/55.29 thf(4126,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2098_mult_Ocomm__neutral)). 120.83/55.29 thf(19379,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4126])). 120.83/55.29 thf(2121,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2396_mod__mult__mult2)). 120.83/55.29 thf(12249,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121])). 120.83/55.29 thf(2790,axiom,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4560_times__code__int__def)). 120.83/55.29 thf(14658,plain,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2790])). 120.83/55.29 thf(1444,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3128_n__less__m__mult__n)). 120.83/55.29 thf(9914,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444])). 120.83/55.29 thf(285,axiom,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4140_Re_Opos__bounded)). 120.83/55.29 thf(5897,plain,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 120.83/55.29 thf(4206,axiom,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__special_I2_J)). 120.83/55.29 thf(19661,plain,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4206])). 120.83/55.29 thf(553,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4412_powr__add)). 120.83/55.29 thf(6772,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])). 120.83/55.29 thf(4935,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_int__one__le__iff__zero__less)). 120.83/55.29 thf(22421,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4935])). 120.83/55.29 thf(529,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2289_mult__right_Ozero)). 120.83/55.29 thf(6702,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 120.83/55.29 thf(3340,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_dvd__mult2)). 120.83/55.29 thf(16562,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3340])). 120.83/55.29 thf(4377,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_power2__less__0)). 120.83/55.29 thf(20308,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4377])). 120.83/55.29 thf(2441,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_comm__mult__strict__left__mono)). 120.83/55.29 thf(13420,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2441])). 120.83/55.29 thf(1236,axiom,(((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3805_fact__Suc__0__nat)). 120.83/55.29 thf(9187,plain,(((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236])). 120.83/55.29 thf(1726,axiom,((! [A:$i,B:$i]: (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A) != zero_zero_rat) <= (zero_zero_rat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_field__power__not__zero)). 120.83/55.29 thf(10895,plain,((! [A:$i,B:$i]: (~ ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A) = zero_zero_rat) | (zero_zero_rat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726])). 120.83/55.29 thf(528,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2454_dvd__mod__imp__dvd)). 120.83/55.29 thf(6700,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 120.83/55.29 thf(4683,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2421_mod__add__left__eq)). 120.83/55.29 thf(21520,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4683])). 120.83/55.29 thf(2782,axiom,((! [A:$i]: ((zero_zero_real = A) <=> (one_one_real = (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3836_exp__eq__one__iff)). 120.83/55.29 thf(14622,plain,((! [A:$i]: (((zero_zero_real = A) => (one_one_real = (hAPP_real_real @ exp_real @ A))) & ((one_one_real = (hAPP_real_real @ exp_real @ A)) => (zero_zero_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2782])). 120.83/55.29 thf(1859,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3361_real__less__half__sum)). 120.83/55.29 thf(11408,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859])). 120.83/55.29 thf(1696,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2022_add__le__cancel__left)). 120.83/55.29 thf(10801,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696])). 120.83/55.29 thf(3862,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2804_inv__inv__aux)). 120.83/55.29 thf(18343,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3862])). 120.83/55.29 thf(3656,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_power2__le__imp__le)). 120.83/55.29 thf(17601,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3656])). 120.83/55.29 thf(4757,axiom,((! [A:$i]: (((hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_P1175774780nt_int @ product_snd_int_int @ (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4236_mod__pos__pos__1__number__of)). 120.83/55.29 thf(21833,plain,((! [A:$i]: (((hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_P1175774780nt_int @ product_snd_int_int @ (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4757])). 120.83/55.29 thf(2287,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_mult__neg__pos)). 120.83/55.29 thf(12860,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287])). 120.83/55.29 thf(1974,axiom,((! [A:$i]: ((A = one_one_real) <=> (A = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1952_one__reorient)). 120.83/55.29 thf(11783,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974])). 120.83/55.29 thf(1586,axiom,((! [A:$i,B:$i,C:$i]: ((zero_zero_nat != C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2538_div__mult__mult2)). 120.83/55.29 thf(10422,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_zero_nat = C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586])). 120.83/55.29 thf(3102,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3765_Parity_Otransfer__int__nat__relations)). 120.83/55.29 thf(15738,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3102])). 120.83/55.29 thf(1734,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_comm__mult__left__mono)). 120.83/55.29 thf(10932,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734])). 120.83/55.29 thf(2302,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_real @ real_int @ A) = (hAPP_nat_real @ real_nat @ (hAPP_int_nat @ nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4449_real__nat__eq__real)). 120.83/55.29 thf(12907,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_real @ real_int @ A) = (hAPP_nat_real @ real_nat @ (hAPP_int_nat @ nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302])). 120.83/55.29 thf(2636,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1684_mult__le__cancel2)). 120.83/55.29 thf(14128,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2636])). 120.83/55.29 thf(3683,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (inv @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2126_inv__less__p__minus__1)). 120.83/55.29 thf(17719,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (inv @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3683])). 120.83/55.29 thf(4819,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_zprime__power__zdvd__cancel__right)). 120.83/55.29 thf(22038,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4819])). 120.83/55.29 thf(217,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ (dist_dist_complex @ A) @ B) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4546_dist__complex__def)). 120.83/55.29 thf(5665,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ (dist_dist_complex @ A) @ B) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 120.83/55.29 thf(4761,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring__mult__number__of)). 120.83/55.29 thf(21848,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4761])). 120.83/55.29 thf(2115,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2435_mod__add__self2)). 120.83/55.29 thf(12217,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115])). 120.83/55.29 thf(1162,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3064_less__eq__Suc__le)). 120.83/55.29 thf(8939,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162])). 120.83/55.29 thf(844,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3145_of__nat__0__less__iff)). 120.83/55.29 thf(7830,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])). 120.83/55.29 thf(3353,axiom,((! [A:$i,B:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_arith__simps_I32_J)). 120.83/55.29 thf(16594,plain,((! [A:$i,B:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3353])). 120.83/55.29 thf(4786,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ (hAPP_f1673103573at_int @ cOMBC_nat_int_int @ A) @ B) @ C) = (hAPP_int_int @ (hAPP_nat_fun_int_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__Int__Oint_U)). 120.83/55.29 thf(21929,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ (hAPP_f1673103573at_int @ cOMBC_nat_int_int @ A) @ B) @ C) = (hAPP_int_int @ (hAPP_nat_fun_int_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4786])). 120.83/55.29 thf(4792,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hAPP_int_int @ (standardRes @ C) @ B) = (hAPP_int_int @ (standardRes @ C) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2650_StandardRes__prop2)). 120.83/55.29 thf(21943,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((((hAPP_int_int @ (standardRes @ C) @ B) = (hAPP_int_int @ (standardRes @ C) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => ((hAPP_int_int @ (standardRes @ C) @ B) = (hAPP_int_int @ (standardRes @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4792])). 120.83/55.29 thf(1402,axiom,((one_one_real = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_numeral__1__eq__1)). 120.83/55.29 thf(9764,plain,((one_one_real = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402])). 120.83/55.29 thf(1055,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sin @ A)) @ zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3736_sin__less__zero)). 120.83/55.29 thf(8554,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sin @ A)) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055])). 120.83/55.29 thf(4015,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ G))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ G)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ F))) @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1558_xzgcda__linear__aux1)). 120.83/55.29 thf(18888,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ G))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ G)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ F))) @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4015])). 120.83/55.29 thf(3995,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4253_less__code__int__def)). 120.83/55.29 thf(18814,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3995])). 120.83/55.29 thf(1184,axiom,((! [A:$i,B:$i]: ((((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (div_mod_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4238_mod__neg__neg)). 120.83/55.29 thf(9007,plain,((! [A:$i,B:$i]: (((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (div_mod_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184])). 120.83/55.29 thf(758,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1249_less__1__mult)). 120.83/55.29 thf(7505,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])). 120.83/55.29 thf(2788,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_mult__strict__left__mono)). 120.83/55.29 thf(14654,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2788])). 120.83/55.29 thf(806,axiom,((! [A:$i]: ((((hAPP_int_nat @ number_number_of_nat @ A) != zero_zero_nat) => (zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((one_one_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_power__0__left__number__of)). 120.83/55.29 thf(7688,plain,((! [A:$i]: (((~ ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) => (zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((one_one_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_int_nat @ number_number_of_nat @ A))) | ~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 120.83/55.29 thf(920,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2844_of__nat__Suc)). 120.83/55.29 thf(8094,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[920])). 120.83/55.29 thf(3437,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3116_power__gt1)). 120.83/55.29 thf(16858,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3437])). 120.83/55.29 thf(825,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2910_of__nat__0__le__iff)). 120.83/55.29 thf(7760,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 120.83/55.29 thf(3233,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1642_nat__add__left__cancel__le)). 120.83/55.29 thf(16219,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3233])). 120.83/55.29 thf(112,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4402_real__of__int__ceiling__ge)). 120.83/55.29 thf(5328,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 120.83/55.29 thf(2527,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3506_arcsin__lt__bounded)). 120.83/55.29 thf(13725,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2527])). 120.83/55.29 thf(4824,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2744_nat__add__distrib)). 120.83/55.29 thf(22063,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4824])). 120.83/55.29 thf(1545,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2400_zmod__simps_I4_J)). 120.83/55.29 thf(10256,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545])). 120.83/55.29 thf(1801,axiom,((! [A:$i,B:$i]: ((divmod_int @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4197_divmod__int__mod__div)). 120.83/55.29 thf(11195,plain,((! [A:$i,B:$i]: ((divmod_int @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801])). 120.83/55.29 thf(3253,axiom,((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ one_one_int) @ zEven)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2894_one__not__even)). 120.83/55.29 thf(16276,plain,((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ one_one_int) @ zEven)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3253])). 120.83/55.29 thf(2949,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ B) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2978_of__nat__power)). 120.83/55.29 thf(15197,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ B) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2949])). 120.83/55.29 thf(2297,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int) = (hAPP_int_rat @ ring_1_of_int_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4678_of__int__rat)). 120.83/55.29 thf(12892,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int) = (hAPP_int_rat @ ring_1_of_int_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297])). 120.83/55.29 thf(3809,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <= (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3245_even__plus__one__div__two)). 120.83/55.29 thf(18148,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3809])). 120.83/55.29 thf(2616,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4497_zgcd__zminus)). 120.83/55.29 thf(14046,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2616])). 120.83/55.29 thf(2158,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2977_of__nat__power)). 120.83/55.29 thf(12375,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158])). 120.83/55.29 thf(664,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (ratreal @ (hAPP_int_rat @ number_number_of_rat @ B))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4714_Ratreal__number__of__quotient)). 120.83/55.29 thf(7170,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (ratreal @ (hAPP_int_rat @ number_number_of_rat @ B))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])). 120.83/55.29 thf(3934,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4277_transfer__nat__int__factorial__closure)). 120.83/55.29 thf(18607,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3934])). 120.83/55.29 thf(859,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ fact @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4564_fact__lt)). 120.83/55.29 thf(7882,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ fact @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])). 120.83/55.29 thf(1347,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_dvd__mult)). 120.83/55.29 thf(9584,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347])). 120.83/55.29 thf(1480,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2120_mult__1__left)). 120.83/55.29 thf(10029,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480])). 120.83/55.29 thf(704,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D)) => (((hAPP_int_int @ (div_mod_int @ B) @ D) = (hAPP_int_int @ (div_mod_int @ A) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ B)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2437_mod__diff__cong)). 120.83/55.29 thf(7305,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D)) => (((hAPP_int_int @ (div_mod_int @ B) @ D) = (hAPP_int_int @ (div_mod_int @ A) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ B)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 120.83/55.29 thf(4227,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ sRStar @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3287_SRStar__card)). 120.83/55.29 thf(19729,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ sRStar @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4227])). 120.83/55.29 thf(3164,axiom,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_mult__zero__left)). 120.83/55.29 thf(15958,plain,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3164])). 120.83/55.29 thf(3292,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2038_add__less__imp__less__left)). 120.83/55.29 thf(16406,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3292])). 120.83/55.29 thf(2519,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3028_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.29 thf(13683,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2519])). 120.83/55.29 thf(2962,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2138_diff__add__cancel)). 120.83/55.29 thf(15235,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2962])). 120.83/55.29 thf(3882,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_zprime__zdvd__zmult)). 120.83/55.29 thf(18412,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3882])). 120.83/55.29 thf(2390,axiom,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ A) = (hAPP_int_int @ number_number_of_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2823_number__of__int)). 120.83/55.29 thf(13231,plain,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ A) = (hAPP_int_int @ number_number_of_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390])). 120.83/55.29 thf(1415,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_power2__less__imp__less)). 120.83/55.29 thf(9822,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415])). 120.83/55.29 thf(3791,axiom,((! [A:$i]: ((hAPP_int_int @ succ @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3294_succ__def)). 120.83/55.29 thf(18081,plain,((! [A:$i]: ((hAPP_int_int @ succ @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3791])). 120.83/55.29 thf(1193,axiom,((! [A:$i,B:$i,C:$i]: (((zero_zero_int != C) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4686_mult__rat__cancel)). 120.83/55.29 thf(9048,plain,((! [A:$i,B:$i,C:$i]: (((~ (zero_zero_int = C)) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193])). 120.83/55.29 thf(4025,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4990_gcd__neg1__int)). 120.83/55.29 thf(18928,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4025])). 120.83/55.29 thf(2865,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1353_mult__right__less__imp__less)). 120.83/55.29 thf(14911,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2865])). 120.83/55.29 thf(4552,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zle__refl)). 120.83/55.29 thf(21051,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4552])). 120.83/55.29 thf(3266,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ B)) != (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ A))) <= ((D = C) & (A != B))) <= (E != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_add__scale__eq__noteq)). 120.83/55.29 thf(16324,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ A))) | ~ ((D = C) & ~ (A = B)) | (E = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3266])). 120.83/55.29 thf(1102,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1651_add__mult__distrib)). 120.83/55.29 thf(8751,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102])). 120.83/55.29 thf(1916,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) <=> (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1595_nat__add__right__cancel)). 120.83/55.29 thf(11597,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (A = C)) & ((A = C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916])). 120.83/55.29 thf(1174,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2110_mult__1__right)). 120.83/55.29 thf(8975,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174])). 120.83/55.29 thf(2764,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3811_fact__ge__Suc__0__nat)). 120.83/55.29 thf(14558,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2764])). 120.83/55.29 thf(4525,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_one__neq__zero)). 120.83/55.29 thf(20903,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4525])). 120.83/55.29 thf(3480,axiom,((! [A:$i,B:$i]: (((zero_zero_real = B) & (zero_zero_real = A)) <=> (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1694_realpow__two__sum__zero__iff)). 120.83/55.29 thf(17000,plain,((! [A:$i,B:$i]: ((((zero_zero_real = B) & (zero_zero_real = A)) => (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((zero_zero_real = B) & (zero_zero_real = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3480])). 120.83/55.29 thf(4329,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3475_best__odd__division__abs)). 120.83/55.29 thf(20157,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4329])). 120.83/55.29 thf(2791,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4445_number__of__le__real__of__int__iff)). 120.83/55.29 thf(14661,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2791])). 120.83/55.29 thf(1336,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) = (frct @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4712_Frct__def)). 120.83/55.29 thf(9556,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) = (frct @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336])). 120.83/55.29 thf(3772,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_zmult__assoc)). 120.83/55.29 thf(18022,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3772])). 120.83/55.29 thf(1042,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ A)) @ zero_zero_real)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5169_isCont__root__zero)). 120.83/55.29 thf(8508,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ A)) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042])). 120.83/55.29 thf(2591,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => ((? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) @ one_one_nat))) <= (B != one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4037_coprime__bezout__strong)). 120.83/55.29 thf(13936,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (? [C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) @ one_one_nat)) | (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2591])). 120.83/55.29 thf(1893,axiom,((! [A:$i,B:$i]: ((B != zero_zero_complex) => (zero_zero_complex != (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_field__power__not__zero)). 120.83/55.29 thf(11528,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_complex)) => (~ (zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893])). 120.83/55.29 thf(655,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (standardRes @ A) @ B) = (hAPP_int_int @ (div_mod_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2336_StandardRes__def)). 120.83/55.29 thf(7148,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (standardRes @ A) @ B) = (hAPP_int_int @ (div_mod_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])). 120.83/55.29 thf(2422,axiom,((hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ nat) @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2777_transfer__morphism__nat__int)). 120.83/55.29 thf(13352,plain,((hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ nat) @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2422])). 120.83/55.29 thf(4775,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2029_add__le__cancel__right)). 120.83/55.29 thf(21887,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4775])). 120.83/55.29 thf(3625,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_dvd__trans)). 120.83/55.29 thf(17486,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3625])). 120.83/55.29 thf(1998,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.29 thf(11852,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998])). 120.83/55.29 thf(1779,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1309_power__add)). 120.83/55.29 thf(11121,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779])). 120.83/55.29 thf(767,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2103_mult_Ocomm__neutral)). 120.83/55.29 thf(7535,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ one_on1684967323de_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])). 120.83/55.29 thf(2299,axiom,((! [A:$i,B:$i]: (((A != B) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_order__le__neq__implies__less)). 120.83/55.29 thf(12898,plain,((! [A:$i,B:$i]: (((~ (A = B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2299])). 120.83/55.29 thf(3005,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3515_zmult__zminus)). 120.83/55.29 thf(15402,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3005])). 120.83/55.29 thf(2647,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)) <=> (C = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1852_nat__eq__add__iff1)). 120.83/55.29 thf(14162,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)) => (C = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B))) & ((C = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2647])). 120.83/55.29 thf(1673,axiom,((! [A:$i]: ((one_on1684967323de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ A)) <= (A != zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2556_div__self)). 120.83/55.29 thf(10725,plain,((! [A:$i]: ((one_on1684967323de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ A)) | (A = zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673])). 120.83/55.29 thf(3890,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_semiring__add__number__of)). 120.83/55.29 thf(18445,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3890])). 120.83/55.29 thf(138,axiom,((one_one_real = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3582_cos__two__pi)). 120.83/55.29 thf(5406,plain,((one_one_real = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 120.83/55.29 thf(2547,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1236_power__mono)). 120.83/55.29 thf(13795,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2547])). 120.83/55.29 thf(2691,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3173_lemma__realpow__diff)). 120.83/55.29 thf(14308,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2691])). 120.83/55.29 thf(1903,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2034_add__less__imp__less__left)). 120.83/55.29 thf(11555,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903])). 120.83/55.29 thf(1558,axiom,((! [A:$i]: ((A = one_one_nat) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2316_gcd__lcm__complete__lattice__nat_Ole__bot)). 120.83/55.29 thf(10313,plain,((! [A:$i]: ((A = one_one_nat) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558])). 120.83/55.29 thf(277,axiom,((! [A:$i]: ((expi @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ (hAPP_real_real @ exp_real @ (hAPP_complex_real @ re @ A)))) @ (cis @ (hAPP_complex_real @ im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4143_expi__def)). 120.83/55.29 thf(5875,plain,((! [A:$i]: ((expi @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ (hAPP_real_real @ exp_real @ (hAPP_complex_real @ re @ A)))) @ (cis @ (hAPP_complex_real @ im @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 120.83/55.29 thf(4453,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))) @ one_one_int) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2753_Little__Fermat)). 120.83/55.29 thf(20602,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))) @ one_one_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4453])). 120.83/55.29 thf(2433,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_zero__neq__one)). 120.83/55.29 thf(13386,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433])). 120.83/55.29 thf(2418,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2439_mod__diff__left__eq)). 120.83/55.29 thf(13337,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2418])). 120.83/55.29 thf(3040,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1202_not__square__less__zero)). 120.83/55.29 thf(15503,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3040])). 120.83/55.29 thf(1342,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1385_mult__left__le__one__le)). 120.83/55.29 thf(9571,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342])). 120.83/55.29 thf(1631,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2953_of__nat__add)). 120.83/55.29 thf(10593,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631])). 120.83/55.29 thf(667,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1576_add__number__of__diff1)). 120.83/55.29 thf(7179,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 120.83/55.29 thf(4893,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4970_coprime__plus__one__int)). 120.83/55.29 thf(22282,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4893])). 120.83/55.29 thf(2389,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3898_real__root__commute)). 120.83/55.29 thf(13228,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389])). 120.83/55.29 thf(3714,axiom,((! [A:$i,B:$i]: ((xzgcd @ A @ B) = (xzgcda @ A @ B @ A @ B @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4201_xzgcd__def)). 120.83/55.29 thf(17816,plain,((! [A:$i,B:$i]: ((xzgcd @ A @ B) = (xzgcda @ A @ B @ A @ B @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3714])). 120.83/55.29 thf(178,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_mult__nonneg__nonneg)). 120.83/55.29 thf(5530,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 120.83/55.29 thf(2298,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ pls)) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3199_Suc__diff__eq__diff__pred)). 120.83/55.29 thf(12895,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ pls)) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298])). 120.83/55.29 thf(2555,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_dvd__power__le)). 120.83/55.29 thf(13814,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2555])). 120.83/55.29 thf(4319,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)) @ C)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2466_zcong__zmod)). 120.83/55.29 thf(20084,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4319])). 120.83/55.29 thf(2841,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3915_real__root__inverse)). 120.83/55.29 thf(14836,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2841])). 120.83/55.29 thf(4931,axiom,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_number__of__Pls)). 120.83/55.29 thf(22406,plain,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4931])). 120.83/55.29 thf(4013,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ zero_zero_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.29 thf(18883,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ zero_zero_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4013])). 120.83/55.29 thf(321,axiom,((! [A:$i]: ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ zero_zero_nat) @ A) = (divmod_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4209_divmod__nat__zero)). 120.83/55.29 thf(6020,plain,((! [A:$i]: ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ zero_zero_nat) @ A) = (divmod_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 120.83/55.29 thf(1820,axiom,(((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ fact_fact_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3804_Fact_Ofact__0__nat)). 120.83/55.29 thf(11255,plain,(((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ fact_fact_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820])). 120.83/55.29 thf(245,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4418_real__le__floor)). 120.83/55.29 thf(5751,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 120.83/55.29 thf(4450,axiom,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> (((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat) & (zero_zero_int = A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_power__eq__0__iff__number__of)). 120.83/55.29 thf(20585,plain,((! [A:$i,B:$i]: ((((zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) => (~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat) & (zero_zero_int = A))) & ((~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat) & (zero_zero_int = A)) => (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4450])). 120.83/55.29 thf(465,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1818_mult__diff__mult)). 120.83/55.29 thf(6482,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 120.83/55.29 thf(1854,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arcsin) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5173_isCont__arcsin)). 120.83/55.29 thf(11395,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arcsin) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854])). 120.83/55.29 thf(1274,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ arctan @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3377_arctan__monotone)). 120.83/55.29 thf(9340,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ arctan @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274])). 120.83/55.29 thf(320,axiom,((! [A:$i,B:$i]: ? [C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D)) = A) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4544_polar__Ex)). 120.83/55.29 thf(6015,plain,((! [A:$i,B:$i]: ? [C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D)) = A) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 120.83/55.29 thf(730,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1237_power__mono)). 120.83/55.29 thf(7393,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])). 120.83/55.29 thf(3561,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) => (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1918_add__imp__eq)). 120.83/55.29 thf(17257,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) => (C = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3561])). 120.83/55.29 thf(2332,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2461_zmod__simps_I3_J)). 120.83/55.29 thf(13017,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332])). 120.83/55.29 thf(3807,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1993_add__le__imp__le__left)). 120.83/55.29 thf(18145,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3807])). 120.83/55.29 thf(1210,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ D) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) @ E)) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = one_one_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_convex__bound__lt)). 120.83/55.29 thf(9090,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ D) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) @ E)) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = one_one_rat) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210])). 120.83/55.29 thf(4389,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))) <= (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2801_divmod__int__relI)). 120.83/55.29 thf(20348,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))) | ~ (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4389])). 120.83/55.29 thf(272,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ ln @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3870_DERIV__ln__divide)). 120.83/55.29 thf(5839,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ ln @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 120.83/55.29 thf(4113,axiom,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4508_zgcd__zdvd__zgcd__zmult)). 120.83/55.29 thf(19334,plain,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4113])). 120.83/55.29 thf(1000,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ one_on1645066479umeral)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.29 thf(8375,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ one_on1645066479umeral)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000])). 120.83/55.29 thf(140,axiom,((! [A:$i,B:$i]: ((hAPP_n1699378549t_bool @ (ord_at4362885an_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5075_atLeastLessThanSuc__atLeastAtMost)). 120.83/55.29 thf(5411,plain,((! [A:$i,B:$i]: ((hAPP_n1699378549t_bool @ (ord_at4362885an_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 120.83/55.29 thf(3520,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_dvd__mult)). 120.83/55.29 thf(17125,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3520])). 120.83/55.29 thf(1652,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim856651990g_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4472_le__ceiling__eq)). 120.83/55.29 thf(10652,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim856651990g_real @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim856651990g_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652])). 120.83/55.29 thf(3850,axiom,((one_one_complex = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_numeral__1__eq__1)). 120.83/55.29 thf(18312,plain,((one_one_complex = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3850])). 120.83/55.29 thf(1622,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C) = one_one_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((A = one_one_nat) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4349_coprime__common__divisor__nat)). 120.83/55.29 thf(10561,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C) = one_one_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((A = one_one_nat) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622])). 120.83/55.29 thf(4362,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2409_zmod__simps_I1_J)). 120.83/55.29 thf(20253,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4362])). 120.83/55.29 thf(404,axiom,((one_one_real = (ratreal @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4699_one__real__code)). 120.83/55.29 thf(6296,plain,((one_one_real = (ratreal @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 120.83/55.29 thf(1978,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1630_add__less__mono)). 120.83/55.29 thf(11791,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978])). 120.83/55.29 thf(3728,axiom,((! [A:$i,B:$i,C:$i]: (((? [D:$i]: ((is_int @ D) & ! [E:$i]: (((E = D) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ E)) @ A) @ C)))) <= (is_int @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4533_zcong__lineq__unique)). 120.83/55.29 thf(17859,plain,((! [A:$i,B:$i,C:$i]: (? [D:$i]: ((is_int @ D) & ! [E:$i]: ((E = D) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ E)) @ A) @ C))) | ~ (is_int @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D))) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3728])). 120.83/55.29 thf(2338,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ prime @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4203_coprime__prime__dvd__ex)). 120.83/55.29 thf(13038,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ prime @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338])). 120.83/55.29 thf(3596,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2582_div__power)). 120.83/55.29 thf(17389,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3596])). 120.83/55.29 thf(838,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3146_of__nat__0__less__iff)). 120.83/55.29 thf(7814,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])). 120.83/55.29 thf(2803,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1421_power__less__power__Suc)). 120.83/55.29 thf(14712,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2803])). 120.83/55.29 thf(2725,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2462_zdiff__zmod__left)). 120.83/55.29 thf(14420,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2725])). 120.83/55.29 thf(2825,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3543_minus__numeral__code_I6_J)). 120.83/55.29 thf(14785,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2825])). 120.83/55.29 thf(4733,axiom,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3203_mod2__Suc__Suc)). 120.83/55.29 thf(21747,plain,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4733])). 120.83/55.29 thf(2522,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_le__number__of__eq__not__less)). 120.83/55.29 thf(13709,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B))) => (~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2522])). 120.83/55.29 thf(1791,axiom,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_dvdI)). 120.83/55.29 thf(11170,plain,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791])). 120.83/55.29 thf(675,axiom,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (image_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4615_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J)). 120.83/55.29 thf(7217,plain,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (image_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])). 120.83/55.29 thf(4007,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_f1594865479ol_int @ (hAPP_f1926459811ol_int @ big_co230513141nt_int @ A) @ B))) <= (! [C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ A @ C)))) <= (is_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4945_transfer__nat__int__sum__prod__closure_I1_J)). 120.83/55.29 thf(18852,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_f1594865479ol_int @ (hAPP_f1926459811ol_int @ big_co230513141nt_int @ A) @ B))) | ~ (! [C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ A @ C)))) | ~ (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4007])). 120.83/55.29 thf(3579,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))) <=> ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ C)) | (zero_zero_complex = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1268_dvd__mult__cancel__right)). 120.83/55.29 thf(17331,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))) => ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ C)) | (zero_zero_complex = B))) & (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ C)) | (zero_zero_complex = B)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3579])). 120.83/55.29 thf(2145,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4710_Fract__number__of__quotient)). 120.83/55.29 thf(12333,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145])). 120.83/55.29 thf(4042,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5142_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J)). 120.83/55.29 thf(18984,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4042])). 120.83/55.29 thf(4869,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4996_coprime__rmult__int)). 120.83/55.29 thf(22204,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4869])). 120.83/55.29 thf(337,axiom,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_atMost_nat @ A) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5186_atLeast0AtMost)). 120.83/55.29 thf(6064,plain,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_atMost_nat @ A) = (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 120.83/55.29 thf(3105,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1760_zero__less__diff)). 120.83/55.29 thf(15751,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3105])). 120.83/55.29 thf(3905,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2522_pos__imp__zdiv__neg__iff)). 120.83/55.29 thf(18513,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3905])). 120.83/55.29 thf(852,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ B)) @ (hAPP_nat_nat @ C @ A))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))))) <= (! [D:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))) @ (hAPP_nat_nat @ C @ D))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3264_dvd_Olift__Suc__mono__less__iff)). 120.83/55.29 thf(7859,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ B)) @ (hAPP_nat_nat @ C @ A))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))))) & ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ B)) @ (hAPP_nat_nat @ C @ A))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))) | ~ (! [D:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))) @ (hAPP_nat_nat @ C @ D))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[852])). 120.83/55.29 thf(3019,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_power__mult)). 120.83/55.29 thf(15449,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3019])). 120.83/55.29 thf(335,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3734_sin__cos__eq)). 120.83/55.29 thf(6058,plain,((! [A:$i]: ((hAPP_real_real @ sin @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 120.83/55.29 thf(494,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_dvd__mult2)). 120.83/55.29 thf(6588,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 120.83/55.29 thf(2995,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <=> ((zero_zero_rat != A) | (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_sum__power2__gt__zero__iff)). 120.83/55.29 thf(15364,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (~ (zero_zero_rat = A) | ~ (B = zero_zero_rat))) & ((~ (zero_zero_rat = A) | ~ (B = zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2995])). 120.83/55.29 thf(2307,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4452_real__of__int__floor__add__one__gt)). 120.83/55.29 thf(12927,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307])). 120.83/55.29 thf(184,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hAPP_real_real @ arctan @ (hAPP_real_real @ tan @ A)) = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3623_arctan__tan)). 120.83/55.29 thf(5545,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hAPP_real_real @ arctan @ (hAPP_real_real @ tan @ A)) = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 120.83/55.29 thf(2414,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_power__commutes)). 120.83/55.29 thf(13322,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414])). 120.83/55.29 thf(2044,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2952_of__nat__le__iff)). 120.83/55.29 thf(11984,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044])). 120.83/55.29 thf(1130,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (tendsto_nat_real @ C @ D @ sequentially)) => (((? [E:$i]: ! [F:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ F)) @ (hAPP_nat_real @ A @ F))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ E) @ F)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ B))) <= (hBOOL @ (tendsto_nat_real @ A @ B @ sequentially)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5034_LIMSEQ__le)). 120.83/55.29 thf(8827,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (tendsto_nat_real @ C @ D @ sequentially)) => (((? [E:$i]: ! [F:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ C @ F)) @ (hAPP_nat_real @ A @ F))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ E) @ F)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ B))) | ~ (hBOOL @ (tendsto_nat_real @ A @ B @ sequentially)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130])). 120.83/55.29 thf(2575,axiom,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_dvdI)). 120.83/55.29 thf(13875,plain,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2575])). 120.83/55.29 thf(55,axiom,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3966_cmod__unit__one)). 120.83/55.29 thf(5142,plain,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 120.83/55.29 thf(390,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2446_mod__mod__cancel)). 120.83/55.29 thf(6250,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 120.83/55.29 thf(4711,axiom,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3268_not__neg__1)). 120.83/55.29 thf(21660,plain,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4711])). 120.83/55.29 thf(3171,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1489_one__less__power)). 120.83/55.29 thf(15979,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3171])). 120.83/55.29 thf(1243,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2673_mod__div__decomp)). 120.83/55.29 thf(9209,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243])). 120.83/55.29 thf(1167,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1714_dvd__diff__nat)). 120.83/55.29 thf(8959,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167])). 120.83/55.29 thf(629,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_zero__le__mult__iff)). 120.83/55.29 thf(7019,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])). 120.83/55.29 thf(3555,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1743_diff__cancel2)). 120.83/55.29 thf(17242,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3555])). 120.83/55.29 thf(434,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1783_real__mult__commute)). 120.83/55.29 thf(6388,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 120.83/55.29 thf(691,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3461_pi__less__4)). 120.83/55.29 thf(7269,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 120.83/55.29 thf(2679,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3620_tan__30)). 120.83/55.29 thf(14263,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2679])). 120.83/55.29 thf(761,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1441_power__strict__increasing)). 120.83/55.29 thf(7518,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])). 120.83/55.29 thf(2382,axiom,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_semiring__norm_I112_J)). 120.83/55.29 thf(13200,plain,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382])). 120.83/55.29 thf(733,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ B)) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ D) = A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4185_divides__primepow)). 120.83/55.29 thf(7410,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => (((? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ B)) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ D) = A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => (? [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ B)) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ D) = A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])). 120.83/55.29 thf(3590,axiom,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_number__of__mult)). 120.83/55.29 thf(17374,plain,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3590])). 120.83/55.29 thf(3269,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2843_of__nat__Suc)). 120.83/55.29 thf(16333,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3269])). 120.83/55.29 thf(3276,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) @ one_one_real)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ one_one_real)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3712_LIMSEQ__inverse__realpow__zero__lemma)). 120.83/55.29 thf(16356,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) @ one_one_real)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ one_one_real)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3276])). 120.83/55.29 thf(2247,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4722_one__less__Fract__iff)). 120.83/55.29 thf(12705,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247])). 120.83/55.29 thf(4657,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1306_power__add)). 120.83/55.29 thf(21444,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4657])). 120.83/55.29 thf(4111,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4279_fact__ge__zero__int)). 120.83/55.29 thf(19329,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4111])). 120.83/55.29 thf(2970,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1667_add__gr__0)). 120.83/55.29 thf(15258,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2970])). 120.83/55.29 thf(409,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A)))) <=> (~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A)))))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1533_inf__period_I4_J)). 120.83/55.29 thf(6307,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A)))) => (~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A))))) & ((~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A)))) => (~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A)))))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 120.83/55.29 thf(3515,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3206_Suc__div__eq__add3__div)). 120.83/55.29 thf(17110,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3515])). 120.83/55.29 thf(4226,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A)))) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2234_Int2_Oaux____1)). 120.83/55.29 thf(19727,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A)))) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4226])). 120.83/55.29 thf(4239,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_mult__less__cancel__right__disj)). 120.83/55.29 thf(19771,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4239])). 120.83/55.29 thf(2855,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3696_real__of__nat__div)). 120.83/55.29 thf(14879,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2855])). 120.83/55.29 thf(1647,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3929_real__root__pos__pos)). 120.83/55.29 thf(10639,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647])). 120.83/55.29 thf(3585,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sr @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2718_SRStar__SR__prop)). 120.83/55.29 thf(17363,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sr @ B))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3585])). 120.83/55.29 thf(182,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3720_sin__30)). 120.83/55.29 thf(5540,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 120.83/55.29 thf(1381,axiom,((! [A:$i]: (((hAPP_real_real @ sqrt @ A) = zero_zero_real) <=> (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3314_real__sqrt__eq__0__iff)). 120.83/55.29 thf(9688,plain,((! [A:$i]: ((((hAPP_real_real @ sqrt @ A) = zero_zero_real) => (A = zero_zero_real)) & ((A = zero_zero_real) => ((hAPP_real_real @ sqrt @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381])). 120.83/55.29 thf(2584,axiom,((! [A:$i]: ((bezw @ A @ zero_zero_nat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4155_bezw__0)). 120.83/55.29 thf(13914,plain,((! [A:$i]: ((bezw @ A @ zero_zero_nat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584])). 120.83/55.29 thf(1191,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2865_not__less__eq)). 120.83/55.29 thf(9041,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191])). 120.83/55.29 thf(2072,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1709_dvd_Oord__eq__le__trans)). 120.83/55.29 thf(12073,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072])). 120.83/55.29 thf(115,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3415_machin)). 120.83/55.29 thf(5334,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 120.83/55.29 thf(4083,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_add__number__of__eq)). 120.83/55.29 thf(19218,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4083])). 120.83/55.29 thf(4624,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1445_power__less__imp__less__exp)). 120.83/55.29 thf(21320,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4624])). 120.83/55.29 thf(1884,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4348_gcd__add__mult__nat)). 120.83/55.29 thf(11499,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884])). 120.83/55.29 thf(895,axiom,((! [A:$i,B:$i]: ((((bezw @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ zero_zero_int)) <= (B = zero_zero_nat)) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))) = (bezw @ A @ B)) <= (zero_zero_nat != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4230_bezw_Osimps)). 120.83/55.29 thf(7999,plain,((! [A:$i,B:$i]: ((((bezw @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ zero_zero_int)) | ~ (B = zero_zero_nat)) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))) = (bezw @ A @ B)) | (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[895])). 120.83/55.29 thf(18,axiom,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ ii)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3995_complex__of__real__i)). 120.83/55.29 thf(4999,plain,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ ii)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 120.83/55.29 thf(3373,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3920_real__root__lt__0__iff)). 120.83/55.29 thf(16665,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3373])). 120.83/55.29 thf(1860,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3650_real__of__nat__le__iff)). 120.83/55.29 thf(11410,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860])). 120.83/55.29 thf(3894,axiom,((! [A:$i]: ((is_int @ A) => ((A != zero_zero_int) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__less__power2)). 120.83/55.29 thf(18458,plain,((! [A:$i]: ((is_int @ A) => (((~ (A = zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (~ (A = zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3894])). 120.83/55.29 thf(2345,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3648_real__of__nat__less__iff)). 120.83/55.29 thf(13059,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345])). 120.83/55.29 thf(4835,axiom,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ B)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2135_diff__add__cancel)). 120.83/55.29 thf(22097,plain,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ B)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4835])). 120.83/55.29 thf(2083,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4498_zgcd__zminus2)). 120.83/55.29 thf(12100,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083])). 120.83/55.29 thf(3382,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2258_pinf_I10_J)). 120.83/55.29 thf(16697,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3382])). 120.83/55.29 thf(1334,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ((hAPP_nat_nat @ suc @ B) = A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2871_le__Suc__eq)). 120.83/55.29 thf(9544,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ((hAPP_nat_nat @ suc @ B) = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ((hAPP_nat_nat @ suc @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334])). 120.83/55.29 thf(374,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2442_dvd__mod__iff)). 120.83/55.30 thf(6200,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 120.83/55.30 thf(2914,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <=> ((zero_zero_nat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1848_nat__mult__dvd__cancel__disj)). 120.83/55.30 thf(15082,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((zero_zero_nat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)))) & (((zero_zero_nat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2914])). 120.83/55.30 thf(3935,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D) = one_one_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ B)) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4962_coprime__exp2__int)). 120.83/55.30 thf(18609,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D) = one_one_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ B)) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3935])). 120.83/55.30 thf(4770,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_zadd__power3)). 120.83/55.30 thf(21870,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4770])). 120.83/55.30 thf(4190,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (standardRes @ C) @ A)) @ (hAPP_int_int @ (standardRes @ C) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2320_StandardRes__prop4)). 120.83/55.30 thf(19595,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (standardRes @ C) @ A)) @ (hAPP_int_int @ (standardRes @ C) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4190])). 120.83/55.30 thf(3123,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.30 thf(15811,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3123])). 120.83/55.30 thf(3722,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2005_add__mono)). 120.83/55.30 thf(17844,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3722])). 120.83/55.30 thf(2086,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zOdd)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3096_odd__minus__even)). 120.83/55.30 thf(12110,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zOdd)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086])). 120.83/55.30 thf(3247,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4477_reals__Archimedean__6b__int)). 120.83/55.30 thf(16259,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3247])). 120.83/55.30 thf(4648,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4484_zgcd__zdvd2)). 120.83/55.30 thf(21416,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4648])). 120.83/55.30 thf(2198,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (~ (! [B:$i]: ((! [C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C) != A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4665_obtain__pos__sum)). 120.83/55.30 thf(12542,plain,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (~ (! [B:$i]: (! [C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => (~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C) = A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198])). 120.83/55.30 thf(3033,axiom,((! [A:$i,B:$i]: (((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ B)) @ (hAPP_nat_complex @ semiri2020571505omplex @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3099_of__nat__diff)). 120.83/55.30 thf(15486,plain,((! [A:$i,B:$i]: (((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ B)) @ (hAPP_nat_complex @ semiri2020571505omplex @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3033])). 120.83/55.30 thf(2173,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ A)) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3409_natceiling__add__one)). 120.83/55.30 thf(12437,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ A)) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173])). 120.83/55.30 thf(4670,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => (! [D:$i,E:$i]: ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A)))) <=> (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1535_inf__period_I4_J)). 120.83/55.30 thf(21477,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => (! [D:$i,E:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A))))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4670])). 120.83/55.30 thf(3497,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_split__mult__neg__le)). 120.83/55.30 thf(17061,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3497])). 120.83/55.30 thf(4514,axiom,((! [A:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_int) <=> ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2661_neq__one__mod__two)). 120.83/55.30 thf(20848,plain,((! [A:$i]: ((((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_int) => (~ ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int))) & ((~ ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int)) => ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4514])). 120.83/55.30 thf(507,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ inverse_inverse_rat @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4651_divide__rat__def)). 120.83/55.30 thf(6635,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ inverse_inverse_rat @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 120.83/55.30 thf(4397,axiom,((! [A:$i]: (((zero_zero_complex = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_complex @ number528085621omplex @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3218_of__nat__number__of__lemma)). 120.83/55.30 thf(20390,plain,((! [A:$i]: (((zero_zero_complex = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_complex @ number528085621omplex @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4397])). 120.83/55.30 thf(3839,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3418_zdvd__antisym__abs)). 120.83/55.30 thf(18251,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3839])). 120.83/55.30 thf(1963,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1662_power2__diff)). 120.83/55.30 thf(11751,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963])). 120.83/55.30 thf(2162,axiom,((! [A:$i,B:$i,C:$i]: (((zero_zero_int != C) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2533_div__mult__mult1)). 120.83/55.30 thf(12385,plain,((! [A:$i,B:$i,C:$i]: (((~ (zero_zero_int = C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162])). 120.83/55.30 thf(3289,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3176_lemma__realpow__diff)). 120.83/55.30 thf(16399,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3289])). 120.83/55.30 thf(352,axiom,((! [A:$i]: ((big_co1705425894at_nat @ cOMBI_nat @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ one_one_nat) @ A)) = (hAPP_nat_nat @ fact_fact_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5074_fact__altdef__nat)). 120.83/55.30 thf(6124,plain,((! [A:$i]: ((big_co1705425894at_nat @ cOMBI_nat @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ one_one_nat) @ A)) = (hAPP_nat_nat @ fact_fact_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 120.83/55.30 thf(1839,axiom,((! [A:$i]: (zero_zero_real != (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3762_real__of__nat__fact__not__zero)). 120.83/55.30 thf(11339,plain,((! [A:$i]: ~ (zero_zero_real = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839])). 120.83/55.30 thf(238,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ B)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_mult__dvd__mono)). 120.83/55.30 thf(5734,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ B)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 120.83/55.30 thf(2266,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_nat__power__less__imp__less)). 120.83/55.30 thf(12773,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266])). 120.83/55.30 thf(1114,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.30 thf(8783,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114])). 120.83/55.30 thf(4620,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2105_mult__1__right)). 120.83/55.30 thf(21310,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4620])). 120.83/55.30 thf(1330,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4441_real__of__int__le__zero__cancel__iff)). 120.83/55.30 thf(9522,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330])). 120.83/55.30 thf(3824,axiom,((pls = (hAPP_int_int @ succ @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3295_succ__Min)). 120.83/55.30 thf(18200,plain,((pls = (hAPP_int_int @ succ @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3824])). 120.83/55.30 thf(944,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_int @ number_number_of_int @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ number_number_of_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1548_left__diff__distrib__number__of)). 120.83/55.30 thf(8168,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_int @ number_number_of_int @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ number_number_of_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[944])). 120.83/55.30 thf(855,axiom,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2339_semiring__div__class_Omod__div__equality_H)). 120.83/55.30 thf(7870,plain,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[855])). 120.83/55.30 thf(4293,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (legacy_zgcd @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4494_zgcd__left__commute)). 120.83/55.30 thf(19987,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (legacy_zgcd @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4293])). 120.83/55.30 thf(4271,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_mult__pos__pos)). 120.83/55.30 thf(19914,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4271])). 120.83/55.30 thf(2585,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3468_pi__half__less__two)). 120.83/55.30 thf(13917,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585])). 120.83/55.30 thf(2751,axiom,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1664_power2__diff)). 120.83/55.30 thf(14501,plain,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2751])). 120.83/55.30 thf(482,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ A) = (hAPP_complex_real @ im @ (cis @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4147_Im__cis)). 120.83/55.30 thf(6550,plain,((! [A:$i]: ((hAPP_real_real @ sin @ A) = (hAPP_complex_real @ im @ (cis @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 120.83/55.30 thf(1427,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_add__number__of__eq)). 120.83/55.30 thf(9861,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427])). 120.83/55.30 thf(316,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ sin @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ cos @ A))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3666_sin__diff2)). 120.83/55.30 thf(6000,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ sin @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ cos @ A))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 120.83/55.30 thf(919,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_power__one__right)). 120.83/55.30 thf(8091,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[919])). 120.83/55.30 thf(4252,axiom,((! [A:$i]: (((hAPP_int_nat @ phi @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ zprime @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2775_phi__prime)). 120.83/55.30 thf(19842,plain,((! [A:$i]: (((hAPP_int_nat @ phi @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4252])). 120.83/55.30 thf(3527,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => (((C = zero_zero_int) <= (zero_zero_int != A)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2792_self__remainder)). 120.83/55.30 thf(17146,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => ((C = zero_zero_int) | (zero_zero_int = A) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3527])). 120.83/55.30 thf(2406,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3711_two__realpow__gt)). 120.83/55.30 thf(13301,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406])). 120.83/55.30 thf(987,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3526_zminus__zmod)). 120.83/55.30 thf(8329,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])). 120.83/55.30 thf(4358,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ pred @ A)) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4049_diff__bin__simps_I8_J)). 120.83/55.30 thf(20240,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ pred @ A)) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4358])). 120.83/55.30 thf(4186,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2934_of__nat__less__imp__less)). 120.83/55.30 thf(19571,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4186])). 120.83/55.30 thf(19,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4220_divmod__nat__rel)). 120.83/55.30 thf(5002,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 120.83/55.30 thf(842,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3338_real__sqrt__two__gt__zero)). 120.83/55.30 thf(7827,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])). 120.83/55.30 thf(3136,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4330_gcd__semilattice__nat_Oinf__le2)). 120.83/55.30 thf(15858,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3136])). 120.83/55.30 thf(824,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2866_add__Suc__shift)). 120.83/55.30 thf(7757,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 120.83/55.30 thf(1664,axiom,((! [A:$i,B:$i]: ((((B = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_power2__eq__imp__eq)). 120.83/55.30 thf(10699,plain,((! [A:$i,B:$i]: ((B = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664])). 120.83/55.30 thf(3207,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1968_add__0__right)). 120.83/55.30 thf(16104,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3207])). 120.83/55.30 thf(4251,axiom,((? [A:$i]: ((is_int @ A) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & ! [B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))) => (B = A)) <= (is_int @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439__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)). 120.83/55.30 thf(19835,plain,((? [A:$i]: ((is_int @ A) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & ! [B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))) => (B = A)) | ~ (is_int @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4251])). 120.83/55.30 thf(2245,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2463_zdiff__zmod__right)). 120.83/55.30 thf(12700,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245])). 120.83/55.30 thf(1759,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ abs_abs_real @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3914_real__root__abs)). 120.83/55.30 thf(11037,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ abs_abs_real @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759])). 120.83/55.30 thf(1414,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3328_real__sqrt__lt__0__iff)). 120.83/55.30 thf(9817,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414])). 120.83/55.30 thf(2952,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.30 thf(15206,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2952])). 120.83/55.30 thf(4219,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1969_add__0__right)). 120.83/55.30 thf(19703,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4219])). 120.83/55.30 thf(1148,axiom,(((code_c271388182l_size @ zero_z126310315umeral) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4058_code__numeral_Osize_I1_J)). 120.83/55.30 thf(8888,plain,(((code_c271388182l_size @ zero_z126310315umeral) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148])). 120.83/55.30 thf(4897,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B))) <=> ((A != zero_zero_int) | (B = zero_zero_nat))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3447_zero__less__zpower__abs__iff)). 120.83/55.30 thf(22293,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B))) => (~ (A = zero_zero_int) | (B = zero_zero_nat))) & ((~ (A = zero_zero_int) | (B = zero_zero_nat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4897])). 120.83/55.30 thf(4233,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ B)) @ one_one_nat))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2751_Euler_Oaux__1)). 120.83/55.30 thf(19744,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ B)) @ one_one_nat))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4233])). 120.83/55.30 thf(1717,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1943_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.30 thf(10858,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717])). 120.83/55.30 thf(952,axiom,((! [A:$i]: ((zero_zero_nat != A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4031_coprime__minus1)). 120.83/55.30 thf(8199,plain,((! [A:$i]: ((~ (zero_zero_nat = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])). 120.83/55.30 thf(2366,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3066_diff__less__Suc)). 120.83/55.30 thf(13131,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366])). 120.83/55.30 thf(31,axiom,((! [A:$i,B:$i]: ((one_one_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) <=> ((A = one_one_real) & (zero_zero_real = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3961_Complex__eq__1)). 120.83/55.30 thf(5044,plain,((! [A:$i,B:$i]: (((one_one_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) => ((A = one_one_real) & (zero_zero_real = B))) & (((A = one_one_real) & (zero_zero_real = B)) => (one_one_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 120.83/55.30 thf(2615,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_number__of__Bit0)). 120.83/55.30 thf(14043,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2615])). 120.83/55.30 thf(893,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3868_log__less__cancel__iff)). 120.83/55.30 thf(7994,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[893])). 120.83/55.30 thf(3284,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3060_Suc__leI)). 120.83/55.30 thf(16386,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3284])). 120.83/55.30 thf(1189,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4009_coprime__lmul2)). 120.83/55.30 thf(9031,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189])). 120.83/55.30 thf(2594,axiom,((! [A:$i,B:$i]: ((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = one_on1645066479umeral) <= (zero_zero_nat = B)) & (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) <= (zero_zero_nat != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1832_realpow__num__eq__if)). 120.83/55.30 thf(13949,plain,((! [A:$i,B:$i]: ((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = one_on1645066479umeral) | ~ (zero_zero_nat = B)) & (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) | (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2594])). 120.83/55.30 thf(155,axiom,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = (hAPP_nat_real @ semiri132038758t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4127_complex__Re__of__nat)). 120.83/55.30 thf(5455,plain,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = (hAPP_nat_real @ semiri132038758t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 120.83/55.30 thf(3986,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ C) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2532_zmod__eq__dvd__iff)). 120.83/55.30 thf(18784,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C))) => ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3986])). 120.83/55.30 thf(660,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1397_power__less__imp__less__base)). 120.83/55.30 thf(7161,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])). 120.83/55.30 thf(2506,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1256_zero__less__power)). 120.83/55.30 thf(13649,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2506])). 120.83/55.30 thf(1358,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [B:$i]: ((hAPP_real_real @ exp_real @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3943_exp__total)). 120.83/55.30 thf(9618,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [B:$i]: ((hAPP_real_real @ exp_real @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358])). 120.83/55.30 thf(2882,axiom,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ zero_z891286103de_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.30 thf(14978,plain,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ zero_z891286103de_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2882])). 120.83/55.30 thf(3646,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ F)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F)) @ zero_zero_int))) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_zdiv__mono2__neg__lemma)). 120.83/55.30 thf(17567,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ F)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F)) @ zero_zero_int)) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3646])). 120.83/55.30 thf(810,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_mult__mono)). 120.83/55.30 thf(7710,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 120.83/55.30 thf(4570,axiom,((! [A:$i]: ((is_int @ A) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ A) = one_one_int) <= (zero_zero_int != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2553_div__self)). 120.83/55.30 thf(21138,plain,((! [A:$i]: ((is_int @ A) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ A) = one_one_int) | (zero_zero_int = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4570])). 120.83/55.30 thf(3700,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_int)) & (((hAPP_int_int @ number_number_of_int @ A) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3281_int__nat__number__of)). 120.83/55.30 thf(17773,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_int)) & (((hAPP_int_int @ number_number_of_int @ A) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3700])). 120.83/55.30 thf(232,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_dvd__trans)). 120.83/55.30 thf(5719,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 120.83/55.30 thf(3720,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1580_diff__bin__simps_I4_J)). 120.83/55.30 thf(17838,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3720])). 120.83/55.30 thf(4833,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_mult__dvd__mono)). 120.83/55.30 thf(22092,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4833])). 120.83/55.30 thf(1653,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3040_zadd__int__left)). 120.83/55.30 thf(10657,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653])). 120.83/55.30 thf(2076,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.30 thf(12083,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076])). 120.83/55.30 thf(4475,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit0 @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_rel__simps_I25_J)). 120.83/55.30 thf(20706,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit0 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit0 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4475])). 120.83/55.30 thf(3403,axiom,((! [A:$i,B:$i]: (((B = zero_zero_nat) | (zero_zero_nat = A)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1621_mult__is__0)). 120.83/55.30 thf(16751,plain,((! [A:$i,B:$i]: ((((B = zero_zero_nat) | (zero_zero_nat = A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = zero_zero_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (zero_zero_nat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3403])). 120.83/55.30 thf(4930,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ zero_zero_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2457_zdiv__zero)). 120.83/55.30 thf(22403,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ zero_zero_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4930])). 120.83/55.30 thf(3810,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_zdvd__imp__le)). 120.83/55.30 thf(18151,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3810])). 120.83/55.30 thf(2625,axiom,((! [A:$i,B:$i]: ((zero_zero_real != B) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ B)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ sqrt @ B) @ A))) <= (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ B))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3880_DERIV__real__sqrt__generic)). 120.83/55.30 thf(14075,plain,((! [A:$i,B:$i]: ((~ (zero_zero_real = B)) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ B)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ sqrt @ B) @ A))) | ~ (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ B))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2625])). 120.83/55.30 thf(1638,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_dvd__triv__right)). 120.83/55.30 thf(10612,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638])). 120.83/55.30 thf(2276,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4432_ge__one__powr__ge__zero)). 120.83/55.30 thf(12809,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276])). 120.83/55.30 thf(4142,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_unique__quotient__lemma)). 120.83/55.30 thf(19428,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4142])). 120.83/55.30 thf(2561,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.30 thf(13829,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561])). 120.83/55.30 thf(989,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2194_zero__less__double__add__iff__zero__less__single__add)). 120.83/55.30 thf(8334,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[989])). 120.83/55.30 thf(1423,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2415_zmod__simps_I2_J)). 120.83/55.30 thf(9849,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423])). 120.83/55.30 thf(2211,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4404_powr__gt__zero)). 120.83/55.30 thf(12591,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211])). 120.83/55.30 thf(4121,axiom,((! [A:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ A) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2822_number__of__int)). 120.83/55.30 thf(19361,plain,((! [A:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ A) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4121])). 120.83/55.30 thf(594,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_dvd__mult)). 120.83/55.30 thf(6915,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 120.83/55.30 thf(2231,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2007_add__mono)). 120.83/55.30 thf(12650,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231])). 120.83/55.30 thf(3871,axiom,((one_one_nat = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_nat__numeral__1__eq__1)). 120.83/55.30 thf(18383,plain,((one_one_nat = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3871])). 120.83/55.30 thf(1748,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2460_zmod__zmult1__eq)). 120.83/55.30 thf(11003,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748])). 120.83/55.30 thf(3183,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3035_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.30 thf(16016,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3183])). 120.83/55.30 thf(4299,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1209_zero__le__one)). 120.83/55.30 thf(20020,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4299])). 120.83/55.30 thf(793,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) != (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3462_pi__half__neq__two)). 120.83/55.30 thf(7640,plain,((~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])). 120.83/55.30 thf(3354,axiom,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ fact @ A)))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4570_euclid__bound)). 120.83/55.30 thf(16597,plain,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ fact @ A)))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3354])). 120.83/55.30 thf(3613,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_quartic__square__square)). 120.83/55.30 thf(17440,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3613])). 120.83/55.30 thf(2251,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ D)) => ((? [E:$i]: ((is_int @ E) & ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ E) @ D)))) <= ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int))) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4531_int__relprime__power__divisors)). 120.83/55.30 thf(12715,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ D)) => (? [E:$i]: ((is_int @ E) & ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ E) @ D))) | ~ ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int))) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2251])). 120.83/55.30 thf(4438,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ B)) <= (! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ C))) <= (is_int @ D))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2217_int__le__induct)). 120.83/55.30 thf(20550,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ B)) | ~ (! [D:$i]: (((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ one_one_int)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ C)) | ~ (is_int @ D))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4438])). 120.83/55.30 thf(4250,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.30 thf(19832,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4250])). 120.83/55.30 thf(172,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ D))))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A)) => (((hAPP_real_real @ B @ A) = (hAPP_real_real @ B @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ D)))) <= (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ E) @ zero_zero_real)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5177_DERIV__isconst2)). 120.83/55.30 thf(5507,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ D))))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A)) => (((hAPP_real_real @ B @ A) = (hAPP_real_real @ B @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ D)))) | ~ (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ E) @ zero_zero_real)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 120.83/55.30 thf(46,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ A)) = (hAPP_complex_complex @ uminus473333897omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3978_complex__i__mult__minus)). 120.83/55.30 thf(5102,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ A)) = (hAPP_complex_complex @ uminus473333897omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 120.83/55.30 thf(4373,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1451_power__strict__increasing__iff)). 120.83/55.30 thf(20284,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4373])). 120.83/55.30 thf(3902,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s1) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096)). 120.83/55.30 thf(18503,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s1) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3902])). 120.83/55.30 thf(4392,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3521_uminus__dvd__conv_I2_J)). 120.83/55.30 thf(20367,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4392])). 120.83/55.30 thf(2599,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_even__less__0__iff)). 120.83/55.30 thf(13971,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2599])). 120.83/55.30 thf(2088,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3406_real__sqrt__ge__abs1)). 120.83/55.30 thf(12115,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088])). 120.83/55.30 thf(3055,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2982_of__nat__power)). 120.83/55.30 thf(15563,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3055])). 120.83/55.30 thf(527,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4004_DERIV__neg__imp__decreasing)). 120.83/55.30 thf(6696,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])). 120.83/55.30 thf(195,axiom,(((hAPP_complex_real @ im @ zero_zero_complex) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4096_Im_Ozero)). 120.83/55.30 thf(5594,plain,(((hAPP_complex_real @ im @ zero_zero_complex) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 120.83/55.30 thf(1799,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4613_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J)). 120.83/55.30 thf(11191,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799])). 120.83/55.30 thf(3997,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3120_power__gt1)). 120.83/55.30 thf(18821,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3997])). 120.83/55.30 thf(3444,axiom,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ A) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4138_cmod__def)). 120.83/55.30 thf(16880,plain,((! [A:$i]: ((hAPP_complex_real @ norm_norm_complex @ A) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3444])). 120.83/55.30 thf(2489,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = A) & ((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat)) <=> (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_power__eq__0__iff__number__of)). 120.83/55.30 thf(13583,plain,((! [A:$i,B:$i]: ((((zero_zero_nat = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) & ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) => ((zero_zero_nat = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489])). 120.83/55.30 thf(3707,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) @ (hAPP_int_int @ number_number_of_int @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1856_Wilson__Russ)). 120.83/55.30 thf(17799,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) @ (hAPP_int_int @ number_number_of_int @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3707])). 120.83/55.30 thf(4771,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_power__le__dvd)). 120.83/55.30 thf(21873,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4771])). 120.83/55.30 thf(2813,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1656_mult__le__mono)). 120.83/55.30 thf(14745,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2813])). 120.83/55.30 thf(3965,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ F) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_zdiv__mono2__lemma)). 120.83/55.30 thf(18705,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E)) @ F))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ F) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3965])). 120.83/55.30 thf(3015,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2732_StandardRes__SRStar__prop1a)). 120.83/55.30 thf(15439,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3015])). 120.83/55.30 thf(1035,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1647_add__leD2)). 120.83/55.30 thf(8491,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035])). 120.83/55.30 thf(2497,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) <=> (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3048_less__Suc0)). 120.83/55.30 thf(13622,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) => (zero_zero_nat = A)) & ((zero_zero_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497])). 120.83/55.30 thf(1228,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ inverse_inverse_real @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3838_real__mult__inverse__cancel2)). 120.83/55.30 thf(9158,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ inverse_inverse_real @ C)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228])). 120.83/55.30 thf(274,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ uminus_uminus_real @ A))) & ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) => ((hAPP_real_real @ abs_abs_real @ A) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3494_abs__real__def)). 120.83/55.30 thf(5843,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ uminus_uminus_real @ A))) & ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) => ((hAPP_real_real @ abs_abs_real @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 120.83/55.30 thf(3748,axiom,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_zcong__zmult__self)). 120.83/55.30 thf(17945,plain,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3748])). 120.83/55.30 thf(1234,axiom,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) & ((hAPP_real_real @ cos @ A) = zero_zero_real) & ! [B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (zero_zero_real = (hAPP_real_real @ cos @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (A = B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3593_cos__is__zero)). 120.83/55.30 thf(9177,plain,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) & ((hAPP_real_real @ cos @ A) = zero_zero_real) & ! [B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (zero_zero_real = (hAPP_real_real @ cos @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (A = B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234])). 120.83/55.30 thf(3219,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4503_zgcd__zmult__distrib2__abs)). 120.83/55.30 thf(16159,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3219])). 120.83/55.30 thf(4279,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ A @ (hAPP_int_int @ B @ C)) = (hAPP_int_int @ (hAPP_f1356864277nt_int @ (hAPP_f747162069nt_int @ cOMBB_int_int_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U)). 120.83/55.30 thf(19946,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ A @ (hAPP_int_int @ B @ C)) = (hAPP_int_int @ (hAPP_f1356864277nt_int @ (hAPP_f747162069nt_int @ cOMBB_int_int_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4279])). 120.83/55.30 thf(1085,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) <=> (((B = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = A)) | ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3052_one__is__add)). 120.83/55.30 thf(8683,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (((B = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = A)) | ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = B)))) & ((((B = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = A)) | ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) & (zero_zero_nat = B))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085])). 120.83/55.30 thf(2373,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = A) & (zero_zero_nat != B)) <=> (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1814_nat__power__eq__0__iff)). 120.83/55.30 thf(13158,plain,((! [A:$i,B:$i]: ((((zero_zero_nat = A) & ~ (zero_zero_nat = B)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) & ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) => ((zero_zero_nat = A) & ~ (zero_zero_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373])). 120.83/55.30 thf(1672,axiom,((! [A:$i,B:$i]: ((A != B) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1721_dvd_Oless__imp__not__eq)). 120.83/55.30 thf(10721,plain,((! [A:$i,B:$i]: (~ (A = B) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672])). 120.83/55.30 thf(3556,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1978_add__0)). 120.83/55.30 thf(17245,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3556])). 120.83/55.30 thf(705,axiom,((zero_z126310315umeral != one_on1645066479umeral)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_one__neq__zero)). 120.83/55.30 thf(7308,plain,((~ (zero_z126310315umeral = one_on1645066479umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])). 120.83/55.30 thf(407,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_dvd__triv__right)). 120.83/55.30 thf(6303,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 120.83/55.30 thf(2859,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real)) <=> ((zero_zero_real = B) & (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_sum__power2__le__zero__iff)). 120.83/55.30 thf(14889,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real)) => ((zero_zero_real = B) & (A = zero_zero_real))) & (((zero_zero_real = B) & (A = zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2859])). 120.83/55.30 thf(269,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A))) @ (hAPP_real_real @ uminus_uminus_real @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3498_ln__one__minus__pos__upper__bound)). 120.83/55.30 thf(5826,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A))) @ (hAPP_real_real @ uminus_uminus_real @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 120.83/55.30 thf(4818,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4978_gcd__int_Oleft__commute)). 120.83/55.30 thf(22035,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4818])). 120.83/55.30 thf(3542,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | (B = A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1733_less__eq__real__def)). 120.83/55.30 thf(17200,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | (B = A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3542])). 120.83/55.30 thf(4028,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ B)) @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1525_zcong__zdiff)). 120.83/55.30 thf(18937,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ B)) @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4028])). 120.83/55.30 thf(2508,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3011_power__Suc)). 120.83/55.30 thf(13654,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2508])). 120.83/55.30 thf(711,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.30 thf(7325,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])). 120.83/55.30 thf(106,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2081_eq__iff__diff__eq__0)). 120.83/55.30 thf(5302,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = zero_zero_real) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 120.83/55.30 thf(1909,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = one_one_nat) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat)) <=> (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4352_coprime__mul__eq__nat)). 120.83/55.30 thf(11570,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = one_one_nat) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat)) => (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))) & ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C) = one_one_nat) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909])). 120.83/55.30 thf(1080,axiom,((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3276_neg__number__of__Min)). 120.83/55.30 thf(8672,plain,((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080])). 120.83/55.30 thf(4290,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) => (C = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1916_add__imp__eq)). 120.83/55.30 thf(19980,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) => (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4290])). 120.83/55.30 thf(1681,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1511_number__of__diff)). 120.83/55.30 thf(10756,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681])). 120.83/55.30 thf(2978,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_878_comm__semiring__class_Odistrib)). 120.83/55.30 thf(15296,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2978])). 120.83/55.30 thf(448,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ A) @ B) @ C) = (hAPP_f448129468l_bool @ A @ (hAPP_i1948725293t_bool @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo)). 120.83/55.30 thf(6432,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ A) @ B) @ C) = (hAPP_f448129468l_bool @ A @ (hAPP_i1948725293t_bool @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 120.83/55.30 thf(3950,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1426_power__gt1__lemma)). 120.83/55.30 thf(18649,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3950])). 120.83/55.30 thf(215,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_real_real @ exp_real @ B) = (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3827_exp__inj__iff)). 120.83/55.30 thf(5655,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_real_real @ exp_real @ B) = (hAPP_real_real @ exp_real @ A))) & (((hAPP_real_real @ exp_real @ B) = (hAPP_real_real @ exp_real @ A)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 120.83/55.30 thf(4505,axiom,(((t = zero_zero_int) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J)). 120.83/55.30 thf(20819,plain,(((t = zero_zero_int) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4505])). 120.83/55.30 thf(3106,axiom,((! [A:$i]: ((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (A = (hAPP_real_real @ tan @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3626_tan__total__pos)). 120.83/55.30 thf(15756,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (A = (hAPP_real_real @ tan @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3106])). 120.83/55.30 thf(3767,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_less__special_I4_J)). 120.83/55.30 thf(18004,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3767])). 120.83/55.30 thf(1601,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1347_mult__less__imp__less__right)). 120.83/55.30 thf(10490,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601])). 120.83/55.30 thf(2303,axiom,((! [A:$i,B:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2494_mod__mult__self1__is__0)). 120.83/55.30 thf(12910,plain,((! [A:$i,B:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303])). 120.83/55.30 thf(363,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B))) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2483_div__dvd__div)). 120.83/55.30 thf(6163,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B))))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 120.83/55.30 thf(902,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ one_one_rat) @ A) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_power__one)). 120.83/55.30 thf(8026,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ one_one_rat) @ A) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])). 120.83/55.30 thf(2097,axiom,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1395_zero__less__two)). 120.83/55.30 thf(12147,plain,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097])). 120.83/55.30 thf(1705,axiom,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2332_mod__div__trivial)). 120.83/55.30 thf(10826,plain,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705])). 120.83/55.30 thf(1698,axiom,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3226_nat__2)). 120.83/55.30 thf(10808,plain,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698])). 120.83/55.30 thf(1371,axiom,((! [A:$i]: ((A = zero_zero_real) <=> (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1896_zero__reorient)). 120.83/55.30 thf(9658,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371])). 120.83/55.30 thf(4708,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (! [E:$i]: ((is_int @ E) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D)) @ A))))) <= (! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: (((E != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B))) <= (is_int @ G)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5102_aset_I10_J)). 120.83/55.30 thf(21641,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (! [E:$i]: ((is_int @ E) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A)))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D)) @ A))))) | ~ (! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: (~ (E = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)) | ~ (is_int @ G)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4708])). 120.83/55.30 thf(3733,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ one_one_int)) <=> ((hAPP_int_int @ abs_abs_int @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3425_zdvd1__eq)). 120.83/55.30 thf(17887,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ one_one_int)) => ((hAPP_int_int @ abs_abs_int @ A) = one_one_int)) & (((hAPP_int_int @ abs_abs_int @ A) = one_one_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3733])). 120.83/55.30 thf(634,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ A)) @ A) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3850_sqrt__divide__self__eq)). 120.83/55.30 thf(7063,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ A)) @ A) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])). 120.83/55.30 thf(4054,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4747_nat__number__of__Bit0)). 120.83/55.30 thf(19058,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4054])). 120.83/55.30 thf(576,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ tan) @ A)) <= ((hAPP_real_real @ cos @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5160_isCont__tan)). 120.83/55.30 thf(6848,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ tan) @ A)) | ((hAPP_real_real @ cos @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 120.83/55.30 thf(935,axiom,((one_on1684967323de_int != zero_z891286103de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_zero__neq__one)). 120.83/55.30 thf(8145,plain,((~ (one_on1684967323de_int = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[935])). 120.83/55.30 thf(4812,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)) @ zero_zero_int)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2656_zmult2__lemma__aux2)). 120.83/55.30 thf(22015,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)) @ zero_zero_int)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4812])). 120.83/55.30 thf(2694,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1349_mult__right__less__imp__less)). 120.83/55.30 thf(14317,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2694])). 120.83/55.30 thf(446,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sin @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3644_sin__le__one)). 120.83/55.30 thf(6427,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sin @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 120.83/55.30 thf(2745,axiom,((! [A:$i,B:$i,C:$i]: (((B = zero_zero_nat) | (C = A)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1623_mult__cancel2)). 120.83/55.30 thf(14477,plain,((! [A:$i,B:$i,C:$i]: ((((B = zero_zero_nat) | (C = A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => ((B = zero_zero_nat) | (C = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2745])). 120.83/55.30 thf(3944,axiom,((! [A:$i]: (A = (hAPP_int_nat @ nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2854_nat__int)). 120.83/55.30 thf(18632,plain,((! [A:$i]: (A = (hAPP_int_nat @ nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3944])). 120.83/55.30 thf(826,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ B))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_mult__less__cancel__left__disj)). 120.83/55.30 thf(7762,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ B))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ B))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 120.83/55.30 thf(3729,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ B))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))))) & (((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add__nat__number__of)). 120.83/55.30 thf(17870,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ B))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))))) & (((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3729])). 120.83/55.30 thf(2999,axiom,((! [A:$i,B:$i]: (is_int @ (hAPP_nat_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint)). 120.83/55.30 thf(15383,plain,((! [A:$i,B:$i]: (is_int @ (hAPP_nat_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2999])). 120.83/55.30 thf(16,axiom,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3967_complex__inverse)). 120.83/55.30 thf(4994,plain,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ uminus_uminus_real @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 120.83/55.30 thf(1348,axiom,((! [A:$i,B:$i,C:$i]: ((C = A) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1931_add__right__cancel)). 120.83/55.30 thf(9586,plain,((! [A:$i,B:$i,C:$i]: (((C = A) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348])). 120.83/55.30 thf(2476,axiom,((is_int @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_t____)). 120.83/55.30 thf(13536,plain,((is_int @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476])). 120.83/55.30 thf(484,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2301_mult_Odiff__left)). 120.83/55.30 thf(6556,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 120.83/55.30 thf(3211,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) => (A = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2279_mult__left__cancel)). 120.83/55.30 thf(16123,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) => (A = B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3211])). 120.83/55.30 thf(3669,axiom,((! [A:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = one_one_int) | ((hAPP_int_int @ number_number_of_int @ min) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1685_neg__one__power)). 120.83/55.30 thf(17659,plain,((! [A:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = one_one_int) | ((hAPP_int_int @ number_number_of_int @ min) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3669])). 120.83/55.30 thf(2549,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_mult__strict__left__mono__neg)). 120.83/55.30 thf(13799,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549])). 120.83/55.30 thf(3080,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1431_power__gt1__lemma)). 120.83/55.30 thf(15665,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3080])). 120.83/55.30 thf(2539,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1768_diff__add__assoc2)). 120.83/55.30 thf(13763,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2539])). 120.83/55.30 thf(3303,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_semiring__mult__number__of)). 120.83/55.30 thf(16440,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => (((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3303])). 120.83/55.30 thf(1506,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.30 thf(10116,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506])). 120.83/55.30 thf(23,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (of_real_complex @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3990_Complex__mult__complex__of__real)). 120.83/55.30 thf(5021,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (of_real_complex @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 120.83/55.30 thf(4480,axiom,((! [A:$i,B:$i]: ((((hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (posDivAlg @ A @ B)) <= (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A) = (posDivAlg @ A @ B)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2679_posDivAlg_Osimps)). 120.83/55.30 thf(20721,plain,((! [A:$i,B:$i]: ((((hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (posDivAlg @ A @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A) = (posDivAlg @ A @ B)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4480])). 120.83/55.30 thf(531,axiom,((! [A:$i]: ((hAPP_real_real @ arctan @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ arctan @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3481_arctan__minus)). 120.83/55.30 thf(6708,plain,((! [A:$i]: ((hAPP_real_real @ arctan @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ arctan @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 120.83/55.30 thf(1136,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.30 thf(8852,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136])). 120.83/55.30 thf(2545,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.30 thf(13789,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2545])). 120.83/55.30 thf(4823,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2084_diff__self)). 120.83/55.30 thf(22060,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4823])). 120.83/55.30 thf(2520,axiom,((! [A:$i]: ((A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3780_odd__nat__div__two__times__two__plus__one)). 120.83/55.30 thf(13686,plain,((! [A:$i]: ((A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520])). 120.83/55.30 thf(2178,axiom,((! [A:$i]: ((A = zero_zero_nat) <=> ((hAPP_nat_int @ semiri1621563631at_int @ A) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2975_int__eq__0__conv)). 120.83/55.30 thf(12461,plain,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_nat_int @ semiri1621563631at_int @ A) = zero_zero_int)) & (((hAPP_nat_int @ semiri1621563631at_int @ A) = zero_zero_int) => (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178])). 120.83/55.30 thf(2242,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4435_powr__divide)). 120.83/55.30 thf(12692,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242])). 120.83/55.30 thf(3244,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4728_Fract__le__one__iff)). 120.83/55.30 thf(16247,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3244])). 120.83/55.30 thf(1684,axiom,((! [A:$i]: ((quickcheck_int_of @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) = (hAPP_int_int @ number_number_of_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4256_int__of__number)). 120.83/55.30 thf(10765,plain,((! [A:$i]: ((quickcheck_int_of @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) = (hAPP_int_int @ number_number_of_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684])). 120.83/55.30 thf(3322,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.30 thf(16497,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3322])). 120.83/55.30 thf(2931,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1627_trans__less__add1)). 120.83/55.30 thf(15137,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2931])). 120.83/55.30 thf(2057,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3339_real__sqrt__two__gt__one)). 120.83/55.30 thf(12025,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057])). 120.83/55.30 thf(3601,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.30 thf(17406,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3601])). 120.83/55.30 thf(2896,axiom,((! [A:$i,B:$i]: (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))) = (bezw @ A @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4231_bezw__non__0)). 120.83/55.30 thf(15018,plain,((! [A:$i,B:$i]: (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ B @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))) = (bezw @ A @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2896])). 120.83/55.30 thf(3843,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5137_Divides_Otransfer__int__nat__function__closures_I1_J)). 120.83/55.30 thf(18268,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3843])). 120.83/55.30 thf(2810,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1754_le__diff__iff)). 120.83/55.30 thf(14735,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2810])). 120.83/55.30 thf(2109,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1790_real__mult__order)). 120.83/55.30 thf(12196,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109])). 120.83/55.30 thf(4861,axiom,((pls = (hAPP_int_int @ bit0 @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Bit0__Pls)). 120.83/55.30 thf(22186,plain,((pls = (hAPP_int_int @ bit0 @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4861])). 120.83/55.30 thf(2221,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.30 thf(12618,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221])). 120.83/55.30 thf(3035,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1632_add__lessD1)). 120.83/55.30 thf(15491,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3035])). 120.83/55.30 thf(4667,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => ((hAPP_int_int @ (inv @ B) @ A) != zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2139_inv__not__0)). 120.83/55.30 thf(21470,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (~ ((hAPP_int_int @ (inv @ B) @ A) = zero_zero_int))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4667])). 120.83/55.30 thf(4583,axiom,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4488_zgcd__1)). 120.83/55.30 thf(21178,plain,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4583])). 120.83/55.30 thf(573,axiom,((! [A:$i,B:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_complex_complex @ invers1449016382omplex @ (rcis @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4267_rcis__inverse)). 120.83/55.30 thf(6833,plain,((! [A:$i,B:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_complex_complex @ invers1449016382omplex @ (rcis @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])). 120.83/55.30 thf(4107,axiom,((! [A:$i]: (pls = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ pls) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mult__Pls)). 120.83/55.30 thf(19312,plain,((! [A:$i]: (pls = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ pls) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4107])). 120.83/55.30 thf(1944,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4068_complex__cnj__mult)). 120.83/55.30 thf(11683,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944])). 120.83/55.30 thf(1220,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2373_mod__0)). 120.83/55.30 thf(9132,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220])). 120.83/55.30 thf(2563,axiom,((! [A:$i,B:$i]: (((B != zero_zero_rat) | (A != zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_sum__squares__gt__zero__iff)). 120.83/55.30 thf(13835,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_rat) | ~ (A = zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B)))) => (~ (B = zero_zero_rat) | ~ (A = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563])). 120.83/55.30 thf(3990,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2417_mod__add__eq)). 120.83/55.30 thf(18799,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3990])). 120.83/55.30 thf(1169,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ one_on1645066479umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1470_power__Suc__less)). 120.83/55.30 thf(8964,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ one_on1645066479umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169])). 120.83/55.30 thf(11,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3965_complex__mult)). 120.83/55.30 thf(4979,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 120.83/55.30 thf(73,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2374_mod__0)). 120.83/55.30 thf(5201,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 120.83/55.30 thf(2600,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_dvd__power__le)). 120.83/55.30 thf(13976,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2600])). 120.83/55.30 thf(4852,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_less__number__of)). 120.83/55.30 thf(22159,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4852])). 120.83/55.30 thf(3413,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1713_dvd_Oorder__trans)). 120.83/55.30 thf(16793,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3413])). 120.83/55.30 thf(3252,axiom,(((hAPP_n1108039445umeral @ semiri1619134803umeral @ zero_zero_nat) = zero_z126310315umeral)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2925_of__nat__0)). 120.83/55.30 thf(16274,plain,(((hAPP_n1108039445umeral @ semiri1619134803umeral @ zero_zero_nat) = zero_z126310315umeral)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3252])). 120.83/55.30 thf(2735,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1866_add__nonneg__pos)). 120.83/55.30 thf(14452,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2735])). 120.83/55.30 thf(3911,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (nat_tsub @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3186_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)). 120.83/55.30 thf(18530,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (nat_tsub @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3911])). 120.83/55.30 thf(365,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3640_sin__npi2)). 120.83/55.30 thf(6168,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 120.83/55.30 thf(440,axiom,((! [A:$i,B:$i]: (((A = (hAPP_int_nat @ nat @ (archim1246769320r_real @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4035_floor__eq4)). 120.83/55.30 thf(6402,plain,((! [A:$i,B:$i]: ((A = (hAPP_int_nat @ nat @ (archim1246769320r_real @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 120.83/55.30 thf(3050,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3067_mult__Suc)). 120.83/55.30 thf(15546,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3050])). 120.83/55.30 thf(2392,axiom,((! [A:$i,B:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2133_add__diff__cancel)). 120.83/55.30 thf(13237,plain,((! [A:$i,B:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392])). 120.83/55.30 thf(1826,axiom,((is_int @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint)). 120.83/55.30 thf(11284,plain,((is_int @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826])). 120.83/55.30 thf(2607,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.30 thf(14013,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2607])). 120.83/55.30 thf(3621,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4961_gcd__dvd2__int)). 120.83/55.30 thf(17477,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3621])). 120.83/55.30 thf(863,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <=> ((B != A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1701_dvd_Oless__le)). 120.83/55.30 thf(7891,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ (B = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) & ((~ (B = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[863])). 120.83/55.30 thf(3150,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4409_powr__less__cancel__iff)). 120.83/55.30 thf(15901,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3150])). 120.83/55.30 thf(3010,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2270_pinf_I9_J)). 120.83/55.30 thf(15417,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3010])). 120.83/55.30 thf(4844,axiom,((! [A:$i,B:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => ((hAPP_int_int @ number_number_of_int @ min) = (hAPP_int_int @ (legendre @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)) => ((hAPP_int_int @ (legendre @ A) @ B) = one_one_int))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) => (zero_zero_int = (hAPP_int_int @ (legendre @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1686_Legendre__def)). 120.83/55.30 thf(22129,plain,((! [A:$i,B:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => ((hAPP_int_int @ number_number_of_int @ min) = (hAPP_int_int @ (legendre @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)) => ((hAPP_int_int @ (legendre @ A) @ B) = one_one_int))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) => (zero_zero_int = (hAPP_int_int @ (legendre @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4844])). 120.83/55.30 thf(2468,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1777_le__diff__conv)). 120.83/55.30 thf(13515,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2468])). 120.83/55.30 thf(3308,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((is_int @ B) & (is_int @ D) & (is_int @ F)) => ((((zero_zero_int != D) => (F = B)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ E) @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2790_unique__remainder)). 120.83/55.30 thf(16455,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((is_int @ B) & (is_int @ D) & (is_int @ F)) => (((~ (zero_zero_int = D)) => (F = B)) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ E) @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3308])). 120.83/55.30 thf(3343,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1469_power__Suc__less)). 120.83/55.30 thf(16569,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3343])). 120.83/55.30 thf(1732,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.30 thf(10926,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732])). 120.83/55.30 thf(3278,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2051_add__strict__mono)). 120.83/55.30 thf(16360,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3278])). 120.83/55.30 thf(4696,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zle__trans)). 120.83/55.30 thf(21576,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4696])). 120.83/55.30 thf(2566,axiom,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A)) = zero_zero_real) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3752_lemma__STAR__cos)). 120.83/55.30 thf(13853,plain,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A)) = zero_zero_real) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2566])). 120.83/55.30 thf(3661,axiom,(((hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ s) @ one_one_int)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1836__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096)). 120.83/55.30 thf(17638,plain,(((hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ s) @ one_one_int)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3661])). 120.83/55.30 thf(3184,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1577_add__number__of__diff1)). 120.83/55.30 thf(16019,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3184])). 120.83/55.30 thf(3260,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_le__imp__power__dvd)). 120.83/55.30 thf(16301,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3260])). 120.83/55.30 thf(113,axiom,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ one_one_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_one__dvd)). 120.83/55.30 thf(5330,plain,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ one_one_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 120.83/55.30 thf(1366,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_power__one__right)). 120.83/55.30 thf(9641,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366])). 120.83/55.30 thf(997,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_power__commutes)). 120.83/55.30 thf(8358,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])). 120.83/55.30 thf(100,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ real_nat @ A))) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3677_sin__2npi)). 120.83/55.30 thf(5285,plain,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ real_nat @ A))) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 120.83/55.30 thf(914,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> ((A != B) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_real__less__def)). 120.83/55.30 thf(8073,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (~ (A = B) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))) & ((~ (A = B) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])). 120.83/55.30 thf(36,axiom,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ zero_zero_real) = (of_real_complex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3988_complex__of__real__def)). 120.83/55.30 thf(5066,plain,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ zero_zero_real) = (of_real_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 120.83/55.30 thf(4947,axiom,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ A) = one_one_int)) & ((A != zero_zero_nat) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ A) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1432_power__0__left)). 120.83/55.30 thf(22464,plain,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ A) = one_one_int)) & ((~ (A = zero_zero_nat)) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4947])). 120.83/55.30 thf(4779,axiom,((! [A:$i]: ((? [B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = A)) <=> (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3787_odd__Suc__mult__two__ex)). 120.83/55.30 thf(21905,plain,((! [A:$i]: (((? [B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = A)) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (? [B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4779])). 120.83/55.30 thf(3956,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2940_less__imp__of__nat__less)). 120.83/55.30 thf(18668,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3956])). 120.83/55.30 thf(3447,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3325_real__sqrt__ge__0__iff)). 120.83/55.30 thf(16893,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3447])). 120.83/55.30 thf(2602,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.30 thf(13981,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2602])). 120.83/55.30 thf(3054,axiom,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)))) & (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4479_real__lb__ub__int)). 120.83/55.30 thf(15559,plain,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)))) & (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3054])). 120.83/55.30 thf(4680,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)). 120.83/55.30 thf(21511,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4680])). 120.83/55.30 thf(964,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)) <=> (C = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1932_add__right__cancel)). 120.83/55.30 thf(8238,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)) => (C = A)) & ((C = A) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])). 120.83/55.30 thf(1511,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1792_real__mult__le__cancel__iff2)). 120.83/55.30 thf(10131,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511])). 120.83/55.30 thf(977,axiom,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ prime @ A))) => (? [B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4208_not__prime__ex__mk)). 120.83/55.30 thf(8297,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ prime @ A))) => (? [B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])). 120.83/55.30 thf(769,axiom,((! [A:$i]: ((zero_zero_real = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_dvd__0__left)). 120.83/55.30 thf(7540,plain,((! [A:$i]: ((zero_zero_real = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])). 120.83/55.30 thf(108,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2327_mod__mod__trivial)). 120.83/55.30 thf(5313,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 120.83/55.30 thf(2257,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1329_mult__right__le__imp__le)). 120.83/55.30 thf(12741,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257])). 120.83/55.30 thf(3091,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1759_diff__less)). 120.83/55.30 thf(15702,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3091])). 120.83/55.30 thf(3155,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arccos) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5172_isCont__arccos)). 120.83/55.30 thf(15915,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arccos) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3155])). 120.83/55.30 thf(995,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2143_add__nonpos__nonpos)). 120.83/55.30 thf(8354,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])). 120.83/55.30 thf(4311,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2605_pos__imp__zdiv__pos__iff)). 120.83/55.30 thf(20052,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4311])). 120.83/55.30 thf(4144,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((one_one_int = (hAPP_int_int @ abs_abs_int @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B))) <= (zero_zero_int != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3449_zdvd__mult__cancel1)). 120.83/55.30 thf(19433,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((((one_one_int = (hAPP_int_int @ abs_abs_int @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B)) => (one_one_int = (hAPP_int_int @ abs_abs_int @ A)))) | (zero_zero_int = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4144])). 120.83/55.30 thf(717,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1380_mult__le__cancel__left__neg)). 120.83/55.30 thf(7346,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 120.83/55.30 thf(3173,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)) => ((C = A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1481_power__eq__imp__eq__base)). 120.83/55.30 thf(15984,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)) => ((C = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3173])). 120.83/55.30 thf(3937,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) => (((A = (hAPP_int_int @ (inv @ B) @ (hAPP_int_int @ (inv @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1893_inv__inv)). 120.83/55.30 thf(18613,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) => ((A = (hAPP_int_int @ (inv @ B) @ (hAPP_int_int @ (inv @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3937])). 120.83/55.30 thf(1026,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ D)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_power__le__dvd)). 120.83/55.30 thf(8462,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ D)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])). 120.83/55.30 thf(514,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3733_cos__sin__eq)). 120.83/55.30 thf(6656,plain,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 120.83/55.30 thf(2317,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_add__number__of__left)). 120.83/55.30 thf(12959,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317])). 120.83/55.30 thf(68,axiom,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (cis @ A)) @ (cis @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4151_cis__divide)). 120.83/55.30 thf(5189,plain,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (cis @ A)) @ (cis @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 120.83/55.30 thf(2169,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3282_div__nat__number__of)). 120.83/55.30 thf(12414,plain,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169])). 120.83/55.30 thf(2451,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => ((? [D:$i]: (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ E))) @ (hAPP_real_real @ A @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3887_DERIV__pos__inc__left)). 120.83/55.30 thf(13463,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => (? [D:$i]: (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ E))) @ (hAPP_real_real @ A @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451])). 120.83/55.30 thf(2192,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3491_real__add__le__0__iff)). 120.83/55.30 thf(12521,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192])). 120.83/55.30 thf(696,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_real_real @ (log @ B) @ A)) = A)) <= (one_one_real != B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4461_powr__log__cancel)). 120.83/55.30 thf(7281,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_real_real @ (log @ B) @ A)) = A)) | (one_one_real = B) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 120.83/55.30 thf(444,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3561_cos__minus)). 120.83/55.30 thf(6413,plain,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 120.83/55.30 thf(288,axiom,((! [A:$i,B:$i]: (((code_S1047413653umeral @ A) = (code_S1047413653umeral @ B)) <=> (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4074_code__numeral_Oinject)). 120.83/55.30 thf(5904,plain,((! [A:$i,B:$i]: ((((code_S1047413653umeral @ A) = (code_S1047413653umeral @ B)) => (A = B)) & ((A = B) => ((code_S1047413653umeral @ A) = (code_S1047413653umeral @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 120.83/55.30 thf(1238,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2145_add__nonpos__nonpos)). 120.83/55.30 thf(9196,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238])). 120.83/55.30 thf(418,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3572_cos__monotone__0__pi)). 120.83/55.30 thf(6339,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 120.83/55.30 thf(3355,axiom,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (natceiling @ (hAPP_int_real @ number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3392_natceiling__number__of__eq)). 120.83/55.30 thf(16601,plain,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (natceiling @ (hAPP_int_real @ number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3355])). 120.83/55.30 thf(3127,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1337_mult__left__less__imp__less)). 120.83/55.30 thf(15826,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3127])). 120.83/55.30 thf(1021,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ B @ A)) <= (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ C)) => (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ suc @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3354_nat__induct)). 120.83/55.30 thf(8446,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ B @ A)) | ~ (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ C)) => (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ suc @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021])). 120.83/55.30 thf(4826,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_power2__eq__square__number__of)). 120.83/55.30 thf(22073,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4826])). 120.83/55.30 thf(3107,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1281_one__le__power)). 120.83/55.30 thf(15761,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3107])). 120.83/55.30 thf(913,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) <= ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2096_diff__eq__diff__less)). 120.83/55.30 thf(8068,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)))) | ~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])). 120.83/55.30 thf(520,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arctan) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5162_isCont__arctan)). 120.83/55.30 thf(6677,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ arctan) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 120.83/55.30 thf(3416,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4308_gcd__semilattice__nat_Oinf__left__idem)). 120.83/55.30 thf(16800,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3416])). 120.83/55.30 thf(32,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3983_i__mult__Complex)). 120.83/55.30 thf(5053,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 120.83/55.30 thf(2592,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3034_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.30 thf(13939,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592])). 120.83/55.30 thf(56,axiom,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4088_cnj_Obounded)). 120.83/55.30 thf(5145,plain,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 120.83/55.30 thf(346,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A))) <=> (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A))))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1529_inf__period_I3_J)). 120.83/55.30 thf(6101,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A))) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A)))) & ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ D) @ A))) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ E) @ C))) @ A))))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 120.83/55.30 thf(1612,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4675_eq__rat_I3_J)). 120.83/55.30 thf(10529,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612])). 120.83/55.30 thf(2187,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3825_exp__less__cancel__iff)). 120.83/55.30 thf(12493,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187])). 120.83/55.30 thf(3765,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2202_add__less__le__mono)). 120.83/55.30 thf(17999,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3765])). 120.83/55.30 thf(2197,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (? [C:$i]: ((B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3250_realpow__pos__nth2)). 120.83/55.30 thf(12538,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (? [C:$i]: ((B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197])). 120.83/55.30 thf(2327,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1359_mult__le__less__imp__less)). 120.83/55.30 thf(13006,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327])). 120.83/55.30 thf(2167,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (div_mod_int @ A) @ zero_zero_int) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2368_mod__by__0)). 120.83/55.30 thf(12404,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (div_mod_int @ A) @ zero_zero_int) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167])). 120.83/55.30 thf(2534,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_zero__less__mult__pos)). 120.83/55.30 thf(13750,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534])). 120.83/55.30 thf(3095,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_sum__squares__ge__zero)). 120.83/55.30 thf(15714,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3095])). 120.83/55.30 thf(1881,axiom,((! [A:$i,B:$i]: (((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) = zero_z891286103de_int) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2588_dvd__eq__mod__eq__0__number__of)). 120.83/55.30 thf(11488,plain,((! [A:$i,B:$i]: ((((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) = zero_z891286103de_int) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B))) => ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) = zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881])). 120.83/55.30 thf(2272,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3018_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.30 thf(12792,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272])). 120.83/55.30 thf(4606,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) => ((! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ A @ D)))) <= (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2242_int__gr__induct)). 120.83/55.30 thf(21258,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) => ((! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ A @ D)))) | ~ (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4606])). 120.83/55.30 thf(4208,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1485_one__less__power)). 120.83/55.30 thf(19667,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4208])). 120.83/55.30 thf(673,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3333_real__sqrt__lt__1__iff)). 120.83/55.30 thf(7205,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])). 120.83/55.30 thf(416,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_complex_real @ re @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4128_abs__Re__le__cmod)). 120.83/55.30 thf(6335,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_complex_real @ re @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 120.83/55.30 thf(2954,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_dvd__0__right)). 120.83/55.30 thf(15211,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2954])). 120.83/55.30 thf(144,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_dvd__refl)). 120.83/55.30 thf(5423,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 120.83/55.30 thf(4240,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (standardRes @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2648_StandardRes__lbound)). 120.83/55.30 thf(19783,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (standardRes @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4240])). 120.83/55.30 thf(4498,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2112_mult__1)). 120.83/55.30 thf(20787,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4498])). 120.83/55.30 thf(1279,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E)) @ C))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E)) @ C)))) <= (zero_zero_int != C)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2802_zmult1__lemma)). 120.83/55.30 thf(9355,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E)) @ C))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E)) @ C)))) | (zero_zero_int = C) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279])). 120.83/55.30 thf(1743,axiom,((! [A:$i]: (((hAPP_nat_nat @ suc @ zero_zero_nat) = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3050_dvd__1__iff__1)). 120.83/55.30 thf(10986,plain,((! [A:$i]: ((((hAPP_nat_nat @ suc @ zero_zero_nat) = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743])). 120.83/55.30 thf(3788,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_rel__simps_I20_J)). 120.83/55.30 thf(18073,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3788])). 120.83/55.30 thf(897,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1338_mult__left__less__imp__less)). 120.83/55.30 thf(8009,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])). 120.83/55.30 thf(868,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1429_power__gt1__lemma)). 120.83/55.30 thf(7917,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[868])). 120.83/55.30 thf(1057,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_one__dvd)). 120.83/55.30 thf(8562,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057])). 120.83/55.30 thf(3832,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_zcong__1)). 120.83/55.30 thf(18222,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3832])). 120.83/55.30 thf(3817,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2739_nat__less__eq__zless)). 120.83/55.30 thf(18172,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3817])). 120.83/55.30 thf(3237,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1423_power__less__power__Suc)). 120.83/55.30 thf(16232,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3237])). 120.83/55.30 thf(203,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ real_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3676_natceiling__le)). 120.83/55.30 thf(5615,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ real_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 120.83/55.30 thf(4072,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A) = zero_zero_int) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2601_div__pos__pos__trivial)). 120.83/55.30 thf(19171,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A) = zero_zero_int) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4072])). 120.83/55.30 thf(4052,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ zero_zero_int) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2088_diff__0__right)). 120.83/55.30 thf(19053,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ zero_zero_int) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4052])). 120.83/55.30 thf(429,axiom,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4086_cnj_Opos__bounded)). 120.83/55.30 thf(6375,plain,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 120.83/55.30 thf(372,axiom,((real_nat = semiri132038758t_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3642_real__of__nat__def)). 120.83/55.30 thf(6195,plain,((real_nat = semiri132038758t_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 120.83/55.30 thf(324,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ sin @ A) @ (hAPP_real_real @ cos @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3862_DERIV__sin)). 120.83/55.30 thf(6028,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ sin @ A) @ (hAPP_real_real @ cos @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 120.83/55.30 thf(2010,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4169_prime__divprod__eq)). 120.83/55.30 thf(11884,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010])). 120.83/55.30 thf(973,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1819_mult__diff__mult)). 120.83/55.30 thf(8282,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[973])). 120.83/55.30 thf(2872,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1746_diff__add__inverse)). 120.83/55.30 thf(14941,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2872])). 120.83/55.30 thf(4550,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_zero__le__mult__iff)). 120.83/55.30 thf(21034,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4550])). 120.83/55.30 thf(4687,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_rel__simps_I33_J)). 120.83/55.30 thf(21533,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4687])). 120.83/55.30 thf(1967,axiom,((! [A:$i]: ((((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ A)) = zero_zero_nat) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4780_nat__number__of__Bit1)). 120.83/55.30 thf(11762,plain,((! [A:$i]: ((((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ A)) = zero_zero_nat) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967])). 120.83/55.30 thf(990,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5139_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J)). 120.83/55.30 thf(8339,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])). 120.83/55.30 thf(1675,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat) = (natceiling @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3725_natceiling__eq)). 120.83/55.30 thf(10731,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat) = (natceiling @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675])). 120.83/55.30 thf(2487,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_real_real @ cos @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3567_cos__ge__minus__one)). 120.83/55.30 thf(13576,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_real_real @ cos @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487])). 120.83/55.30 thf(1013,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_mult__2__right)). 120.83/55.30 thf(8414,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013])). 120.83/55.30 thf(665,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2414_zmod__simps_I2_J)). 120.83/55.30 thf(7173,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 120.83/55.30 thf(2704,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (hBOOL @ (hAPP_rat_bool @ A @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)))) <=> (? [C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ zero_zero_rat))) & (hBOOL @ (hAPP_rat_bool @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1679_unity__coeff__ex)). 120.83/55.30 thf(14353,plain,((! [A:$i,B:$i]: (((? [C:$i]: (hBOOL @ (hAPP_rat_bool @ A @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ zero_zero_rat))) & (hBOOL @ (hAPP_rat_bool @ A @ C))))) & ((? [C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ zero_zero_rat))) & (hBOOL @ (hAPP_rat_bool @ A @ C)))) => (? [C:$i]: (hBOOL @ (hAPP_rat_bool @ A @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2704])). 120.83/55.30 thf(3149,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4438_real__of__int__lt__zero__cancel__iff)). 120.83/55.30 thf(15896,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3149])). 120.83/55.30 thf(3603,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ C) @ A)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_dvd__power__le)). 120.83/55.30 thf(17412,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ C) @ A)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3603])). 120.83/55.30 thf(3280,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ nat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3200_one__less__nat__eq)). 120.83/55.30 thf(16365,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3280])). 120.83/55.30 thf(3959,axiom,((! [A:$i,B:$i]: ((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (negDivAlg @ A @ B)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))) & (((negDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))) <= (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2666_negDivAlg_Osimps)). 120.83/55.30 thf(18677,plain,((! [A:$i,B:$i]: ((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (negDivAlg @ A @ B)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))) & (((negDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3959])). 120.83/55.30 thf(4396,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) = one_one_int) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4998_coprime__mult__int)). 120.83/55.30 thf(20387,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) = one_one_int) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4396])). 120.83/55.30 thf(4716,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) <=> ((hAPP_int_nat @ nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2726_nat__0__iff)). 120.83/55.30 thf(21673,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => ((hAPP_int_nat @ nat @ A) = zero_zero_nat)) & (((hAPP_int_nat @ nat @ A) = zero_zero_nat) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4716])). 120.83/55.30 thf(1809,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.30 thf(11221,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809])). 120.83/55.30 thf(3963,axiom,((! [A:$i,B:$i]: (((! [C:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) <= (zero_zero_int != C))) => (hBOOL @ (hAPP_int_bool @ A @ C))) <= (hBOOL @ (hAPP_int_bool @ (accp_int @ quickc1265749348ro_rel) @ C))) <= (is_int @ C))) => (hBOOL @ (hAPP_int_bool @ A @ B))) <= (hBOOL @ (hAPP_int_bool @ (accp_int @ quickc1265749348ro_rel) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4270_around__zero_Opinduct)). 120.83/55.30 thf(18696,plain,((! [A:$i,B:$i]: (((! [C:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) | (zero_zero_int = C))) => (hBOOL @ (hAPP_int_bool @ A @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (accp_int @ quickc1265749348ro_rel) @ C)) | ~ (is_int @ C))) => (hBOOL @ (hAPP_int_bool @ A @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (accp_int @ quickc1265749348ro_rel) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3963])). 120.83/55.30 thf(3179,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ C)) => ((hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) <= (! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ suc @ D))) => (hBOOL @ (hAPP_nat_bool @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3289_zero__induct__lemma)). 120.83/55.30 thf(16004,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ C)) => ((hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) | ~ (! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ suc @ D))) => (hBOOL @ (hAPP_nat_bool @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3179])). 120.83/55.30 thf(3826,axiom,((! [A:$i]: ((((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)) = one_one_int) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2807_EvenOdd_Oneg__one__even__power)). 120.83/55.30 thf(18205,plain,((! [A:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)) = one_one_int) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3826])). 120.83/55.30 thf(2909,axiom,(((hAPP_i1732201573de_int @ quickcheck_of_int @ zero_zero_int) = zero_z891286103de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4563_zero__code__int__def)). 120.83/55.30 thf(15065,plain,(((hAPP_i1732201573de_int @ quickcheck_of_int @ zero_zero_int) = zero_z891286103de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2909])). 120.83/55.30 thf(3865,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <=> ((zero_zero_int = A) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1266_dvd__mult__cancel__left)). 120.83/55.30 thf(18351,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => ((zero_zero_int = A) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)))) & (((zero_zero_int = A) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3865])). 120.83/55.30 thf(2718,axiom,((! [A:$i,B:$i,C:$i]: (((A = B) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1846_nat__mult__eq__cancel1)). 120.83/55.30 thf(14398,plain,((! [A:$i,B:$i,C:$i]: ((((A = B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) => (A = B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2718])). 120.83/55.30 thf(4853,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__Bit1__Bit0)). 120.83/55.30 thf(22164,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4853])). 120.83/55.30 thf(1159,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3086_Divides_Otransfer__int__nat__functions_I2_J)). 120.83/55.30 thf(8931,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159])). 120.83/55.30 thf(2881,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ nat_size @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_nat_nat @ nat_size @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4056_nat_Osize_I2_J)). 120.83/55.30 thf(14975,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ nat_size @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_nat_nat @ nat_size @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2881])). 120.83/55.30 thf(2963,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2918_of__nat__less__0__iff)). 120.83/55.30 thf(15238,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2963])). 120.83/55.30 thf(1065,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4690_mult__rat)). 120.83/55.30 thf(8619,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065])). 120.83/55.30 thf(2807,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2471_div__by__0)). 120.83/55.30 thf(14725,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2807])). 120.83/55.30 thf(900,axiom,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.30 thf(8016,plain,((! [A:$i,B:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[900])). 120.83/55.30 thf(2792,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_rat @ number_number_of_rat @ B) = (hAPP_int_rat @ number_number_of_rat @ A)) <=> (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_eq__number__of)). 120.83/55.30 thf(14666,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((hAPP_int_rat @ number_number_of_rat @ B) = (hAPP_int_rat @ number_number_of_rat @ A)) => (A = B)) & ((A = B) => ((hAPP_int_rat @ number_number_of_rat @ B) = (hAPP_int_rat @ number_number_of_rat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2792])). 120.83/55.30 thf(4105,axiom,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))) => ((hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (negDivAlg @ A @ B))) & (((negDivAlg @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2669_negDivAlg__eqn)). 120.83/55.30 thf(19302,plain,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))) => ((hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (negDivAlg @ A @ B))) & (((negDivAlg @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4105])). 120.83/55.30 thf(146,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ cos @ A) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3865_DERIV__cos)). 120.83/55.30 thf(5428,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ cos @ A) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 120.83/55.30 thf(899,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1424_power__less__power__Suc)). 120.83/55.30 thf(8014,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[899])). 120.83/55.30 thf(1361,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1565_le__add__iff2)). 120.83/55.30 thf(9624,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361])). 120.83/55.30 thf(3217,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.30 thf(16144,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3217])). 120.83/55.30 thf(3677,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2727_zless__nat__conj)). 120.83/55.30 thf(17687,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3677])). 120.83/55.30 thf(1344,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1425_power__less__power__Suc)). 120.83/55.30 thf(9576,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344])). 120.83/55.30 thf(3879,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2232_MultInv__prop4)). 120.83/55.30 thf(18402,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3879])). 120.83/55.30 thf(3761,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ A)) @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ A)) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2222_aux______3)). 120.83/55.30 thf(17985,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ A)) @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (multInv @ D) @ A)) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3761])). 120.83/55.30 thf(4410,axiom,((! [A:$i,B:$i]: ((((B = zero_zero_int) | (A = zero_zero_int)) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = zero_zero_int)) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_divisors__zero)). 120.83/55.30 thf(20448,plain,((! [A:$i,B:$i]: ((B = zero_zero_int) | (A = zero_zero_int) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = zero_zero_int) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4410])). 120.83/55.30 thf(3880,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_mult__2)). 120.83/55.30 thf(18404,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3880])). 120.83/55.30 thf(4094,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4960_gcd__dvd1__int)). 120.83/55.30 thf(19255,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4094])). 120.83/55.30 thf(3715,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_dvd__0__right)). 120.83/55.30 thf(17819,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3715])). 120.83/55.30 thf(2846,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2419_mod__add__eq)). 120.83/55.30 thf(14855,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2846])). 120.83/55.30 thf(1866,axiom,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ B))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3551_nat__mult__distrib__neg)). 120.83/55.30 thf(11435,plain,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ B))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866])). 120.83/55.30 thf(1464,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1383_mult__le__cancel__left__pos)). 120.83/55.30 thf(9977,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464])). 120.83/55.30 thf(1517,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = B) => (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3347_real__sqrt__sum__squares__eq__cancel2)). 120.83/55.30 thf(10152,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = B) => (zero_zero_real = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517])). 120.83/55.30 thf(3026,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2456_dvd__mod__imp__dvd)). 120.83/55.30 thf(15466,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3026])). 120.83/55.30 thf(951,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) <=> (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3764_even__difference__nat)). 120.83/55.30 thf(8187,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) => (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))) & ((((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])). 120.83/55.30 thf(311,axiom,((quickcheck_of_int = number1226105091de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4558_number__of__code__int__def)). 120.83/55.30 thf(5978,plain,((quickcheck_of_int = number1226105091de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 120.83/55.30 thf(1070,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => ((A = B) <=> ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1287_power__inject__exp)). 120.83/55.30 thf(8636,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C)) => (((A = B) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A))) & (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070])). 120.83/55.30 thf(808,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1906_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.30 thf(7698,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 120.83/55.30 thf(3993,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ pls)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_rel__simps_I29_J)). 120.83/55.30 thf(18806,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3993])). 120.83/55.30 thf(1996,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ fact @ A)) = (hAPP_nat_nat @ fact @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4566_fact_Osimps_I2_J)). 120.83/55.30 thf(11845,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ fact @ A)) = (hAPP_nat_nat @ fact @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996])). 120.83/55.30 thf(264,axiom,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3829_real__sqrt__inverse)). 120.83/55.30 thf(5811,plain,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 120.83/55.30 thf(4045,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1387_mult__right__le__one__le)). 120.83/55.30 thf(18994,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4045])). 120.83/55.30 thf(4444,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D)) => ((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ B))) @ D))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2237_MultInv__zcong__prop2)). 120.83/55.30 thf(20570,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D)) => ((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ B))) @ D))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4444])). 120.83/55.30 thf(424,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3684_cos__add)). 120.83/55.30 thf(6360,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 120.83/55.30 thf(3435,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3142_of__nat__0__less__iff)). 120.83/55.30 thf(16850,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ semiri151668891at_rat @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3435])). 120.83/55.30 thf(3295,axiom,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2496_mod__mult__self2__is__0)). 120.83/55.30 thf(16414,plain,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3295])). 120.83/55.30 thf(1856,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1418_power__increasing__iff)). 120.83/55.30 thf(11400,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856])). 120.83/55.30 thf(1686,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1375_mult__strict__mono)). 120.83/55.30 thf(10771,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686])). 120.83/55.30 thf(2517,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1755_dvd__diffD)). 120.83/55.30 thf(13676,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2517])). 120.83/55.30 thf(4850,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)). 120.83/55.30 thf(22154,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4850])). 120.83/55.30 thf(3023,axiom,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1222_zero__less__one)). 120.83/55.30 thf(15459,plain,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3023])). 120.83/55.30 thf(3256,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2147_add__increasing2)). 120.83/55.30 thf(16284,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3256])). 120.83/55.30 thf(2464,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.30 thf(13504,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464])). 120.83/55.30 thf(2349,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1319_mult__left__le__imp__le)). 120.83/55.30 thf(13074,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349])). 120.83/55.30 thf(3973,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2747_Nat__Transfer_Otransfer__nat__int__functions_I4_J)). 120.83/55.30 thf(18745,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3973])). 120.83/55.30 thf(1273,axiom,((! [A:$i]: ((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_z126310315umeral) <= ((hAPP_int_nat @ number_number_of_nat @ A) != zero_zero_nat)) & (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_power__0__left__number__of)). 120.83/55.30 thf(9333,plain,((! [A:$i]: ((((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_z126310315umeral) | ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) & (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273])). 120.83/55.30 thf(2285,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) <=> (((C = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & ((! [D:$i,E:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E) = B) => (hBOOL @ (hAPP_nat_bool @ A @ D))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C)))) <= (zero_zero_nat != C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2733_split__div)). 120.83/55.30 thf(12834,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) => (((C = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & (! [D:$i,E:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E) = B) => (hBOOL @ (hAPP_nat_bool @ A @ D))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C))) | (zero_zero_nat = C)))) & ((((C = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & (! [D:$i,E:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E) = B) => (hBOOL @ (hAPP_nat_bool @ A @ D))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C))) | (zero_zero_nat = C))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285])). 120.83/55.30 thf(3654,axiom,((! [A:$i]: (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4971_coprime__minus__one__int)). 120.83/55.30 thf(17595,plain,((! [A:$i]: (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3654])). 120.83/55.30 thf(2449,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4181_prime__g__one)). 120.83/55.30 thf(13458,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449])). 120.83/55.30 thf(2453,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2430_mod__add__self1)). 120.83/55.30 thf(13468,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453])). 120.83/55.30 thf(4638,axiom,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ (hAPP_int_int @ bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1582_diff__bin__simps_I6_J)). 120.83/55.30 thf(21364,plain,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ (hAPP_int_int @ bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4638])). 120.83/55.30 thf(1353,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((posDivAlg @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (div_mod_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2757_posDivAlg__div__mod)). 120.83/55.30 thf(9603,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((posDivAlg @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (div_mod_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353])). 120.83/55.30 thf(677,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ uminus_uminus_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3913_real__root__minus)). 120.83/55.30 thf(7222,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ uminus_uminus_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 120.83/55.30 thf(224,axiom,((! [A:$i,B:$i,C:$i]: (((A = B) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))) <= (C != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1788_real__mult__left__cancel)). 120.83/55.30 thf(5687,plain,((! [A:$i,B:$i,C:$i]: ((((A = B) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) => (A = B))) | (C = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 120.83/55.30 thf(4184,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_semiring__mult__2)). 120.83/55.30 thf(19566,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4184])). 120.83/55.30 thf(3777,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_zadd__0__right)). 120.83/55.30 thf(18039,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3777])). 120.83/55.30 thf(4547,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_mult__left__mono__neg)). 120.83/55.30 thf(21026,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4547])). 120.83/55.30 thf(2864,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1308_power__add)). 120.83/55.30 thf(14908,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2864])). 120.83/55.30 thf(1658,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2389_mod__mult__mult1)). 120.83/55.30 thf(10676,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658])). 120.83/55.30 thf(359,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) <=> ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A) = zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2517_dvd__eq__mod__eq__0)). 120.83/55.30 thf(6148,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A) = zero_z891286103de_int)) & (((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A) = zero_z891286103de_int) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 120.83/55.30 thf(1824,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_arith__simps_I32_J)). 120.83/55.30 thf(11278,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824])). 120.83/55.30 thf(751,axiom,((! [A:$i]: (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.30 thf(7486,plain,((! [A:$i]: (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])). 120.83/55.30 thf(4794,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4985_abs__gcd__int)). 120.83/55.30 thf(21951,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4794])). 120.83/55.30 thf(303,axiom,((! [A:$i]: (zero_z126310315umeral != (code_S1047413653umeral @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4082_code__numeral_Osimps_I2_J)). 120.83/55.30 thf(5951,plain,((! [A:$i]: ~ (zero_z126310315umeral = (code_S1047413653umeral @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 120.83/55.30 thf(4038,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5011_transfer__nat__int__gcd__closures_I1_J)). 120.83/55.30 thf(18971,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4038])). 120.83/55.30 thf(1530,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1980_add__0)). 120.83/55.30 thf(10203,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530])). 120.83/55.30 thf(2113,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1839_nat__less__add__iff2)). 120.83/55.30 thf(12211,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113])). 120.83/55.30 thf(4103,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_nat_int @ semiri1621563631at_int @ A) = (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3256_Nat__Transfer_Otransfer__int__nat__relations_I1_J)). 120.83/55.30 thf(19287,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_nat_int @ semiri1621563631at_int @ A) = (hAPP_nat_int @ semiri1621563631at_int @ B))) & (((hAPP_nat_int @ semiri1621563631at_int @ A) = (hAPP_nat_int @ semiri1621563631at_int @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4103])). 120.83/55.30 thf(1772,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => ((? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ E))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3888_DERIV__neg__dec__left)). 120.83/55.30 thf(11088,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => (? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ E))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772])). 120.83/55.30 thf(1982,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3085_zmod__int)). 120.83/55.30 thf(11801,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982])). 120.83/55.30 thf(3860,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C)) @ (hAPP_int_int @ (legacy_zgcd @ A) @ C))) <= ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4516_zgcd__zmult__zdvd__zgcd)). 120.83/55.30 thf(18338,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C)) @ (hAPP_int_int @ (legacy_zgcd @ A) @ C))) | ~ ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3860])). 120.83/55.30 thf(1340,axiom,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1966_add_Ocomm__neutral)). 120.83/55.30 thf(9566,plain,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340])). 120.83/55.30 thf(4057,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1682_number__of2)). 120.83/55.30 thf(19070,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4057])). 120.83/55.30 thf(4515,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I19_J)). 120.83/55.30 thf(20855,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4515])). 120.83/55.30 thf(4266,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1204_pos__add__strict)). 120.83/55.30 thf(19896,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4266])). 120.83/55.30 thf(3418,axiom,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ d22set @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3359_d22set__fin)). 120.83/55.30 thf(16805,plain,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ d22set @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3418])). 120.83/55.30 thf(4399,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_zcong__id)). 120.83/55.30 thf(20402,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4399])). 120.83/55.30 thf(1896,axiom,((! [A:$i,B:$i]: (((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3936_real__root__pow__pos)). 120.83/55.30 thf(11536,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896])). 120.83/55.30 thf(4262,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))) <=> ((A = C) | (D = B))) <= ((is_int @ A) & (is_int @ B) & (is_int @ C) & (is_int @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_crossproduct__eq)). 120.83/55.30 thf(19879,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))) => ((A = C) | (D = B))) & (((A = C) | (D = B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))))) | ~ ((is_int @ A) & (is_int @ B) & (is_int @ C) & (is_int @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4262])). 120.83/55.30 thf(4485,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 120.83/55.30 thf(20739,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4485])). 120.83/55.30 thf(3,axiom,((! [A:$i]: ? [B:$i,C:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ C)) @ (hAPP_real_real @ sin @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4002_complex__split__polar)). 120.83/55.30 thf(4951,plain,((! [A:$i]: ? [B:$i,C:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ C)) @ (hAPP_real_real @ sin @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 120.83/55.30 thf(644,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4173_prime__divexp__n)). 120.83/55.30 thf(7091,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])). 120.83/55.30 thf(1052,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ A) != A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2837_n__not__Suc__n)). 120.83/55.30 thf(8544,plain,((! [A:$i]: ~ ((hAPP_nat_nat @ suc @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052])). 120.83/55.30 thf(3630,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_cube__square)). 120.83/55.30 thf(17503,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3630])). 120.83/55.30 thf(4706,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2759_Int2_Oaux__2)). 120.83/55.30 thf(21632,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4706])). 120.83/55.30 thf(1088,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2853_Zero__not__Suc)). 120.83/55.30 thf(8704,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088])). 120.83/55.30 thf(2848,axiom,((! [A:$i,B:$i,C:$i]: ((~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1649_add__leE)). 120.83/55.30 thf(14860,plain,((! [A:$i,B:$i,C:$i]: (~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2848])). 120.83/55.30 thf(1132,axiom,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_number__of__Bit1)). 120.83/55.30 thf(8835,plain,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132])). 120.83/55.30 thf(2500,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) => ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1737_diffs0__imp__equal)). 120.83/55.30 thf(13635,plain,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) => ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2500])). 120.83/55.30 thf(4360,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_mult__strict__left__mono)). 120.83/55.30 thf(20248,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4360])). 120.83/55.30 thf(3434,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.30 thf(16847,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3434])). 120.83/55.30 thf(3692,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_zcong__refl)). 120.83/55.30 thf(17742,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3692])). 120.83/55.30 thf(3218,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) <=> (? [C:$i]: ((A = (hAPP_nat_nat @ suc @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3047_less__Suc__eq__0__disj)). 120.83/55.30 thf(16147,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (? [C:$i]: ((A = (hAPP_nat_nat @ suc @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) | (A = zero_zero_nat))) & ((? [C:$i]: ((A = (hAPP_nat_nat @ suc @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) | (A = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3218])). 120.83/55.30 thf(723,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2082_eq__iff__diff__eq__0)). 120.83/55.30 thf(7365,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex)) & (((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 120.83/55.30 thf(1737,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1799_realpow__minus__mult)). 120.83/55.30 thf(10946,plain,((! [A:$i,B:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737])). 120.83/55.30 thf(1667,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2479_div__by__1)). 120.83/55.30 thf(10708,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667])). 120.83/55.30 thf(2001,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2021_add__right__mono)). 120.83/55.30 thf(11860,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001])). 120.83/55.30 thf(3174,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3074_diff__Suc__eq__diff__pred)). 120.83/55.30 thf(15987,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3174])). 120.83/55.30 thf(2967,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((? [E:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ E) = A)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B))) <= (zero_zero_nat != C)) <= (hBOOL @ (hAPP_nat_bool @ prime @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4204_prime__power__exp)). 120.83/55.30 thf(15249,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ E) = A) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B)) | (zero_zero_nat = C) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2967])). 120.83/55.30 thf(827,axiom,((! [A:$i,B:$i]: ((zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> ((zero_zero_rat = A) & ((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_power__eq__0__iff__number__of)). 120.83/55.30 thf(7774,plain,((! [A:$i,B:$i]: (((zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) => ((zero_zero_rat = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat))) & (((zero_zero_rat = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat)) => (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 120.83/55.30 thf(267,axiom,((! [A:$i,B:$i]: ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (divmod_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4211_divmod__nat__div__mod)). 120.83/55.30 thf(5818,plain,((! [A:$i,B:$i]: ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (divmod_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 120.83/55.30 thf(3952,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A) = (hAPP_int_int @ (nat_tsub @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & (((hAPP_int_int @ (nat_tsub @ B) @ A) = zero_zero_int) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3232_tsub__def)). 120.83/55.30 thf(18653,plain,((! [A:$i,B:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A) = (hAPP_int_int @ (nat_tsub @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & (((hAPP_int_int @ (nat_tsub @ B) @ A) = zero_zero_int) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3952])). 120.83/55.30 thf(4788,axiom,((hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_zprime__2)). 120.83/55.30 thf(21937,plain,((hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4788])). 120.83/55.30 thf(3873,axiom,((! [A:$i,B:$i]: ((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5022_normalize__stable)). 120.83/55.30 thf(18386,plain,((! [A:$i,B:$i]: (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3873])). 120.83/55.30 thf(2939,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((zero_zero_nat != B) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4183_prime__factor__lt)). 120.83/55.30 thf(15168,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((~ (zero_zero_nat = B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2939])). 120.83/55.30 thf(4652,axiom,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4047_add__Min__right)). 120.83/55.30 thf(21431,plain,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4652])). 120.83/55.30 thf(4700,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2469_zpower__zmod)). 120.83/55.30 thf(21615,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4700])). 120.83/55.30 thf(290,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3573_cos__monotone__minus__pi__0_H)). 120.83/55.30 thf(5915,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 120.83/55.30 thf(3690,axiom,((! [A:$i]: ((is_int @ A) => ((~ (! [B:$i]: (A != (hAPP_nat_int @ semiri1621563631at_int @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3260_nonneg__int__cases)). 120.83/55.30 thf(17735,plain,((! [A:$i]: ((is_int @ A) => (~ (! [B:$i]: ~ (A = (hAPP_nat_int @ semiri1621563631at_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3690])). 120.83/55.30 thf(1178,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2933_of__nat__less__imp__less)). 120.83/55.30 thf(8985,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178])). 120.83/55.30 thf(3045,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_zero__less__mult__pos)). 120.83/55.30 thf(15523,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3045])). 120.83/55.30 thf(4255,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D)) => (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))) => ((zero_zero_int != B) => (D = (hAPP_int_int @ (div_mod_int @ A) @ B))))) <= ((is_int @ D) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2655_divmod__int__rel__mod__eq)). 120.83/55.30 thf(19850,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D)) => (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))) => ((~ (zero_zero_int = B)) => (D = (hAPP_int_int @ (div_mod_int @ A) @ B))))) | ~ ((is_int @ D) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4255])). 120.83/55.30 thf(65,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ B)) @ A)) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4145_cos__n__Re__cis__pow__n)). 120.83/55.30 thf(5181,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ re @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ B)) @ A)) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 120.83/55.30 thf(41,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ B) @ C)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3993_complex__of__real__add__Complex)). 120.83/55.30 thf(5080,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ B) @ C)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 120.83/55.30 thf(1847,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (hBOOL @ (hAPP_real_bool @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))) <=> (? [C:$i]: ((hBOOL @ (hAPP_real_bool @ A @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ zero_zero_real)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1676_unity__coeff__ex)). 120.83/55.30 thf(11364,plain,((! [A:$i,B:$i]: (((? [C:$i]: (hBOOL @ (hAPP_real_bool @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_real_bool @ A @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ zero_zero_real)))))) & ((? [C:$i]: ((hBOOL @ (hAPP_real_bool @ A @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ zero_zero_real))))) => (? [C:$i]: (hBOOL @ (hAPP_real_bool @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847])). 120.83/55.30 thf(3802,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (inv @ C) @ A)) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2215_wset__inv__mem__mem)). 120.83/55.30 thf(18132,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (inv @ C) @ A)) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3802])). 120.83/55.30 thf(1375,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3174_lemma__realpow__diff)). 120.83/55.30 thf(9667,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375])). 120.83/55.30 thf(2409,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4406_powr__less__mono2__neg)). 120.83/55.30 thf(13308,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409])). 120.83/55.30 thf(4749,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5010_gcd__ge__0__int)). 120.83/55.30 thf(21813,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4749])). 120.83/55.30 thf(4911,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s1) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_s1)). 120.83/55.30 thf(22343,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s1) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4911])). 120.83/55.30 thf(3082,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.30 thf(15669,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3082])). 120.83/55.30 thf(3660,axiom,((! [A:$i,B:$i]: ((is_int @ A) => ((((B = zero_zero_nat) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) & (((hAPP_nat_int @ semiri1621563631at_int @ B) = A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <=> (B = (hAPP_int_nat @ nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3167_nat__eq__iff)). 120.83/55.30 thf(17619,plain,((! [A:$i,B:$i]: ((is_int @ A) => (((((B = zero_zero_nat) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & (((hAPP_nat_int @ semiri1621563631at_int @ B) = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (B = (hAPP_int_nat @ nat @ A))) & ((B = (hAPP_int_nat @ nat @ A)) => (((B = zero_zero_nat) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & (((hAPP_nat_int @ semiri1621563631at_int @ B) = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3660])). 120.83/55.30 thf(791,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2101_mult_Ocomm__neutral)). 120.83/55.30 thf(7629,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 120.83/55.30 thf(3540,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2249_minf_I10_J)). 120.83/55.30 thf(17196,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3540])). 120.83/55.30 thf(496,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1808_add__diff__add)). 120.83/55.30 thf(6593,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 120.83/55.30 thf(2055,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2948_of__nat__le__iff)). 120.83/55.30 thf(12019,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055])). 120.83/55.30 thf(2971,axiom,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__special_I3_J)). 120.83/55.30 thf(15265,plain,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2971])). 120.83/55.30 thf(3116,axiom,((! [A:$i]: ((is_int @ A) => (~ (! [B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ C)) != A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3288_int__diff__cases)). 120.83/55.30 thf(15793,plain,((! [A:$i]: ((is_int @ A) => (~ (! [B:$i,C:$i]: ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ C)) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3116])). 120.83/55.30 thf(4731,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_less__special_I2_J)). 120.83/55.30 thf(21739,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4731])). 120.83/55.30 thf(3698,axiom,((! [A:$i,B:$i]: (((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A) != zero_zero_int) <= (A != zero_zero_int)) <= (zero_zero_int != B)) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_no__zero__divisors)). 120.83/55.30 thf(17763,plain,((! [A:$i,B:$i]: (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A) = zero_zero_int) | (A = zero_zero_int) | (zero_zero_int = B) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3698])). 120.83/55.30 thf(2816,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3073_diff__Suc__1)). 120.83/55.30 thf(14752,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2816])). 120.83/55.30 thf(535,axiom,((! [A:$i]: (A = (collect_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Collect__def)). 120.83/55.30 thf(6720,plain,((! [A:$i]: (A = (collect_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])). 120.83/55.30 thf(1289,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1732_real__add__left__mono)). 120.83/55.30 thf(9387,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289])). 120.83/55.30 thf(2463,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) <=> ((zero_zero_nat = A) & (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4341_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff)). 120.83/55.30 thf(13495,plain,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) => ((zero_zero_nat = A) & (zero_zero_nat = B))) & (((zero_zero_nat = A) & (zero_zero_nat = B)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463])). 120.83/55.30 thf(1857,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1201_not__square__less__zero)). 120.83/55.30 thf(11403,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857])). 120.83/55.30 thf(1603,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2432_mod__add__self1)). 120.83/55.30 thf(10498,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603])). 120.83/55.30 thf(4621,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) @ C)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_Euler_Oaux____1)). 120.83/55.30 thf(21313,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) @ C)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4621])). 120.83/55.30 thf(2372,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ D)) => ((hBOOL @ (hAPP_nat_bool @ C @ E)) => (hBOOL @ (hAPP_nat_bool @ C @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ E)) @ D)))))) => ((hBOOL @ (hAPP_nat_bool @ C @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ D)) => (hBOOL @ (hAPP_nat_bool @ C @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3252_mod__induct)). 120.83/55.30 thf(13154,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ D)) => ((hBOOL @ (hAPP_nat_bool @ C @ E)) => (hBOOL @ (hAPP_nat_bool @ C @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ E)) @ D)))))) => ((hBOOL @ (hAPP_nat_bool @ C @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ D)) => (hBOOL @ (hAPP_nat_bool @ C @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372])). 120.83/55.30 thf(2279,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_le__imp__power__dvd)). 120.83/55.30 thf(12818,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279])). 120.83/55.30 thf(425,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) = (hAPP_real_real @ sin @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3718_sin__periodic)). 120.83/55.30 thf(6363,plain,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) = (hAPP_real_real @ sin @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 120.83/55.30 thf(3428,axiom,((zero_zero_complex != one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_zero__neq__one)). 120.83/55.30 thf(16832,plain,((~ (zero_zero_complex = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3428])). 120.83/55.30 thf(4890,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_power__even__eq)). 120.83/55.30 thf(22274,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4890])). 120.83/55.30 thf(1965,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1741_diff__less__mono2)). 120.83/55.30 thf(11757,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965])). 120.83/55.30 thf(1597,axiom,((! [A:$i,B:$i]: (is_int @ (big_co1548731110nt_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_000tc__Int__Oint_000tc_)). 120.83/55.30 thf(10458,plain,((! [A:$i,B:$i]: (is_int @ (big_co1548731110nt_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597])). 120.83/55.30 thf(2644,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1584592887nt_int @ (hAPP_f1574055885nt_int @ (hAPP_f434654626nt_int @ cOMBS_2011279539nt_int @ A) @ B) @ C) = (hAPP_i1584592887nt_int @ (hAPP_i1778081398nt_int @ A @ C) @ (hAPP_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__Int__Oint_000tc__fun_Itc__Int__Oint)). 120.83/55.30 thf(14153,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1584592887nt_int @ (hAPP_f1574055885nt_int @ (hAPP_f434654626nt_int @ cOMBS_2011279539nt_int @ A) @ B) @ C) = (hAPP_i1584592887nt_int @ (hAPP_i1778081398nt_int @ A @ C) @ (hAPP_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2644])). 120.83/55.30 thf(205,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ A) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2366_mod__self)). 120.83/55.30 thf(5620,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 120.83/55.30 thf(4236,axiom,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ succ @ A)) = (hAPP_int_int @ succ @ (hAPP_int_int @ bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3292_succ__Bit1)). 120.83/55.30 thf(19758,plain,((! [A:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ succ @ A)) = (hAPP_int_int @ succ @ (hAPP_int_int @ bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4236])). 120.83/55.30 thf(4762,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2909_zero__le__imp__of__nat)). 120.83/55.30 thf(21851,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4762])). 120.83/55.30 thf(3456,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.30 thf(16920,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3456])). 120.83/55.30 thf(2618,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.30 thf(14052,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2618])). 120.83/55.30 thf(3582,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_dvd__trans)). 120.83/55.30 thf(17345,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3582])). 120.83/55.30 thf(3635,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_zadd__assoc)). 120.83/55.30 thf(17531,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3635])). 120.83/55.30 thf(2904,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => ((! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ one_one_nat))) @ (hAPP_nat_int @ B @ D)))) @ one_one_int)))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ zero_zero_nat)) @ A)) => ((? [D:$i]: (((hAPP_nat_int @ B @ D) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3479_nat0__intermed__int__val)). 120.83/55.30 thf(15047,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => ((! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ one_one_nat))) @ (hAPP_nat_int @ B @ D)))) @ one_one_int)))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ zero_zero_nat)) @ A)) => (? [D:$i]: (((hAPP_nat_int @ B @ D) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2904])). 120.83/55.30 thf(947,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1248_less__1__mult)). 120.83/55.30 thf(8177,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])). 120.83/55.30 thf(3740,axiom,(((hAPP_int_nat @ number_number_of_nat @ pls) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_semiring__numeral__0__eq__0)). 120.83/55.30 thf(17912,plain,(((hAPP_int_nat @ number_number_of_nat @ pls) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3740])). 120.83/55.30 thf(1302,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2817_lessI)). 120.83/55.30 thf(9419,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302])). 120.83/55.30 thf(2472,axiom,(((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3664_real__of__nat__one)). 120.83/55.30 thf(13527,plain,(((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2472])). 120.83/55.30 thf(2227,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1443_power__strict__increasing)). 120.83/55.30 thf(12639,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227])). 120.83/55.30 thf(4682,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C))) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4491_zgcd__greatest__iff)). 120.83/55.30 thf(21514,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4682])). 120.83/55.30 thf(1455,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_real @ semiri132038758t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2824_number__of__int)). 120.83/55.30 thf(9957,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_real @ semiri132038758t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455])). 120.83/55.30 thf(3500,axiom,((zero_zero_nat = (hAPP_int_nat @ nat @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2704_transfer__nat__int__numerals_I1_J)). 120.83/55.30 thf(17074,plain,((zero_zero_nat = (hAPP_int_nat @ nat @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3500])). 120.83/55.30 thf(2296,axiom,((! [A:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (zero_zero_real = (hAPP_nat_real @ cos_coeff @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_real @ cos_coeff @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3798_cos__coeff__def)). 120.83/55.30 thf(12885,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (zero_zero_real = (hAPP_nat_real @ cos_coeff @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_real @ cos_coeff @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296])). 120.83/55.30 thf(2424,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2278_divides__le)). 120.83/55.30 thf(13355,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424])). 120.83/55.30 thf(88,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (A = (hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3607_cos__arccos)). 120.83/55.30 thf(5253,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (A = (hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 120.83/55.30 thf(3037,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2819_dvd__1__left)). 120.83/55.30 thf(15495,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3037])). 120.83/55.30 thf(256,axiom,((! [A:$i]: (is_int @ (archim1246769320r_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_000tc__RealDef__Oreal)). 120.83/55.30 thf(5786,plain,((! [A:$i]: (is_int @ (archim1246769320r_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 120.83/55.30 thf(4520,axiom,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5141_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J)). 120.83/55.30 thf(20880,plain,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4520])). 120.83/55.30 thf(1355,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3778_fact__diff__Suc)). 120.83/55.30 thf(9609,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355])). 120.83/55.30 thf(4487,axiom,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_one__is__num__one)). 120.83/55.30 thf(20742,plain,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4487])). 120.83/55.30 thf(1695,axiom,((! [A:$i,B:$i]: (((! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ A))) => ((hBOOL @ (tendsto_nat_real @ B @ A @ sequentially)) <= (! [C:$i]: ((? [D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ B @ D)) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))) <= (! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ (hAPP_nat_real @ B @ (hAPP_nat_nat @ suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5157_increasing__LIMSEQ)). 120.83/55.30 thf(10798,plain,((! [A:$i,B:$i]: (((! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ A))) => ((hBOOL @ (tendsto_nat_real @ B @ A @ sequentially)) | ~ (! [C:$i]: (? [D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ B @ D)) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))) | ~ (! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ (hAPP_nat_real @ B @ (hAPP_nat_nat @ suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695])). 120.83/55.30 thf(1930,axiom,((! [A:$i,B:$i,C:$i]: ((A = C) <= ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1911_add__right__imp__eq)). 120.83/55.30 thf(11642,plain,((! [A:$i,B:$i,C:$i]: ((A = C) | ~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930])). 120.83/55.30 thf(1816,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2009_add__mono)). 120.83/55.30 thf(11243,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816])). 120.83/55.30 thf(4229,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ C)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ (hAPP_i1948725293t_bool @ norRRset @ C)))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4591_RRset2norRR__correct)). 120.83/55.30 thf(19735,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ C)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ (hAPP_i1948725293t_bool @ norRRset @ C)))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4229])). 120.83/55.30 thf(3907,axiom,(((hAPP_int_int @ number_number_of_int @ pls) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_semiring__numeral__0__eq__0)). 120.83/55.30 thf(18521,plain,(((hAPP_int_int @ number_number_of_int @ pls) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3907])). 120.83/55.30 thf(3120,axiom,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_lessThan_nat @ A) = (hAPP_n1699378549t_bool @ (ord_at4362885an_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4951_atLeast0LessThan)). 120.83/55.30 thf(15803,plain,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_lessThan_nat @ A) = (hAPP_n1699378549t_bool @ (ord_at4362885an_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3120])). 120.83/55.30 thf(3069,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3903_real__root__le__mono)). 120.83/55.30 thf(15634,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3069])). 120.83/55.30 thf(3297,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2618_zmod__minus1__right)). 120.83/55.30 thf(16419,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ min))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3297])). 120.83/55.30 thf(193,axiom,((! [A:$i,B:$i]: (((zero_zero_real != (hAPP_real_real @ cos @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))))) <= (zero_zero_real != (hAPP_real_real @ cos @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3613_lemma__tan__add1)). 120.83/55.30 thf(5588,plain,((! [A:$i,B:$i]: (((~ (zero_zero_real = (hAPP_real_real @ cos @ A))) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))))) | (zero_zero_real = (hAPP_real_real @ cos @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 120.83/55.30 thf(3370,axiom,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_power__m1__even)). 120.83/55.30 thf(16656,plain,((! [A:$i]: (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3370])). 120.83/55.30 thf(549,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3446_ln__le__minus__one)). 120.83/55.30 thf(6763,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 120.83/55.30 thf(2856,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (~ (! [C:$i]: (((hAPP_nat_nat @ suc @ C) != B) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3304_Suc__lessE)). 120.83/55.30 thf(14882,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (~ (! [C:$i]: (~ ((hAPP_nat_nat @ suc @ C) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2856])). 120.83/55.30 thf(2079,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_mult__neg__pos)). 120.83/55.30 thf(12091,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079])). 120.83/55.30 thf(873,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4367_divides__mult__nat)). 120.83/55.30 thf(7930,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[873])). 120.83/55.30 thf(1527,axiom,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ zero_zero_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_mult__zero__left)). 120.83/55.30 thf(10195,plain,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ zero_zero_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527])). 120.83/55.30 thf(3486,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3501_minus__pi__half__less__zero)). 120.83/55.30 thf(17033,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3486])). 120.83/55.30 thf(1171,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1326_mult__right__le__imp__le)). 120.83/55.30 thf(8968,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171])). 120.83/55.30 thf(4846,axiom,((! [A:$i]: ((hAPP_int_int @ ring_1_of_int_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4581_of__int__int__eq)). 120.83/55.30 thf(22141,plain,((! [A:$i]: ((hAPP_int_int @ ring_1_of_int_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4846])). 120.83/55.30 thf(2973,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ tan @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3614_tan__gt__zero)). 120.83/55.30 thf(15270,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ tan @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2973])). 120.83/55.30 thf(1265,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B) != zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4379_powr__not__zero)). 120.83/55.30 thf(9288,plain,((! [A:$i,B:$i]: ~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265])). 120.83/55.30 thf(3433,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1922_add__left__imp__eq)). 120.83/55.30 thf(16844,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (C = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3433])). 120.83/55.30 thf(3534,axiom,(((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_semiring__one__add__one__is__two)). 120.83/55.30 thf(17165,plain,(((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3534])). 120.83/55.30 thf(3154,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int != A) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ zero_zero_int @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2793_divmod__int__rel__0)). 120.83/55.30 thf(15912,plain,((! [A:$i]: ((is_int @ A) => ((~ (zero_zero_int = A)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ zero_zero_int @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3154])). 120.83/55.30 thf(1208,axiom,((! [A:$i]: ((hAPP_int_int @ zfact @ A) = (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ d22set @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4810_d22set__prod__zfact)). 120.83/55.30 thf(9085,plain,((! [A:$i]: ((hAPP_int_int @ zfact @ A) = (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ d22set @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208])). 120.83/55.30 thf(437,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_dvd__mult)). 120.83/55.30 thf(6395,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 120.83/55.30 thf(992,axiom,((! [A:$i]: ((quotient_of @ (hAPP_rat_rat @ sgn_sgn_rat @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ sgn_sgn_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (quotient_of @ A)))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4653_rat__sgn__code)). 120.83/55.30 thf(8346,plain,((! [A:$i]: ((quotient_of @ (hAPP_rat_rat @ sgn_sgn_rat @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ sgn_sgn_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (quotient_of @ A)))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])). 120.83/55.30 thf(4838,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2749_add__self__div__2)). 120.83/55.30 thf(22105,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4838])). 120.83/55.30 thf(1756,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ D))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_power__le__dvd)). 120.83/55.30 thf(11026,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ D))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756])). 120.83/55.30 thf(3701,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (standardRes @ B) @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2490_StandardRes__prop1)). 120.83/55.30 thf(17780,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (standardRes @ B) @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3701])). 120.83/55.30 thf(3098,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_zero__le__power2)). 120.83/55.30 thf(15728,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3098])). 120.83/55.30 thf(3932,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ B) @ zero_zero_int)) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5015_gcd__code__int)). 120.83/55.30 thf(18601,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ B) @ zero_zero_int)) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3932])). 120.83/55.30 thf(734,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1947_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.30 thf(7417,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])). 120.83/55.30 thf(835,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1726_dvd_Oless__asym_H)). 120.83/55.30 thf(7806,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[835])). 120.83/55.30 thf(2378,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (code_nat_of_aux @ B) @ A) = (hAPP_nat_nat @ (code_nat_of_aux @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ B) @ one_on1645066479umeral)) @ (hAPP_nat_nat @ suc @ A))) <= (zero_z126310315umeral != B)) & ((A = (hAPP_nat_nat @ (code_nat_of_aux @ B) @ A)) <= (B = zero_z126310315umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3258_nat__of__aux__code)). 120.83/55.30 thf(13184,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (code_nat_of_aux @ B) @ A) = (hAPP_nat_nat @ (code_nat_of_aux @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ B) @ one_on1645066479umeral)) @ (hAPP_nat_nat @ suc @ A))) | (zero_z126310315umeral = B)) & ((A = (hAPP_nat_nat @ (code_nat_of_aux @ B) @ A)) | ~ (B = zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378])). 120.83/55.30 thf(4307,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) @ one_one_int) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)) @ one_one_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1462_zcong__zpower__zmult)). 120.83/55.30 thf(20043,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) @ one_one_int) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)) @ one_one_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4307])). 120.83/55.30 thf(2927,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1371_mult__strict__mono_H)). 120.83/55.30 thf(15126,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2927])). 120.83/55.30 thf(3190,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) <= (zero_zero_int != C)) <= (D != zero_zero_int)) <= ((is_int @ D) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4719_add__rat)). 120.83/55.30 thf(16036,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) | (zero_zero_int = C) | (D = zero_zero_int) | ~ ((is_int @ D) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3190])). 120.83/55.30 thf(1539,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_power2__le__imp__le)). 120.83/55.30 thf(10239,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539])). 120.83/55.30 thf(505,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ sin @ A))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3663_abs__sin__le__one)). 120.83/55.30 thf(6625,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ sin @ A))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 120.83/55.30 thf(479,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2512_dvd__imp__mod__0)). 120.83/55.30 thf(6541,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 120.83/55.30 thf(777,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2688_Divides_Omod__div__equality_H)). 120.83/55.30 thf(7572,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 120.83/55.30 thf(707,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3934_real__root__pow__pos2)). 120.83/55.30 thf(7313,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])). 120.83/55.30 thf(1291,axiom,(((hAPP_nat_rat @ semiri151668891at_rat @ zero_zero_nat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2922_of__nat__0)). 120.83/55.30 thf(9392,plain,(((hAPP_nat_rat @ semiri151668891at_rat @ zero_zero_nat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291])). 120.83/55.30 thf(4368,axiom,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_semiring__numeral__1__eq__1)). 120.83/55.30 thf(20271,plain,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4368])). 120.83/55.30 thf(3554,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1507_less__zeroE)). 120.83/55.30 thf(17239,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3554])). 120.83/55.30 thf(3345,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f429384717t_bool @ (hAPP_f1173902867t_bool @ cOMBB_real_bool_int @ A) @ B) @ C) = (hAPP_real_bool @ A @ (hAPP_int_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__RealDef__Oreal_000tc__HOL__Obool_000tc__Int__Oint_U)). 120.83/55.30 thf(16573,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f429384717t_bool @ (hAPP_f1173902867t_bool @ cOMBB_real_bool_int @ A) @ B) @ C) = (hAPP_real_bool @ A @ (hAPP_int_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3345])). 120.83/55.30 thf(4077,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5134_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J)). 120.83/55.30 thf(19195,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4077])). 120.83/55.30 thf(763,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3814_fact__mod)). 120.83/55.30 thf(7523,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])). 120.83/55.30 thf(131,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_dvd__triv__left)). 120.83/55.30 thf(5387,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 120.83/55.30 thf(940,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4011_coprime__mul)). 120.83/55.30 thf(8159,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])). 120.83/55.30 thf(743,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_mult__right__mono)). 120.83/55.30 thf(7448,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])). 120.83/55.30 thf(4493,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2658_zmult2__lemma__aux4)). 120.83/55.30 thf(20757,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4493])). 120.83/55.30 thf(922,axiom,((! [A:$i,B:$i,C:$i]: ((~ ((hBOOL @ (hAPP_nat_bool @ prime @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4177_coprime__prime)). 120.83/55.30 thf(8100,plain,((! [A:$i,B:$i,C:$i]: (~ ((hBOOL @ (hAPP_nat_bool @ prime @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[922])). 120.83/55.30 thf(3804,axiom,(((hAPP_int_int @ pred @ pls) = min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4043_pred__Pls)). 120.83/55.30 thf(18137,plain,(((hAPP_int_int @ pred @ pls) = min)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3804])). 120.83/55.30 thf(1128,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2209_le__iff__diff__le__0)). 120.83/55.30 thf(8820,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128])). 120.83/55.30 thf(1818,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1400_power__less__imp__less__base)). 120.83/55.30 thf(11248,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818])). 120.83/55.30 thf(4242,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <=> (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_mult__less__cancel__left__disj)). 120.83/55.30 thf(19796,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))) & ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4242])). 120.83/55.30 thf(4699,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = A) & (B = zero_zero_nat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3539_int__zle__neg)). 120.83/55.30 thf(21604,plain,((! [A:$i,B:$i]: ((((zero_zero_nat = A) & (B = zero_zero_nat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) => ((zero_zero_nat = A) & (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4699])). 120.83/55.30 thf(2966,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_mult__strict__left__mono)). 120.83/55.30 thf(15247,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2966])). 120.83/55.30 thf(2263,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.30 thf(12756,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2263])). 120.83/55.30 thf(799,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4316_dvd__gcd__D2__nat)). 120.83/55.30 thf(7668,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 120.83/55.30 thf(422,axiom,((! [A:$i]: ? [B:$i]: (! [C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ tan @ C) = A)) => (B = C)) & ((hAPP_real_real @ tan @ B) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3627_tan__total)). 120.83/55.30 thf(6349,plain,((! [A:$i]: ? [B:$i]: (! [C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ tan @ C) = A)) => (B = C)) & ((hAPP_real_real @ tan @ B) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 120.83/55.30 thf(3827,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A) != zero_zero_int) <= (zero_zero_int != B)) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_field__power__not__zero)). 120.83/55.30 thf(18208,plain,((! [A:$i,B:$i]: (~ ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A) = zero_zero_int) | (zero_zero_int = B) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3827])). 120.83/55.30 thf(2614,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2424_mod__add__left__eq)). 120.83/55.30 thf(14040,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2614])). 120.83/55.30 thf(1865,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ D))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ C)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1820_mult__diff__mult)). 120.83/55.30 thf(11432,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ D))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ C)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865])). 120.83/55.30 thf(1534,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1242_zero__le__power)). 120.83/55.30 thf(10222,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534])). 120.83/55.30 thf(35,axiom,((! [A:$i]: ((hAPP_complex_complex @ uminus473333897omplex @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ uminus473333897omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4070_cnj_Ominus)). 120.83/55.30 thf(5063,plain,((! [A:$i]: ((hAPP_complex_complex @ uminus473333897omplex @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ uminus473333897omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 120.83/55.30 thf(545,axiom,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3634_sin__minus)). 120.83/55.30 thf(6752,plain,((! [A:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])). 120.83/55.30 thf(191,axiom,((! [A:$i]: (((hAPP_int_real @ real_int @ (archim856651990g_real @ A)) = A) <=> (? [B:$i]: (((hAPP_int_real @ real_int @ B) = A) & (is_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4398_real__of__int__ceiling__cancel)). 120.83/55.30 thf(5576,plain,((! [A:$i]: ((((hAPP_int_real @ real_int @ (archim856651990g_real @ A)) = A) => (? [B:$i]: (((hAPP_int_real @ real_int @ B) = A) & (is_int @ B)))) & ((? [B:$i]: (((hAPP_int_real @ real_int @ B) = A) & (is_int @ B))) => ((hAPP_int_real @ real_int @ (archim856651990g_real @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 120.83/55.30 thf(96,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ uminus_uminus_real @ C)) @ (hAPP_real_real @ uminus_uminus_real @ D))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ C)))) @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3496_abs__sum__triangle__ineq)). 120.83/55.30 thf(5273,plain,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ uminus_uminus_real @ C)) @ (hAPP_real_real @ uminus_uminus_real @ D))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ C)))) @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 120.83/55.30 thf(275,axiom,((! [A:$i,B:$i]: ((((! [C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ D)) @ (hAPP_nat_real @ B @ C)))) & ! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ B @ C)))) | (! [C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ (hAPP_nat_real @ B @ D))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))) & ! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ A)))) <= (hBOOL @ (tendsto_nat_real @ B @ A @ sequentially))) <= (hBOOL @ (monoseq_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5037_monoseq__le)). 120.83/55.30 thf(5850,plain,((! [A:$i,B:$i]: ((! [C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ D)) @ (hAPP_nat_real @ B @ C)))) & ! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ B @ C)))) | (! [C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ (hAPP_nat_real @ B @ D))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))) & ! [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ C)) @ A))) | ~ (hBOOL @ (tendsto_nat_real @ B @ A @ sequentially)) | ~ (hBOOL @ (monoseq_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 120.83/55.30 thf(1782,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.30 thf(11129,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782])). 120.83/55.30 thf(3140,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3652_real__of__nat__add)). 120.83/55.30 thf(15867,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3140])). 120.83/55.30 thf(1081,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2247_minf_I10_J)). 120.83/55.30 thf(8673,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081])). 120.83/55.30 thf(3576,axiom,((! [A:$i]: ((image_int_nat @ nat @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) = (hAPP_n1699378549t_bool @ ord_atMost_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5183_SetInterval_Otransfer__nat__int__set__functions_I1_J)). 120.83/55.30 thf(17318,plain,((! [A:$i]: ((image_int_nat @ nat @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) = (hAPP_n1699378549t_bool @ ord_atMost_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3576])). 120.83/55.30 thf(785,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.30 thf(7609,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 120.83/55.30 thf(872,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2996_power__0__Suc)). 120.83/55.30 thf(7927,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])). 120.83/55.30 thf(959,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1775_le__add__diff__inverse)). 120.83/55.30 thf(8219,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[959])). 120.83/55.30 thf(1280,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2902_odd__iff__not__even)). 120.83/55.30 thf(9359,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280])). 120.83/55.30 thf(3616,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 120.83/55.30 thf(17450,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3616])). 120.83/55.30 thf(1918,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3902_real__root__le__iff)). 120.83/55.30 thf(11606,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918])). 120.83/55.30 thf(1990,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1546_right__diff__distrib__number__of)). 120.83/55.30 thf(11828,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990])). 120.83/55.30 thf(2642,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1859_add__pos__nonneg)). 120.83/55.30 thf(14148,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2642])). 120.83/55.30 thf(1186,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ A) & (is_int @ C) & (is_int @ D) & (is_int @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) => ((C = D) <=> (B = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1957_diff__eq__diff__eq)). 120.83/55.30 thf(9012,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ A) & (is_int @ C) & (is_int @ D) & (is_int @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) => (((C = D) => (B = A)) & ((B = A) => (C = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186])). 120.83/55.30 thf(4576,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ number_number_of_int @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ number_number_of_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_left__distrib__number__of)). 120.83/55.30 thf(21155,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ number_number_of_int @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ number_number_of_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4576])). 120.83/55.30 thf(235,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ E)) @ C))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ E)) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ D) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4212_divmod__nat__rel__mult1__eq)). 120.83/55.30 thf(5726,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ E)) @ C))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ E)) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ D) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 120.83/55.30 thf(4212,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5135_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J)). 120.83/55.30 thf(19679,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4212])). 120.83/55.30 thf(3550,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4161_prime__dvd__power__two)). 120.83/55.30 thf(17229,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3550])). 120.83/55.30 thf(571,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3355_real__divide__square__eq)). 120.83/55.30 thf(6827,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 120.83/55.30 thf(4614,axiom,((! [A:$i]: (((((hAPP_int_int @ uminus_uminus_int @ A) = (hAPP_int_int @ abs_abs_int @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) => (A = (hAPP_int_int @ abs_abs_int @ A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3542_zabs__def)). 120.83/55.30 thf(21284,plain,((! [A:$i]: (((((hAPP_int_int @ uminus_uminus_int @ A) = (hAPP_int_int @ abs_abs_int @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) => (A = (hAPP_int_int @ abs_abs_int @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4614])). 120.83/55.30 thf(344,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2450_dvd__mod)). 120.83/55.30 thf(6097,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 120.83/55.30 thf(3313,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2176_zero__le__double__add__iff__zero__le__single__add)). 120.83/55.30 thf(16468,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3313])). 120.83/55.30 thf(1074,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_power2__less__imp__less)). 120.83/55.30 thf(8658,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074])). 120.83/55.30 thf(1656,axiom,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) <= (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B))) & (((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B) = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3544_zmod__zminus2__eq__if)). 120.83/55.30 thf(10666,plain,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) | ~ (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B))) & ((~ ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B) = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656])). 120.83/55.30 thf(2038,axiom,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ one_on1645066479umeral) @ A) = one_on1645066479umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_power__one)). 120.83/55.30 thf(11965,plain,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ one_on1645066479umeral) @ A) = one_on1645066479umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038])). 120.83/55.30 thf(3800,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2603_zdiv__mono2)). 120.83/55.30 thf(18127,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3800])). 120.83/55.30 thf(986,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B)) <= (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2633_div__add__self2)). 120.83/55.30 thf(8326,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B)) | (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[986])). 120.83/55.30 thf(3591,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1427_power__gt1__lemma)). 120.83/55.30 thf(17377,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3591])). 120.83/55.30 thf(326,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) <= (! [D:$i]: ((? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ zero_zero_real)))) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4549_DERIV__nonpos__imp__nonincreasing)). 120.83/55.30 thf(6033,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) | ~ (! [D:$i]: (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ zero_zero_real))) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 120.83/55.30 thf(1224,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2020_add__right__mono)). 120.83/55.30 thf(9149,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224])). 120.83/55.30 thf(1765,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3922_real__root__ge__1__iff)). 120.83/55.30 thf(11052,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765])). 120.83/55.30 thf(3877,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) => ((hAPP_int_int @ (div_mod_int @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2647_mod__pos__neg__trivial)). 120.83/55.30 thf(18396,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) => ((hAPP_int_int @ (div_mod_int @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3877])). 120.83/55.30 thf(1787,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3445_ln__gt__zero__imp__gt__one)). 120.83/55.30 thf(11142,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787])). 120.83/55.30 thf(2374,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.30 thf(13169,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374])). 120.83/55.30 thf(4132,axiom,((! [A:$i,B:$i]: (((one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ B)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))))) & (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4789_zpower__number__of__odd)). 120.83/55.30 thf(19393,plain,((! [A:$i,B:$i]: (((one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ B)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4132])). 120.83/55.30 thf(564,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ pi))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3658_sin__gt__zero__pi)). 120.83/55.30 thf(6805,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ pi)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 120.83/55.30 thf(627,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ real_int @ B)) @ pi))) = (hAPP_real_real @ tan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4454_tan__periodic__int)). 120.83/55.30 thf(7014,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ real_int @ B)) @ pi))) = (hAPP_real_real @ tan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])). 120.83/55.30 thf(1271,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ E) @ F))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) => ((A = E) <= (D != zero_zero_int)))) <= ((is_int @ A) & (is_int @ E) & (is_int @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2791_unique__quotient)). 120.83/55.30 thf(9316,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ E) @ F))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ C @ D) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) => ((A = E) | (D = zero_zero_int)))) | ~ ((is_int @ A) & (is_int @ E) & (is_int @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271])). 120.83/55.30 thf(3379,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__special_I2_J)). 120.83/55.30 thf(16690,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3379])). 120.83/55.30 thf(2273,axiom,((! [A:$i,B:$i]: ((B != zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4346_gcd__le2__nat)). 120.83/55.30 thf(12795,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273])). 120.83/55.30 thf(653,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) <=> (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1942_add__left__cancel)). 120.83/55.30 thf(7138,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) => (C = B)) & ((C = B) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 120.83/55.30 thf(4385,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ B) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2528_zmod__le__nonneg__dividend)). 120.83/55.30 thf(20335,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ B) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4385])). 120.83/55.30 thf(1106,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.30 thf(8764,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106])). 120.83/55.30 thf(2159,axiom,((! [A:$i]: ((of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4111_complex__mult__cnj)). 120.83/55.30 thf(12378,plain,((! [A:$i]: ((of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159])). 120.83/55.30 thf(2715,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1367_mult__strict__mono_H)). 120.83/55.30 thf(14392,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2715])). 120.83/55.30 thf(2494,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_arith__simps_I32_J)). 120.83/55.30 thf(13607,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2494])). 120.83/55.30 thf(2101,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1806_diff__square)). 120.83/55.30 thf(12164,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101])). 120.83/55.30 thf(3430,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3379_real__sqrt__sum__squares__less)). 120.83/55.30 thf(16837,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3430])). 120.83/55.30 thf(210,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_comm__semiring__class_Odistrib)). 120.83/55.30 thf(5639,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 120.83/55.30 thf(558,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_mult__nonpos__nonpos)). 120.83/55.30 thf(6788,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])). 120.83/55.30 thf(3061,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mult__number__of__left)). 120.83/55.30 thf(15602,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3061])). 120.83/55.30 thf(81,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3641_sin__npi)). 120.83/55.30 thf(5234,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 120.83/55.30 thf(4868,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_i345030060t_bool @ A @ C) @ B) = (hAPP_i1948725293t_bool @ (hAPP_i345030060t_bool @ (hAPP_f791698359t_bool @ cOMBC_241247961t_bool @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__fun_Itc__Int__Oint)). 120.83/55.30 thf(22201,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_i345030060t_bool @ A @ C) @ B) = (hAPP_i1948725293t_bool @ (hAPP_i345030060t_bool @ (hAPP_f791698359t_bool @ cOMBC_241247961t_bool @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4868])). 120.83/55.30 thf(3483,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2045_add__less__imp__less__right)). 120.83/55.30 thf(17022,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3483])). 120.83/55.30 thf(1479,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.30 thf(10026,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479])). 120.83/55.30 thf(286,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (natfloor @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3675_le__natfloor)). 120.83/55.30 thf(5900,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (natfloor @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 120.83/55.30 thf(2787,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3329_real__sqrt__gt__0__iff)). 120.83/55.30 thf(14649,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2787])). 120.83/55.30 thf(1438,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1557_dvd__mult__cancel)). 120.83/55.30 thf(9893,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438])). 120.83/55.30 thf(2291,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2049_add__strict__mono)). 120.83/55.30 thf(12870,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291])). 120.83/55.30 thf(3609,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_nat__mult__2)). 120.83/55.30 thf(17429,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3609])). 120.83/55.30 thf(3201,axiom,((! [A:$i]: ((((hAPP_real_real @ ln @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) => (one_one_real = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3432_ln__eq__minus__one)). 120.83/55.30 thf(16083,plain,((! [A:$i]: ((((hAPP_real_real @ ln @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) => (one_one_real = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3201])). 120.83/55.30 thf(354,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ pi)) & ! [C:$i]: ((C = B) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ pi)) & (A = (hAPP_real_real @ cos @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))) & (A = (hAPP_real_real @ cos @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3592_cos__total)). 120.83/55.30 thf(6129,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ pi)) & ! [C:$i]: ((C = B) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ pi)) & (A = (hAPP_real_real @ cos @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))) & (A = (hAPP_real_real @ cos @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 120.83/55.30 thf(2950,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_power__one__right)). 120.83/55.30 thf(15200,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2950])). 120.83/55.30 thf(3968,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((B = (hAPP_int_int @ (div_mod_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2613_mod__pos__pos__trivial)). 120.83/55.30 thf(18714,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (div_mod_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3968])). 120.83/55.30 thf(1401,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2418_mod__add__eq)). 120.83/55.30 thf(9761,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401])). 120.83/55.30 thf(462,axiom,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ A)) @ A) = one_one_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3839_real__mult__inverse__left)). 120.83/55.30 thf(6475,plain,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ A)) @ A) = one_one_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 120.83/55.30 thf(1393,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_zero__less__mult__pos2)). 120.83/55.30 thf(9739,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393])). 120.83/55.30 thf(169,axiom,((! [A:$i]: ((of_real_complex @ A) = (rcis @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4258_rcis__zero__arg)). 120.83/55.30 thf(5498,plain,((! [A:$i]: ((of_real_complex @ A) = (rcis @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 120.83/55.30 thf(4919,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ pls) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__Pls__right)). 120.83/55.30 thf(22364,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ pls) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4919])). 120.83/55.30 thf(1877,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) <= (C != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2535_div__mult__mult1)). 120.83/55.30 thf(11474,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) | (C = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877])). 120.83/55.30 thf(4482,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2225_wset__g__1)). 120.83/55.30 thf(20733,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4482])). 120.83/55.30 thf(976,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.30 thf(8294,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[976])). 120.83/55.30 thf(4613,axiom,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => ((hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (posDivAlg @ A @ B))) & (((posDivAlg @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2769_posDivAlg__eqn)). 120.83/55.30 thf(21279,plain,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => ((hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (posDivAlg @ A @ B))) & (((posDivAlg @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4613])). 120.83/55.30 thf(1346,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3083_zpower__int)). 120.83/55.30 thf(9581,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346])). 120.83/55.30 thf(1240,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_dvd__mult)). 120.83/55.30 thf(9201,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240])). 120.83/55.30 thf(2067,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2185_add__pos__pos)). 120.83/55.30 thf(12059,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067])). 120.83/55.30 thf(2868,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3709_sin__cos__npi)). 120.83/55.30 thf(14929,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2868])). 120.83/55.30 thf(2011,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2868_add__Suc__right)). 120.83/55.30 thf(11888,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011])). 120.83/55.30 thf(1554,axiom,((! [A:$i,B:$i,C:$i]: (((zero_zero_nat = A) | (C = B)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1844_nat__mult__eq__cancel__disj)). 120.83/55.30 thf(10285,plain,((! [A:$i,B:$i,C:$i]: ((((zero_zero_nat = A) | (C = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => ((zero_zero_nat = A) | (C = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554])). 120.83/55.30 thf(1450,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = zero_zero_nat) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1763_diff__is__0__eq)). 120.83/55.30 thf(9932,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450])). 120.83/55.30 thf(2490,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ B @ A)) <= (! [C:$i]: (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ C))))))) <= (! [C:$i]: (hBOOL @ (hAPP_int_bool @ B @ (hAPP_nat_int @ semiri1621563631at_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4548_int__of__nat__induct)). 120.83/55.30 thf(13594,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ B @ A)) | ~ (! [C:$i]: (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ C)))))) | ~ (! [C:$i]: (hBOOL @ (hAPP_int_bool @ B @ (hAPP_nat_int @ semiri1621563631at_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2490])). 120.83/55.30 thf(821,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3587_cos__double__less__one)). 120.83/55.30 thf(7749,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])). 120.83/55.30 thf(1609,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_int_complex @ number528085621omplex @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_power__m1__even)). 120.83/55.30 thf(10518,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_int_complex @ number528085621omplex @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609])). 120.83/55.30 thf(2748,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1403_power__decreasing)). 120.83/55.30 thf(14494,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2748])). 120.83/55.30 thf(4301,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2531_zdvd__mult__div__cancel)). 120.83/55.30 thf(20028,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4301])). 120.83/55.30 thf(2429,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4405_powr__less__mono2)). 120.83/55.30 thf(13376,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429])). 120.83/55.30 thf(1019,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3457_ln__add__one__self__le__self2)). 120.83/55.30 thf(8439,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019])). 120.83/55.30 thf(3774,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (is_RRset @ (hAPP_i1948725293t_bool @ (noXRRset @ B) @ A)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4588_noX__is__RRset)). 120.83/55.30 thf(18027,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (is_RRset @ (hAPP_i1948725293t_bool @ (noXRRset @ B) @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3774])). 120.83/55.30 thf(830,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2412_zmod__simps_I1_J)). 120.83/55.30 thf(7789,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])). 120.83/55.30 thf(782,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2379_mod__mult__right__eq)). 120.83/55.30 thf(7597,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 120.83/55.30 thf(3363,axiom,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ A) = (hAPP_complex_complex @ cnj @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4067_complex__cnj__number__of)). 120.83/55.30 thf(16625,plain,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ A) = (hAPP_complex_complex @ cnj @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3363])). 120.83/55.30 thf(1796,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_add__numeral__0__right)). 120.83/55.30 thf(11184,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796])). 120.83/55.30 thf(421,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3680_sin__cos__squared__add3)). 120.83/55.30 thf(6346,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 120.83/55.30 thf(1095,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2351_div__mod__equality2)). 120.83/55.30 thf(8732,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095])). 120.83/55.30 thf(4143,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4295_Bnor__mem__zg)). 120.83/55.30 thf(19430,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4143])). 120.83/55.30 thf(4832,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_dvd__refl)). 120.83/55.30 thf(22090,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4832])). 120.83/55.30 thf(3399,axiom,((! [A:$i,B:$i]: (((A = zero_z891286103de_int) | (B = zero_z891286103de_int)) <= (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_divisors__zero)). 120.83/55.30 thf(16741,plain,((! [A:$i,B:$i]: ((A = zero_z891286103de_int) | (B = zero_z891286103de_int) | ~ (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3399])). 120.83/55.30 thf(1508,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3940_real__root__inverse__lemma)). 120.83/55.30 thf(10122,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_real_real @ inverse_inverse_real @ A)) = (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508])). 120.83/55.30 thf(4724,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4974_gcd__1__int)). 120.83/55.30 thf(21705,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4724])). 120.83/55.30 thf(4573,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcongm @ A) @ B) @ C)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5153_zcongm__def)). 120.83/55.30 thf(21146,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcongm @ A) @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcongm @ A) @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4573])). 120.83/55.30 thf(3498,axiom,((! [A:$i]: ((one_one_complex = A) <=> (A = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1954_one__reorient)). 120.83/55.30 thf(17064,plain,((! [A:$i]: (((one_one_complex = A) => (A = one_one_complex)) & ((A = one_one_complex) => (one_one_complex = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3498])). 120.83/55.30 thf(2992,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (ratreal @ A)) @ (ratreal @ B))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4693_real__less__code)). 120.83/55.30 thf(15354,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (ratreal @ A)) @ (ratreal @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (ratreal @ A)) @ (ratreal @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2992])). 120.83/55.30 thf(3004,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3033_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.30 thf(15399,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3004])). 120.83/55.30 thf(1485,axiom,((! [A:$i,B:$i,C:$i]: ((C != zero_zero_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1816_divides__exp2)). 120.83/55.30 thf(10047,plain,((! [A:$i,B:$i,C:$i]: ((~ (C = zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485])). 120.83/55.30 thf(2498,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (code_c271388182l_size @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (code_c271388182l_size @ (code_S1047413653umeral @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4062_code__numeral_Osize_I2_J)). 120.83/55.30 thf(13629,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (code_c271388182l_size @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (code_c271388182l_size @ (code_S1047413653umeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2498])). 120.83/55.30 thf(4778,axiom,((! [A:$i,B:$i]: ((((hAPP_P1175774780nt_int @ product_fst_int_int @ (posDivAlg @ B @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4226_div__pos__pos)). 120.83/55.30 thf(21902,plain,((! [A:$i,B:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (posDivAlg @ B @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4778])). 120.83/55.30 thf(2412,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_power__mult)). 120.83/55.30 thf(13316,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412])). 120.83/55.30 thf(3460,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3856_exp__bound)). 120.83/55.30 thf(16932,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3460])). 120.83/55.30 thf(4386,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2885_anything__times__even)). 120.83/55.30 thf(20337,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4386])). 120.83/55.30 thf(3639,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (((hAPP_int_int @ (inv @ B) @ A) != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2128_inv__not__p__minus__1)). 120.83/55.30 thf(17546,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (~ ((hAPP_int_int @ (inv @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3639])). 120.83/55.30 thf(3196,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_int @ number_number_of_int @ B) = (hAPP_int_int @ number_number_of_int @ A)) <=> (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_eq__number__of)). 120.83/55.30 thf(16058,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((hAPP_int_int @ number_number_of_int @ B) = (hAPP_int_int @ number_number_of_int @ A)) => (B = A)) & ((B = A) => ((hAPP_int_int @ number_number_of_int @ B) = (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3196])). 120.83/55.30 thf(318,axiom,((! [A:$i]: ((zero_zero_nat = (natceiling @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3399_natceiling__neg)). 120.83/55.30 thf(6005,plain,((! [A:$i]: ((zero_zero_nat = (natceiling @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 120.83/55.30 thf(1838,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2359_zdiv__zmult1__eq)). 120.83/55.30 thf(11336,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838])). 120.83/55.30 thf(4436,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_less__special_I1_J)). 120.83/55.30 thf(20542,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4436])). 120.83/55.30 thf(4753,axiom,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_nat__1__add__1)). 120.83/55.30 thf(21823,plain,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4753])). 120.83/55.30 thf(1024,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_mult__dvd__mono)). 120.83/55.30 thf(8455,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])). 120.83/55.30 thf(2827,axiom,(((hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) != zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3577_cos__two__neq__zero)). 120.83/55.30 thf(14794,plain,((~ ((hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2827])). 120.83/55.30 thf(4027,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4493_zgcd__assoc)). 120.83/55.30 thf(18934,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ C)) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4027])). 120.83/55.30 thf(459,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2136_diff__add__cancel)). 120.83/55.30 thf(6465,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 120.83/55.30 thf(77,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)) => (A = (hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3604_cos__arccos__abs)). 120.83/55.30 thf(5217,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)) => (A = (hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 120.83/55.30 thf(1110,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2169_add__nonneg__nonneg)). 120.83/55.30 thf(8775,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110])). 120.83/55.30 thf(4943,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)). 120.83/55.30 thf(22450,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4943])). 120.83/55.30 thf(3314,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1693_two__realpow__ge__one)). 120.83/55.30 thf(16473,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3314])). 120.83/55.30 thf(3643,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ B)) => ((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_is__mult__sum2sq)). 120.83/55.30 thf(17559,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ B)) => ((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3643])). 120.83/55.30 thf(3991,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_dvd__mult__right)). 120.83/55.30 thf(18802,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3991])). 120.83/55.30 thf(1831,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((zero_zero_real = (hAPP_real_real @ ln @ A)) <=> (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3442_ln__eq__zero__iff)). 120.83/55.30 thf(11300,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((zero_zero_real = (hAPP_real_real @ ln @ A)) => (A = one_one_real)) & ((A = one_one_real) => (zero_zero_real = (hAPP_real_real @ ln @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831])). 120.83/55.30 thf(2140,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1343_mult__less__imp__less__right)). 120.83/55.30 thf(12310,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140])). 120.83/55.30 thf(4004,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) => (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4521_zprime__imp__zrelprime)). 120.83/55.30 thf(18845,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) => (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4004])). 120.83/55.30 thf(4690,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1526_zdvd__zdiffD)). 120.83/55.30 thf(21546,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4690])). 120.83/55.30 thf(3838,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2521_neg__imp__zdiv__neg__iff)). 120.83/55.30 thf(18248,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3838])). 120.83/55.30 thf(1768,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1982_add__0)). 120.83/55.30 thf(11061,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768])). 120.83/55.30 thf(3675,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3242_neg__one__power__parity)). 120.83/55.30 thf(17675,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)))) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_nat @ nat @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3675])). 120.83/55.30 thf(3025,axiom,((! [A:$i,B:$i,C:$i]: ((zero_z891286103de_int != C) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2623_div__mult__self1)). 120.83/55.30 thf(15463,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_z891286103de_int = C)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3025])). 120.83/55.30 thf(1441,axiom,((! [A:$i,B:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z891286103de_int) <=> (((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat) & (A = zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_power__eq__0__iff__number__of)). 120.83/55.30 thf(9900,plain,((! [A:$i,B:$i]: ((((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z891286103de_int) => (~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat) & (A = zero_z891286103de_int))) & ((~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat) & (A = zero_z891286103de_int)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441])). 120.83/55.30 thf(4330,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ A)) @ zero_zero_int) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2231_MultInv__prop3)). 120.83/55.30 thf(20160,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ B) @ A)) @ zero_zero_int) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4330])). 120.83/55.30 thf(4097,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2443_dvd__mod__iff)). 120.83/55.30 thf(19262,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4097])). 120.83/55.30 thf(2885,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (rsetR @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4595_RsetR__fin)). 120.83/55.30 thf(14986,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (rsetR @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2885])). 120.83/55.30 thf(2419,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((is_int @ A) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_int_nat @ nat @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ zOdd)) => (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (? [E:$i]: ((A = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ E) @ (hAPP_int_nat @ nat @ D))) & (is_int @ E))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_int_nat @ nat @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4529_int__relprime__odd__power__divisors)). 120.83/55.30 thf(13340,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((is_int @ A) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_int_nat @ nat @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ zOdd)) => (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (? [E:$i]: ((A = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ E) @ (hAPP_int_nat @ nat @ D))) & (is_int @ E))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_int_nat @ nat @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419])). 120.83/55.30 thf(2461,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_dvd__trans)). 120.83/55.30 thf(13490,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2461])). 120.83/55.30 thf(790,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2945_of__nat__less__iff)). 120.83/55.30 thf(7624,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])). 120.83/55.30 thf(2228,axiom,((! [A:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_real @ number267125858f_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4394_real__number__of)). 120.83/55.30 thf(12641,plain,((! [A:$i]: ((hAPP_int_real @ real_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_real @ number267125858f_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2228])). 120.83/55.30 thf(2127,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_mult__nonpos__nonneg)). 120.83/55.30 thf(12270,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127])). 120.83/55.30 thf(4884,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4528_Bnor__mem__if)). 120.83/55.30 thf(22252,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4884])). 120.83/55.30 thf(1176,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_mult__neg__neg)). 120.83/55.30 thf(8980,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176])). 120.83/55.30 thf(3695,axiom,((one_one_nat = (hAPP_int_nat @ nat @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2717_transfer__nat__int__numerals_I2_J)). 120.83/55.30 thf(17752,plain,((one_one_nat = (hAPP_int_nat @ nat @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3695])). 120.83/55.30 thf(3377,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1672_mult__less__mono2)). 120.83/55.30 thf(16677,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3377])). 120.83/55.30 thf(1452,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_less__special_I3_J)). 120.83/55.30 thf(9942,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452])). 120.83/55.30 thf(4738,axiom,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3043_transfer__int__nat__numerals_I2_J)). 120.83/55.30 thf(21761,plain,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4738])). 120.83/55.30 thf(2051,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2272_pinf_I9_J)). 120.83/55.30 thf(12005,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051])). 120.83/55.30 thf(2027,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_zero__le__even__power_H)). 120.83/55.30 thf(11933,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027])). 120.83/55.30 thf(2318,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ uminus_uminus_real @ A))) @ (hAPP_real_real @ sin @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ uminus_uminus_real @ A))) @ (hAPP_real_real @ cos @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3742_sin__cos__minus)). 120.83/55.30 thf(12962,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ uminus_uminus_real @ A))) @ (hAPP_real_real @ sin @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ uminus_uminus_real @ A))) @ (hAPP_real_real @ cos @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318])). 120.83/55.30 thf(1201,axiom,(((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_one__add__one__is__two)). 120.83/55.30 thf(9068,plain,(((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201])). 120.83/55.30 thf(2093,axiom,((! [A:$i]: ((hAPP_int_nat @ phi @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ norRRset @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4585_phi__def)). 120.83/55.30 thf(12138,plain,((! [A:$i]: ((hAPP_int_nat @ phi @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ norRRset @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093])). 120.83/55.30 thf(3267,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ one_on1645066479umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1260_less__add__one)). 120.83/55.30 thf(16328,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ one_on1645066479umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3267])). 120.83/55.30 thf(1515,axiom,((! [A:$i,B:$i]: (((A = B) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3059_le__less__Suc__eq)). 120.83/55.30 thf(10143,plain,((! [A:$i,B:$i]: ((((A = B) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ suc @ A))) => (A = B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515])). 120.83/55.30 thf(3841,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = A) <=> (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_add__0__iff)). 120.83/55.30 thf(18257,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = A) => (B = zero_zero_int)) & ((B = zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3841])). 120.83/55.30 thf(366,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((hAPP_int_real @ real_int @ B) = (hAPP_int_real @ real_int @ A)) <=> (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4385_real__of__int__inject)). 120.83/55.30 thf(6171,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((((hAPP_int_real @ real_int @ B) = (hAPP_int_real @ real_int @ A)) => (A = B)) & ((A = B) => ((hAPP_int_real @ real_int @ B) = (hAPP_int_real @ real_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 120.83/55.30 thf(3756,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_less__special_I2_J)). 120.83/55.30 thf(17963,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3756])). 120.83/55.30 thf(2537,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2724_mod__le__divisor)). 120.83/55.30 thf(13758,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2537])). 120.83/55.30 thf(3478,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3133_diff__Suc__less)). 120.83/55.30 thf(16996,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3478])). 120.83/55.30 thf(670,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ one_on1684967323de_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_one__dvd)). 120.83/55.30 thf(7193,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ one_on1684967323de_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])). 120.83/55.30 thf(2470,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2917_of__nat__less__0__iff)). 120.83/55.30 thf(13522,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2470])). 120.83/55.30 thf(1489,axiom,((! [A:$i]: ((zero_zero_nat != A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1607_neq0__conv)). 120.83/55.30 thf(10058,plain,((! [A:$i]: (((~ (zero_zero_nat = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (~ (zero_zero_nat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489])). 120.83/55.30 thf(2893,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zOdd)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3095_even__minus__odd)). 120.83/55.30 thf(15007,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zOdd)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2893])). 120.83/55.30 thf(4554,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2166_add__nonneg__nonneg)). 120.83/55.30 thf(21074,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4554])). 120.83/55.30 thf(4068,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4977_gcd__commute__int)). 120.83/55.30 thf(19149,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4068])). 120.83/55.30 thf(946,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) <= (B != A)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_order__le__neq__implies__less)). 120.83/55.30 thf(8174,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) | (B = A) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[946])). 120.83/55.30 thf(4118,axiom,((! [A:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3550_power3__minus)). 120.83/55.30 thf(19354,plain,((! [A:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4118])). 120.83/55.30 thf(4465,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1521_diff__bin__simps_I7_J)). 120.83/55.30 thf(20656,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4465])). 120.83/55.30 thf(2759,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1322_mult__left__le__imp__le)). 120.83/55.30 thf(14548,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2759])). 120.83/55.30 thf(1940,axiom,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2369_mod__by__0)). 120.83/55.30 thf(11673,plain,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940])). 120.83/55.30 thf(2111,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1803_divides__exp)). 120.83/55.30 thf(12201,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111])). 120.83/55.30 thf(1807,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_mult__strict__left__mono)). 120.83/55.30 thf(11216,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807])). 120.83/55.30 thf(2465,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3077_div__1)). 120.83/55.30 thf(13507,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2465])). 120.83/55.30 thf(2903,axiom,((! [A:$i,B:$i,C:$i]: ((C = B) <=> ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1941_add__left__cancel)). 120.83/55.30 thf(15039,plain,((! [A:$i,B:$i,C:$i]: (((C = B) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C))) & (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) => (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2903])). 120.83/55.30 thf(107,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1785_real__add__mult__distrib)). 120.83/55.30 thf(5310,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 120.83/55.30 thf(4511,axiom,((! [A:$i,B:$i]: ((hBOOL @ A) | (hBOOL @ B) | ~ (hBOOL @ (fdisj @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U)). 120.83/55.30 thf(20840,plain,((! [A:$i,B:$i]: ((hBOOL @ A) | (hBOOL @ B) | ~ (hBOOL @ (fdisj @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4511])). 120.83/55.30 thf(3071,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2172_double__add__le__zero__iff__single__add__le__zero)). 120.83/55.30 thf(15639,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3071])). 120.83/55.30 thf(3606,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3324_real__sqrt__le__0__iff)). 120.83/55.30 thf(17419,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3606])). 120.83/55.30 thf(4411,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4514_zgcd__non__0)). 120.83/55.30 thf(20451,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = (hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4411])). 120.83/55.30 thf(4455,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3419_zdvd__self__abs2)). 120.83/55.30 thf(20606,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4455])). 120.83/55.30 thf(4000,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3216_of__nat__less__two__power)). 120.83/55.30 thf(18832,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4000])). 120.83/55.30 thf(1733,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_zpower__zpower)). 120.83/55.30 thf(10929,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733])). 120.83/55.30 thf(2261,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2144_add__nonpos__nonpos)). 120.83/55.30 thf(12751,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261])). 120.83/55.30 thf(1314,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3806_fact__gt__zero__nat)). 120.83/55.30 thf(9468,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314])). 120.83/55.30 thf(2330,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2931_of__nat__less__imp__less)). 120.83/55.30 thf(13014,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330])). 120.83/55.30 thf(3769,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_real @ (hAPP_f563293398t_real @ (hAPP_f134192053t_real @ cOMBB_int_real_int @ A) @ B) @ C) = (hAPP_int_real @ A @ (hAPP_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__RealDef__Oreal_000tc__Int__Oint_U)). 120.83/55.30 thf(18012,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_real @ (hAPP_f563293398t_real @ (hAPP_f134192053t_real @ cOMBB_int_real_int @ A) @ B) @ C) = (hAPP_int_real @ A @ (hAPP_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3769])). 120.83/55.30 thf(1563,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.30 thf(10338,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563])). 120.83/55.30 thf(3009,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ one_one_real)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.30 thf(15414,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ one_one_real)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3009])). 120.83/55.30 thf(2206,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_zero__less__mult__pos2)). 120.83/55.30 thf(12577,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206])). 120.83/55.30 thf(2138,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1860_add__pos__nonneg)). 120.83/55.30 thf(12305,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138])). 120.83/55.30 thf(954,axiom,((! [A:$i]: (A = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_power__one__right)). 120.83/55.30 thf(8205,plain,((! [A:$i]: (A = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[954])). 120.83/55.30 thf(1032,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ min) @ A) = (hAPP_int_int @ uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3535_mult__Min)). 120.83/55.30 thf(8482,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ min) @ A) = (hAPP_int_int @ uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032])). 120.83/55.30 thf(1212,axiom,(((hAPP_real_real @ sqrt @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3321_real__sqrt__one)). 120.83/55.30 thf(9094,plain,(((hAPP_real_real @ sqrt @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212])). 120.83/55.30 thf(2048,axiom,((! [A:$i,B:$i]: ((((image_nat_int @ semiri1621563631at_int @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) = (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5128_SetInterval_Otransfer__int__nat__set__functions)). 120.83/55.30 thf(11997,plain,((! [A:$i,B:$i]: (((image_nat_int @ semiri1621563631at_int @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) = (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048])). 120.83/55.30 thf(633,axiom,((! [A:$i]: ((? [B:$i]: ((is_int @ B) & ((hAPP_int_real @ real_int @ B) = A))) <=> ((hAPP_int_real @ real_int @ (archim1246769320r_real @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4382_real__of__int__floor__cancel)). 120.83/55.30 thf(7052,plain,((! [A:$i]: (((? [B:$i]: ((is_int @ B) & ((hAPP_int_real @ real_int @ B) = A))) => ((hAPP_int_real @ real_int @ (archim1246769320r_real @ A)) = A)) & (((hAPP_int_real @ real_int @ (archim1246769320r_real @ A)) = A) => (? [B:$i]: ((is_int @ B) & ((hAPP_int_real @ real_int @ B) = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])). 120.83/55.30 thf(2269,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1273_power__increasing)). 120.83/55.30 thf(12783,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269])). 120.83/55.30 thf(732,axiom,((! [A:$i,B:$i]: (((zero_zero_rat = A) | (zero_zero_rat = B)) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_divisors__zero)). 120.83/55.30 thf(7407,plain,((! [A:$i,B:$i]: ((zero_zero_rat = A) | (zero_zero_rat = B) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])). 120.83/55.30 thf(3002,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_dvd__add)). 120.83/55.30 thf(15395,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3002])). 120.83/55.30 thf(4160,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2609_zdiv__zmult2__eq)). 120.83/55.30 thf(19491,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4160])). 120.83/55.30 thf(3588,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1886_add__neg__nonpos)). 120.83/55.30 thf(17370,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3588])). 120.83/55.30 thf(2523,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2010_add__left__mono)). 120.83/55.30 thf(13714,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2523])). 120.83/55.30 thf(1639,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2955_of__nat__add)). 120.83/55.30 thf(10614,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B)) = (hAPP_n522471361de_int @ semiri1424489471de_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639])). 120.83/55.30 thf(4909,axiom,((! [A:$i,B:$i]: ? [C:$i]: (! [D:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ C))) & (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2251_minf_I10_J)). 120.83/55.30 thf(22339,plain,((? [A:$i]: (is_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4909])). 120.83/55.30 thf(1678,axiom,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3013_power__Suc)). 120.83/55.30 thf(10740,plain,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678])). 120.83/55.30 thf(2179,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2509_mod__mult__self2)). 120.83/55.30 thf(12469,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179])). 120.83/55.30 thf(4417,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_self__quotient__aux1)). 120.83/55.30 thf(20476,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4417])). 120.83/55.30 thf(998,axiom,((! [A:$i,B:$i]: (((B != zero_zero_nat) & (zero_z126310315umeral = A)) <=> (zero_z126310315umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1292_power__eq__0__iff)). 120.83/55.30 thf(8361,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_nat) & (zero_z126310315umeral = A)) => (zero_z126310315umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))) & ((zero_z126310315umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) => (~ (B = zero_zero_nat) & (zero_z126310315umeral = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])). 120.83/55.30 thf(3712,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_power2__le__imp__le)). 120.83/55.30 thf(17812,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3712])). 120.83/55.30 thf(1307,axiom,(((hAPP_i1732201573de_int @ number1226105091de_int @ pls) = zero_z891286103de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4257_zero__code__int__code)). 120.83/55.30 thf(9436,plain,(((hAPP_i1732201573de_int @ number1226105091de_int @ pls) = zero_z891286103de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307])). 120.83/55.30 thf(4495,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zadd__zmult__distrib2)). 120.83/55.30 thf(20766,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4495])). 120.83/55.30 thf(1611,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) <= ((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int)) & ((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))) <= (zero_zero_int != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3552_zdiv__zminus2__eq__if)). 120.83/55.30 thf(10524,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))) | ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int)) & ((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))) | (zero_zero_int = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611])). 120.83/55.30 thf(4656,axiom,((! [A:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4227_div__pos__pos__1__number__of)). 120.83/55.30 thf(21441,plain,((! [A:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4656])). 120.83/55.30 thf(4805,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2612_neg__mod__sign)). 120.83/55.30 thf(21989,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4805])). 120.83/55.30 thf(1900,axiom,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3541_nat__zminus__int)). 120.83/55.30 thf(11546,plain,((! [A:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900])). 120.83/55.30 thf(3421,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2056_add__strict__left__mono)). 120.83/55.30 thf(16812,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3421])). 120.83/55.30 thf(4348,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1461_zpower__zdvd__prop1)). 120.83/55.30 thf(20212,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4348])). 120.83/55.30 thf(2564,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3660_sin__ge__minus__one)). 120.83/55.30 thf(13844,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2564])). 120.83/55.30 thf(2801,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2260_minf_I9_J)). 120.83/55.30 thf(14708,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2801])). 120.83/55.30 thf(1143,axiom,((! [A:$i]: (zero_zero_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4674_rat__number__collapse_I4_J)). 120.83/55.30 thf(8871,plain,((! [A:$i]: (zero_zero_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143])). 120.83/55.30 thf(4322,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_q__pos__lemma)). 120.83/55.30 thf(20096,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4322])). 120.83/55.30 thf(4412,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ A) @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Int__Oint_T)). 120.83/55.30 thf(20454,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ A) @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4412])). 120.83/55.30 thf(972,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.30 thf(8279,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])). 120.83/55.30 thf(1899,axiom,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_one__add__one__is__two)). 120.83/55.30 thf(11544,plain,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899])). 120.83/55.30 thf(4631,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_rel__simps_I5_J)). 120.83/55.30 thf(21338,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit1 @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ (hAPP_int_int @ bit1 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4631])). 120.83/55.30 thf(4737,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2041_add__less__imp__less__right)). 120.83/55.30 thf(21759,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4737])). 120.83/55.30 thf(1702,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ semiri132038758t_real @ B)) @ (hAPP_nat_real @ semiri132038758t_real @ A)) = (hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3100_of__nat__diff)). 120.83/55.30 thf(10819,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ semiri132038758t_real @ B)) @ (hAPP_nat_real @ semiri132038758t_real @ A)) = (hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702])). 120.83/55.30 thf(3073,axiom,((zero_z891286103de_int != one_on1684967323de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_one__neq__zero)). 120.83/55.30 thf(15646,plain,((~ (zero_z891286103de_int = one_on1684967323de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3073])). 120.83/55.30 thf(3666,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2884_even__times__anything)). 120.83/55.30 thf(17651,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3666])). 120.83/55.31 thf(306,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ D)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_mult__mono)). 120.83/55.31 thf(5964,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ D)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 120.83/55.31 thf(4375,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => ((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) != D)) <= (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C)) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5099_aset_I5_J)). 120.83/55.31 thf(20290,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => ((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) = D))) | ~ (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C)) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4375])). 120.83/55.31 thf(339,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A))))) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3499_aux5)). 120.83/55.31 thf(6070,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A))))) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 120.83/55.31 thf(3425,axiom,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ cos @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ tan @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= ((hAPP_real_real @ cos @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3857_tan__sec)). 120.83/55.31 thf(16825,plain,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ cos @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ tan @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ((hAPP_real_real @ cos @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3425])). 120.83/55.31 thf(3558,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_comm__semiring__class_Odistrib)). 120.83/55.31 thf(17250,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3558])). 120.83/55.31 thf(2123,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_rat_rat @ abs_abs_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4691_abs__rat)). 120.83/55.31 thf(12255,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_rat_rat @ abs_abs_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123])). 120.83/55.31 thf(1397,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1997_add__le__imp__le__left)). 120.83/55.31 thf(9750,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397])). 120.83/55.31 thf(3703,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ min)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_rel__simps_I13_J)). 120.83/55.31 thf(17784,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ min))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ min)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3703])). 120.83/55.31 thf(4304,axiom,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3267_not__neg__0)). 120.83/55.31 thf(20037,plain,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4304])). 120.83/55.31 thf(1244,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2018_add__right__mono)). 120.83/55.31 thf(9213,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244])). 120.83/55.31 thf(2310,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1453_power__strict__increasing__iff)). 120.83/55.31 thf(12938,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310])). 120.83/55.31 thf(430,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ A)) => ((hAPP_real_real @ uminus_uminus_real @ A) = (hAPP_real_real @ arccos @ (hAPP_real_real @ cos @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3609_arccos__cos2)). 120.83/55.31 thf(6378,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ A)) => ((hAPP_real_real @ uminus_uminus_real @ A) = (hAPP_real_real @ arccos @ (hAPP_real_real @ cos @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 120.83/55.31 thf(2628,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_semiring__mult__2)). 120.83/55.31 thf(14092,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2628])). 120.83/55.31 thf(4551,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit0 @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_rel__simps_I8_J)). 120.83/55.31 thf(21046,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit0 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ (hAPP_int_int @ bit0 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4551])). 120.83/55.31 thf(2017,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1861_add__pos__nonneg)). 120.83/55.31 thf(11901,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017])). 120.83/55.31 thf(3052,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (div_mod_int @ D) @ A))) @ E))))) <= (C != zero_zero_int)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2789_zmult2__lemma)). 120.83/55.31 thf(15552,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (div_mod_int @ D) @ A))) @ E))))) | (C = zero_zero_int) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ C) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3052])). 120.83/55.31 thf(524,axiom,((zero_zero_real = (hAPP_int_real @ real_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4386_real__of__int__zero)). 120.83/55.31 thf(6688,plain,((zero_zero_real = (hAPP_int_real @ real_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 120.83/55.31 thf(1971,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4325_gcd__semilattice__nat_Ole__infI1)). 120.83/55.31 thf(11777,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971])). 120.83/55.31 thf(3947,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_sum__power2__ge__zero)). 120.83/55.31 thf(18641,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3947])). 120.83/55.31 thf(1264,axiom,((! [A:$i,B:$i]: ((A != B) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ fequal_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Rat__Orat_T)). 120.83/55.31 thf(9284,plain,((! [A:$i,B:$i]: (~ (A = B) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ fequal_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264])). 120.83/55.31 thf(3782,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2608_div__prop1)). 120.83/55.31 thf(18059,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3782])). 120.83/55.31 thf(1905,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (int_lcm @ A) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (nat_lcm @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4598_Nitpick_Oint__lcm__def)). 120.83/55.31 thf(11559,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (int_lcm @ A) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (nat_lcm @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905])). 120.83/55.31 thf(2956,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3317_real__sqrt__less__iff)). 120.83/55.31 thf(15215,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2956])). 120.83/55.31 thf(749,axiom,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))))) & ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4784_less__Suc__number__of)). 120.83/55.31 thf(7476,plain,((! [A:$i,B:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))))) & ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))))) & ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 120.83/55.31 thf(4813,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) <=> (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3271_not__neg__eq__ge__0)). 120.83/55.31 thf(22017,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4813])). 120.83/55.31 thf(2857,axiom,((! [A:$i]: ((one_one_rat = A) <=> (one_one_rat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1956_one__reorient)). 120.83/55.31 thf(14886,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2857])). 120.83/55.31 thf(1968,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3172_lemma__realpow__diff)). 120.83/55.31 thf(11769,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968])). 120.83/55.31 thf(1001,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.31 thf(8378,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001])). 120.83/55.31 thf(142,axiom,((! [A:$i]: (zero_zero_real != (hAPP_real_real @ cos @ (hAPP_real_real @ arctan @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3564_cos__arctan__not__zero)). 120.83/55.31 thf(5417,plain,((! [A:$i]: ~ (zero_zero_real = (hAPP_real_real @ cos @ (hAPP_real_real @ arctan @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 120.83/55.31 thf(877,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3595_cos__arccos__lemma1)). 120.83/55.31 thf(7941,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])). 120.83/55.31 thf(3587,axiom,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (noXRRset @ A) @ B) = (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ B) @ (hAPP_i1948725293t_bool @ norRRset @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4772_noXRRset__def)). 120.83/55.31 thf(17367,plain,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (noXRRset @ A) @ B) = (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ B) @ (hAPP_i1948725293t_bool @ norRRset @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3587])). 120.83/55.31 thf(2706,axiom,((! [A:$i]: ((((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ cos @ (hAPP_real_real @ arcsin @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3559_cos__arcsin)). 120.83/55.31 thf(14362,plain,((! [A:$i]: (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ cos @ (hAPP_real_real @ arcsin @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2706])). 120.83/55.31 thf(2153,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3213_le__div__geq)). 120.83/55.31 thf(12361,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153])). 120.83/55.31 thf(2304,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ D)) @ B)) @ C) = E) <=> ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1542_eq__add__iff1)). 120.83/55.31 thf(12913,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ D)) @ B)) @ C) = E) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E))) & (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ D)) @ B)) @ C) = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304])). 120.83/55.31 thf(2457,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3153_realpow__Suc__le__self)). 120.83/55.31 thf(13480,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457])). 120.83/55.31 thf(2091,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B)))) & (((hAPP_int_nat @ nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4752_diff__nat__eq__if)). 120.83/55.31 thf(12123,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B)))) & (((hAPP_int_nat @ nat @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091])). 120.83/55.31 thf(4381,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ one_one_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_one__dvd)). 120.83/55.31 thf(20322,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ one_one_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4381])). 120.83/55.31 thf(4653,axiom,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_one__power2)). 120.83/55.31 thf(21434,plain,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4653])). 120.83/55.31 thf(1232,axiom,((one_one_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4644_Frct__code__post_I3_J)). 120.83/55.31 thf(9168,plain,((one_one_rat = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232])). 120.83/55.31 thf(4593,axiom,((! [A:$i,B:$i,C:$i]: (((B = A) <=> ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1283_power__inject__exp)). 120.83/55.31 thf(21214,plain,((! [A:$i,B:$i,C:$i]: ((((B = A) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) & (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) => (B = A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4593])). 120.83/55.31 thf(698,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3350_real__sqrt__sum__squares__ge__zero)). 120.83/55.31 thf(7289,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])). 120.83/55.31 thf(72,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2132_add__diff__cancel)). 120.83/55.31 thf(5198,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 120.83/55.31 thf(2281,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1624_not__add__less1)). 120.83/55.31 thf(12823,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281])). 120.83/55.31 thf(3874,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2598_zdiv__mono2__neg)). 120.83/55.31 thf(18389,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3874])). 120.83/55.31 thf(1395,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ H))) => ((hAPP_int_int @ (div_mod_int @ D) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ B))) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ C))) @ H)))) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ G) @ H)) = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2486_xzgcda__linear__aux2)). 120.83/55.31 thf(9744,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ H))) => ((hAPP_int_int @ (div_mod_int @ D) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ B))) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ A)) @ C))) @ H)))) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ F)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ G) @ H)) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395])). 120.83/55.31 thf(439,axiom,((zero_zero_real = (hAPP_real_real @ inverse_inverse_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3826_INVERSE__ZERO)). 120.83/55.31 thf(6400,plain,((zero_zero_real = (hAPP_real_real @ inverse_inverse_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 120.83/55.31 thf(2598,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => ((zero_zero_int != D) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) <= (zero_zero_int != C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4720_diff__rat)). 120.83/55.31 thf(13968,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => ((~ (zero_zero_int = D)) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) | (zero_zero_int = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2598])). 120.83/55.31 thf(4906,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2142_add__nonpos__nonpos)). 120.83/55.31 thf(22332,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4906])). 120.83/55.31 thf(4259,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2986_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J)). 120.83/55.31 thf(19871,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4259])). 120.83/55.31 thf(4458,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ t)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096)). 120.83/55.31 thf(20620,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ t)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4458])). 120.83/55.31 thf(1897,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1645_add__le__mono1)). 120.83/55.31 thf(11539,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897])). 120.83/55.31 thf(4108,axiom,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ one_one_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_power__one)). 120.83/55.31 thf(19315,plain,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ one_one_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4108])). 120.83/55.31 thf(3457,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ one_one_nat))) <= (zero_zero_nat != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3246_Suc__mult__two__diff__one)). 120.83/55.31 thf(16923,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ one_one_nat))) | (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3457])). 120.83/55.31 thf(1505,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))) <= ((A = one_on1684967323de_int) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1494_dvd__power)). 120.83/55.31 thf(10111,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B))) | ~ ((A = one_on1684967323de_int) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505])). 120.83/55.31 thf(605,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natfloor @ A)) @ (natfloor @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3386_natfloor__mono)). 120.83/55.31 thf(6950,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natfloor @ A)) @ (natfloor @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])). 120.83/55.31 thf(3041,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4314_gcd__semilattice__nat_Oless__infI1)). 120.83/55.31 thf(15506,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3041])). 120.83/55.31 thf(2532,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (wset @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3357_wset__fin)). 120.83/55.31 thf(13741,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (wset @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532])). 120.83/55.31 thf(3044,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = one_one_rat) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) @ E)))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1466_convex__bound__le)). 120.83/55.31 thf(15520,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ E)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A) = one_one_rat) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) @ E)))))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3044])). 120.83/55.31 thf(2699,axiom,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1229_not__one__less__zero)). 120.83/55.31 thf(14335,plain,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2699])). 120.83/55.31 thf(3917,axiom,((! [A:$i,B:$i,C:$i]: ((C != zero_zero_nat) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2275_pow__divides__eq__int)). 120.83/55.31 thf(18544,plain,((! [A:$i,B:$i,C:$i]: ((~ (C = zero_zero_nat)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3917])). 120.83/55.31 thf(4211,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3230_power__odd__eq)). 120.83/55.31 thf(19676,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4211])). 120.83/55.31 thf(1467,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3007_power__Suc2)). 120.83/55.31 thf(9985,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467])). 120.83/55.31 thf(1089,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ ring_1_of_int_rat @ A)) @ (hAPP_int_rat @ ring_1_of_int_rat @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4680_Fract__of__int__quotient)). 120.83/55.31 thf(8708,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ ring_1_of_int_rat @ A)) @ (hAPP_int_rat @ ring_1_of_int_rat @ B)) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089])). 120.83/55.31 thf(1249,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3525_zmod__zminus__zminus)). 120.83/55.31 thf(9226,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249])). 120.83/55.31 thf(638,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4026_divides__mul)). 120.83/55.31 thf(7074,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 120.83/55.31 thf(3664,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3549_not__zle__0__negative)). 120.83/55.31 thf(17646,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3664])). 120.83/55.31 thf(2888,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_mult__nonneg__nonpos)). 120.83/55.31 thf(14997,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2888])). 120.83/55.31 thf(2238,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2938_less__imp__of__nat__less)). 120.83/55.31 thf(12677,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238])). 120.83/55.31 thf(795,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3907_real__root__mult)). 120.83/55.31 thf(7646,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])). 120.83/55.31 thf(3210,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_P1175774780nt_int @ product_snd_int_int @ (divmod_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4233_mod__int__def)). 120.83/55.31 thf(16120,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_P1175774780nt_int @ product_snd_int_int @ (divmod_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3210])). 120.83/55.31 thf(2213,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.31 thf(12596,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213])). 120.83/55.31 thf(4546,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2810_of__nat__double)). 120.83/55.31 thf(21023,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4546])). 120.83/55.31 thf(4581,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3147_of__nat__0__less__iff)). 120.83/55.31 thf(21170,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4581])). 120.83/55.31 thf(2432,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_int_real @ number267125858f_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_left__distrib__number__of)). 120.83/55.31 thf(13383,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_int_real @ number267125858f_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432])). 120.83/55.31 thf(2104,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ D))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <= (! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B)))) <= (D != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3883_DERIV__const__average)). 120.83/55.31 thf(12173,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ D))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | ~ (! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B))) | (D = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104])). 120.83/55.31 thf(2224,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_rat_rat @ uminus_uminus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4689_minus__rat)). 120.83/55.31 thf(12628,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_rat_rat @ uminus_uminus_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224])). 120.83/55.31 thf(475,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ (hAPP_real_real @ B @ C))) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E))))) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5176_isCont__inv__fun)). 120.83/55.31 thf(6524,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ (hAPP_real_real @ B @ C))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) => (E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 120.83/55.31 thf(1889,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_int_rat @ number_number_of_rat @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ C))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_int_rat @ number_number_of_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1551_left__diff__distrib__number__of)). 120.83/55.31 thf(11516,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_int_rat @ number_number_of_rat @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ C))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_int_rat @ number_number_of_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889])). 120.83/55.31 thf(4889,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2893_odd__pow)). 120.83/55.31 thf(22272,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4889])). 120.83/55.31 thf(3539,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((is_int @ C) & (is_int @ B) & (is_int @ A)) => ((((((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ C) @ A)) => (? [F:$i,G:$i,H:$i]: ((is_int @ F) & (B = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ G) @ (hAPP_int_nat @ nat @ E))) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ H) @ (hAPP_int_nat @ nat @ E)) = C) & (A = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ F) @ (hAPP_int_nat @ nat @ E))) & (is_int @ H) & (is_int @ G))))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ zOdd))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_int_nat @ nat @ E)))) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ (hAPP_int_nat @ nat @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4536_int__triple__relprime__odd__power__divisors)). 120.83/55.31 thf(17182,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((is_int @ C) & (is_int @ B) & (is_int @ A)) => (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ C) @ A)) => (? [F:$i,G:$i,H:$i]: ((is_int @ F) & (B = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ G) @ (hAPP_int_nat @ nat @ E))) & ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ H) @ (hAPP_int_nat @ nat @ E)) = C) & (A = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ F) @ (hAPP_int_nat @ nat @ E))) & (is_int @ H) & (is_int @ G))))) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ zOdd)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_int_nat @ nat @ E))) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ (hAPP_int_nat @ nat @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3539])). 120.83/55.31 thf(4668,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ D))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ D))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (multInv @ D) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (multInv @ D) @ B))) @ D))))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2236_MultInv__zcong__prop3)). 120.83/55.31 thf(21473,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ D)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ D))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ D))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (multInv @ D) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (multInv @ D) @ B))) @ D))))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4668])). 120.83/55.31 thf(3814,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ zero_zero_int) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_mult__zero__left)). 120.83/55.31 thf(18164,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ zero_zero_int) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3814])). 120.83/55.31 thf(2218,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.31 thf(12609,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218])). 120.83/55.31 thf(2363,axiom,((! [A:$i]: ((hAPP_int_rat @ ring_1_of_int_rat @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4679_Fract__of__int__eq)). 120.83/55.31 thf(13122,plain,((! [A:$i]: ((hAPP_int_rat @ ring_1_of_int_rat @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363])). 120.83/55.31 thf(4353,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)) @ E)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_zcong__zadd)). 120.83/55.31 thf(20226,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)) @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4353])). 120.83/55.31 thf(1215,axiom,((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2928_of__nat__0)). 120.83/55.31 thf(9107,plain,((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215])). 120.83/55.31 thf(3311,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2058_add__strict__right__mono)). 120.83/55.31 thf(16464,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3311])). 120.83/55.31 thf(4579,axiom,(((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zero__power2)). 120.83/55.31 thf(21165,plain,(((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4579])). 120.83/55.31 thf(1253,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4029_coprime__plus1)). 120.83/55.31 thf(9237,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253])). 120.83/55.31 thf(2085,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3130_prod__mn__less__k)). 120.83/55.31 thf(12106,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085])). 120.83/55.31 thf(2609,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3175_lemma__realpow__diff)). 120.83/55.31 thf(14020,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2609])). 120.83/55.31 thf(163,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ re @ B))) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4130_complex__Im__mult)). 120.83/55.31 thf(5483,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ re @ B))) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 120.83/55.31 thf(333,axiom,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4141_Re_Ononneg__bounded)). 120.83/55.31 thf(6053,plain,((? [A:$i]: (! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 120.83/55.31 thf(2834,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1240_zero__le__power)). 120.83/55.31 thf(14816,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2834])). 120.83/55.31 thf(2286,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3441_ln__gt__zero__iff)). 120.83/55.31 thf(12857,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286])). 120.83/55.31 thf(3316,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ one_on1645066479umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_on1645066479umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3161_power__Suc__less__one)). 120.83/55.31 thf(16477,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ one_on1645066479umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_on1645066479umeral))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3316])). 120.83/55.31 thf(1993,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1206_pos__add__strict)). 120.83/55.31 thf(11837,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993])). 120.83/55.31 thf(1278,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4077_cnj_Odiff)). 120.83/55.31 thf(9352,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278])). 120.83/55.31 thf(4646,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_even__less__0__iff)). 120.83/55.31 thf(21406,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4646])). 120.83/55.31 thf(3287,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2255_pinf_I10_J)). 120.83/55.31 thf(16395,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3287])). 120.83/55.31 thf(2034,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (A = C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1482_power__eq__imp__eq__base)). 120.83/55.31 thf(11955,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (A = C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034])). 120.83/55.31 thf(450,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.31 thf(6437,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 120.83/55.31 thf(2293,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3777_even__power__nat)). 120.83/55.31 thf(12874,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293])). 120.83/55.31 thf(1503,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1696_dvd_Oorder__refl)). 120.83/55.31 thf(10101,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503])). 120.83/55.31 thf(4270,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_less__special_I2_J)). 120.83/55.31 thf(19909,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4270])). 120.83/55.31 thf(2818,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ norm_norm_complex @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4063_complex__mod__mult__cnj)). 120.83/55.31 thf(14762,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ norm_norm_complex @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2818])). 120.83/55.31 thf(323,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3657_sin__ge__zero)). 120.83/55.31 thf(6026,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 120.83/55.31 thf(2933,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2108_mult__1__right)). 120.83/55.31 thf(15147,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ one_on1645066479umeral) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2933])). 120.83/55.31 thf(2448,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4697_Ratreal__number__collapse_I3_J)). 120.83/55.31 thf(13455,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448])). 120.83/55.31 thf(3065,axiom,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) & ! [B:$i]: (((A = B) | (B = one_one_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) <=> (hBOOL @ (hAPP_nat_bool @ prime @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4184_prime__def)). 120.83/55.31 thf(15614,plain,((! [A:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) & ! [B:$i]: ((A = B) | (B = one_one_nat) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) => (hBOOL @ (hAPP_nat_bool @ prime @ A))) & ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) & ! [B:$i]: ((A = B) | (B = one_one_nat) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3065])). 120.83/55.31 thf(2606,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((B != zero_zero_real) => ((((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ C) @ B) @ A)) <= (((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) = A) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C))))) <= ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))) = A)))) <= (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) = A)) <= (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3894_DERIV__real__root__generic)). 120.83/55.31 thf(13989,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((~ (B = zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (hAPP_n546711566l_real @ root @ C) @ B) @ A)) | ~ (((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) = A) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C))) | ~ ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))) = A))) | ~ (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) = A)) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2606])). 120.83/55.31 thf(570,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3715_cos__npi)). 120.83/55.31 thf(6824,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 120.83/55.31 thf(4172,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2699_Divides_Otransfer__nat__int__functions_I2_J)). 120.83/55.31 thf(19530,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4172])). 120.83/55.31 thf(2906,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4351_coprime__plus__one__nat)). 120.83/55.31 thf(15057,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2906])). 120.83/55.31 thf(4856,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2520_div__neg__pos__less0)). 120.83/55.31 thf(22173,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4856])). 120.83/55.31 thf(3440,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1363_mult__less__le__imp__less)). 120.83/55.31 thf(16869,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3440])). 120.83/55.31 thf(1536,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4783_less__number__of__Suc)). 120.83/55.31 thf(10227,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536])). 120.83/55.31 thf(4285,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) <= (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3224_zEvenI)). 120.83/55.31 thf(19963,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) | ~ (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4285])). 120.83/55.31 thf(3084,axiom,((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1232_not__one__less__zero)). 120.83/55.31 thf(15675,plain,((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3084])). 120.83/55.31 thf(1272,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) <= (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)))) <=> (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1779_nat__diff__split)). 120.83/55.31 thf(9320,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) | ~ (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ D)) | ~ (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272])). 120.83/55.31 thf(3093,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_dvd__mult__left)). 120.83/55.31 thf(15707,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3093])). 120.83/55.31 thf(4037,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((hAPP_int_int @ (legacy_zgcd @ A) @ C) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4485_zgcd__zmult__cancel)). 120.83/55.31 thf(18968,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int) => ((hAPP_int_int @ (legacy_zgcd @ A) @ C) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4037])). 120.83/55.31 thf(4231,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (inv @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2127_inv__g__1)). 120.83/55.31 thf(19740,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ (inv @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4231])). 120.83/55.31 thf(308,axiom,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3721_sin__60)). 120.83/55.31 thf(5969,plain,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 120.83/55.31 thf(2278,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4443_number__of__less__real__of__int__iff)). 120.83/55.31 thf(12813,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ real_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278])). 120.83/55.31 thf(375,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2341_semiring__div__class_Omod__div__equality_H)). 120.83/55.31 thf(6203,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 120.83/55.31 thf(1241,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) => (A = C))) <= ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3104_power__inject__base)). 120.83/55.31 thf(9203,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) => (A = C))) | ~ ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241])). 120.83/55.31 thf(1091,axiom,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4300_gcd__dvd__prod__nat)). 120.83/55.31 thf(8713,plain,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091])). 120.83/55.31 thf(3920,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1563_le__add__iff2)). 120.83/55.31 thf(18553,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3920])). 120.83/55.31 thf(1451,axiom,((! [A:$i]: (((? [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))) => (? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ A @ B)) & (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ B)))))) <= (~ (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3955_exists__least__lemma)). 120.83/55.31 thf(9939,plain,((! [A:$i]: (((? [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))) => (? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ A @ B)) & (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ B)))))) | (hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451])). 120.83/55.31 thf(1914,axiom,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_number__of__Bit0)). 120.83/55.31 thf(11591,plain,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914])). 120.83/55.31 thf(678,axiom,((! [A:$i]: ((one_one_nat = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2315_gcd__lcm__complete__lattice__nat_Obot__unique)). 120.83/55.31 thf(7225,plain,((! [A:$i]: (((one_one_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) => (one_one_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])). 120.83/55.31 thf(2580,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1340_mult__left__less__imp__less)). 120.83/55.31 thf(13896,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2580])). 120.83/55.31 thf(3577,axiom,((! [A:$i,B:$i]: ((B != zero_zero_complex) => (((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A) != zero_zero_complex) <= (A != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_no__zero__divisors)). 120.83/55.31 thf(17321,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_complex)) => (~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A) = zero_zero_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3577])). 120.83/55.31 thf(342,axiom,((! [A:$i,B:$i]: ((hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ fTrue) @ A) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T)). 120.83/55.31 thf(6084,plain,((! [A:$i,B:$i]: ((hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ fTrue) @ A) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 120.83/55.31 thf(80,axiom,((! [A:$i,B:$i]: ((is_int @ A) => (((A = (archim856651990g_real @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_int_real @ real_int @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4470_ceiling__eq3)). 120.83/55.31 thf(5230,plain,((! [A:$i,B:$i]: ((is_int @ A) => ((A = (archim856651990g_real @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_int_real @ real_int @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 120.83/55.31 thf(3325,axiom,((zero_zero_real = (hAPP_real_real @ ln @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3431_ln__one)). 120.83/55.31 thf(16505,plain,((zero_zero_real = (hAPP_real_real @ ln @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3325])). 120.83/55.31 thf(2774,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_comm__mult__left__mono)). 120.83/55.31 thf(14593,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2774])). 120.83/55.31 thf(2452,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4324_gcd__semilattice__nat_Ole__infI2)). 120.83/55.31 thf(13466,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452])). 120.83/55.31 thf(4698,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => ((hBOOL @ (hAPP_int_bool @ B @ D)) <=> (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))))))) => (((? [D:$i]: (hBOOL @ (hAPP_int_bool @ B @ D))) => (? [D:$i]: ((is_int @ D) & (hBOOL @ (hAPP_int_bool @ A @ D))))) <= (? [D:$i]: ! [E:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ E)) <=> (hBOOL @ (hAPP_int_bool @ B @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ D))) <= (is_int @ E))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4006_minusinfinity)). 120.83/55.31 thf(21583,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ D) & (is_int @ E)) => (((hBOOL @ (hAPP_int_bool @ B @ D)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))))) & ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C)))) => (hBOOL @ (hAPP_int_bool @ B @ D)))))) => (((? [D:$i]: (hBOOL @ (hAPP_int_bool @ B @ D))) => (? [D:$i]: ((is_int @ D) & (hBOOL @ (hAPP_int_bool @ A @ D))))) | ~ (? [D:$i]: ! [E:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ E)) => (hBOOL @ (hAPP_int_bool @ B @ E))) & ((hBOOL @ (hAPP_int_bool @ B @ E)) => (hBOOL @ (hAPP_int_bool @ A @ E)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ D)) | ~ (is_int @ E))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4698])). 120.83/55.31 thf(1960,axiom,((! [A:$i,B:$i,C:$i]: (((A = zero_zero_complex) | (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))) <=> (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1264_dvd__mult__cancel__left)). 120.83/55.31 thf(11737,plain,((! [A:$i,B:$i,C:$i]: ((((A = zero_zero_complex) | (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)))) & ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))) => ((A = zero_zero_complex) | (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960])). 120.83/55.31 thf(1218,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2097_diff__eq__diff__less)). 120.83/55.31 thf(9122,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218])). 120.83/55.31 thf(1495,axiom,((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2974_int__0)). 120.83/55.31 thf(10079,plain,((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495])). 120.83/55.31 thf(1154,axiom,((! [A:$i]: ((zero_zero_nat = A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2311_gcd__lcm__complete__lattice__nat_Otop__le)). 120.83/55.31 thf(8906,plain,((! [A:$i]: ((zero_zero_nat = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154])). 120.83/55.31 thf(560,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3562_cos__le__one)). 120.83/55.31 thf(6792,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 120.83/55.31 thf(2399,axiom,((! [A:$i]: (((zero_zero_real = (hAPP_real_real @ sgn_sgn_real @ A)) <= (A = zero_zero_real)) & ((zero_zero_real != A) => (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) => ((hAPP_real_real @ uminus_uminus_real @ one_one_real) = (hAPP_real_real @ sgn_sgn_real @ A))) & (((hAPP_real_real @ sgn_sgn_real @ A) = one_one_real) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3576_sgn__real__def)). 120.83/55.31 thf(13259,plain,((! [A:$i]: (((zero_zero_real = (hAPP_real_real @ sgn_sgn_real @ A)) | ~ (A = zero_zero_real)) & ((~ (zero_zero_real = A)) => (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) => ((hAPP_real_real @ uminus_uminus_real @ one_one_real) = (hAPP_real_real @ sgn_sgn_real @ A))) & (((hAPP_real_real @ sgn_sgn_real @ A) = one_one_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2399])). 120.83/55.31 thf(4441,axiom,((! [A:$i,B:$i]: (((B != zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2628_div__add__self1)). 120.83/55.31 thf(20561,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4441])). 120.83/55.31 thf(4350,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5012_gcd__le2__int)). 120.83/55.31 thf(20217,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4350])). 120.83/55.31 thf(4885,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2035_add__less__imp__less__left)). 120.83/55.31 thf(22255,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4885])). 120.83/55.31 thf(3885,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1318_mult__left__le__imp__le)). 120.83/55.31 thf(18428,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3885])). 120.83/55.31 thf(1188,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) = one_one_nat) | (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D))))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4036_coprime__bezout)). 120.83/55.31 thf(9021,plain,((! [A:$i,B:$i]: (((? [C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) = one_one_nat) | (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (? [C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)) = one_one_nat) | (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188])). 120.83/55.31 thf(1349,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1307_power__add)). 120.83/55.31 thf(9594,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349])). 120.83/55.31 thf(2570,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_power__mult__distrib)). 120.83/55.31 thf(13864,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2570])). 120.83/55.31 thf(630,axiom,((! [A:$i]: ((zero_zero_real = (hAPP_real_real @ cos @ A)) <=> (? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)) | ? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3754_cos__zero__iff)). 120.83/55.31 thf(7031,plain,((! [A:$i]: (((zero_zero_real = (hAPP_real_real @ cos @ A)) => (? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)) | ? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))) & ((? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)) | ? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)))) => (zero_zero_real = (hAPP_real_real @ cos @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 120.83/55.31 thf(2822,axiom,((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1231_not__one__less__zero)). 120.83/55.31 thf(14777,plain,((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2822])). 120.83/55.31 thf(4342,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3548_negative__zless__0)). 120.83/55.31 thf(20192,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4342])). 120.83/55.31 thf(2133,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ (hAPP_nat_bool @ even_odd_even_nat @ A)) @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3789_lemma__STAR__sin)). 120.83/55.31 thf(12290,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ (hAPP_nat_bool @ even_odd_even_nat @ A)) @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133])). 120.83/55.31 thf(4139,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ C)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (inv @ C) @ A)) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2214_wset__mem__inv__mem)). 120.83/55.31 thf(19418,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ C)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (inv @ C) @ A)) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4139])). 120.83/55.31 thf(927,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ one_one_complex)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.31 thf(8112,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ one_one_complex)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[927])). 120.83/55.31 thf(4284,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) != zero_zero_int) => ((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3534_zmod__zminus2__not__zero)). 120.83/55.31 thf(19960,plain,((! [A:$i,B:$i]: ((~ ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = zero_zero_int)) => (~ ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4284])). 120.83/55.31 thf(753,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_nat_nat @ suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4343_gcd__Suc__0)). 120.83/55.31 thf(7491,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_nat_nat @ suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])). 120.83/55.31 thf(2428,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ D)) => ((? [E:$i,F:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ F) = B) & (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ E)))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4481_prime__power__mult)). 120.83/55.31 thf(13370,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ D)) => (? [E:$i,F:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ F) = B) & (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ E))) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2428])). 120.83/55.31 thf(4695,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <=> ((zero_zero_int != A) | (B != zero_zero_int))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff)). 120.83/55.31 thf(21568,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (~ (zero_zero_int = A) | ~ (B = zero_zero_int))) & ((~ (zero_zero_int = A) | ~ (B = zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4695])). 120.83/55.31 thf(1585,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3326_real__sqrt__gt__zero)). 120.83/55.31 thf(10420,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585])). 120.83/55.31 thf(4874,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ pls)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_rel__simps_I12_J)). 120.83/55.31 thf(22220,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4874])). 120.83/55.31 thf(1364,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1988_add__0__left)). 120.83/55.31 thf(9635,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364])). 120.83/55.31 thf(3923,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2594_int__div__less__self)). 120.83/55.31 thf(18562,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3923])). 120.83/55.31 thf(3030,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1373_mult__strict__mono)). 120.83/55.31 thf(15474,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3030])). 120.83/55.31 thf(1840,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3524_zmod__zminus2)). 120.83/55.31 thf(11343,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840])). 120.83/55.31 thf(3996,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ fact_fact_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4284_dvd__fact__int)). 120.83/55.31 thf(18819,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ fact_fact_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3996])). 120.83/55.31 thf(727,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D != zero_zero_int) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))))) <= (zero_zero_int != C))) <= ((is_int @ D) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4713_less__rat)). 120.83/55.31 thf(7382,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (D = zero_zero_int)) => ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))))) | (zero_zero_int = C))) | ~ ((is_int @ D) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])). 120.83/55.31 thf(382,axiom,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2371_mod__by__0)). 120.83/55.31 thf(6228,plain,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 120.83/55.31 thf(2065,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2358_zmod__zdiv__equality)). 120.83/55.31 thf(12052,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065])). 120.83/55.31 thf(3929,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2887_Parity_Oodd__plus__odd)). 120.83/55.31 thf(18577,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3929])). 120.83/55.31 thf(3750,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ C) @ B))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2224_wset__subset)). 120.83/55.31 thf(17949,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ C) @ B))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3750])). 120.83/55.31 thf(213,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4422_ceiling__le__eq)). 120.83/55.31 thf(5647,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 120.83/55.31 thf(4728,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1566_less__add__iff2)). 120.83/55.31 thf(21724,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4728])). 120.83/55.31 thf(4062,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1979_add__0)). 120.83/55.31 thf(19134,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4062])). 120.83/55.31 thf(4592,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_power__even__eq)). 120.83/55.31 thf(21211,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4592])). 120.83/55.31 thf(1643,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_split__mult__neg__le)). 120.83/55.31 thf(10625,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643])). 120.83/55.31 thf(1144,axiom,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4336_gcd__1__nat)). 120.83/55.31 thf(8874,plain,((! [A:$i]: (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144])). 120.83/55.31 thf(4692,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) <= (zero_zero_int != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1674_zdvd__mono)). 120.83/55.31 thf(21555,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))) | (zero_zero_int = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4692])). 120.83/55.31 thf(3273,axiom,((! [A:$i]: (((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_nat_nat @ suc @ zero_zero_nat)) <=> (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3775_odd__nat__equiv__def)). 120.83/55.31 thf(16343,plain,((! [A:$i]: ((((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_nat_nat @ suc @ zero_zero_nat)) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_nat_nat @ suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3273])). 120.83/55.31 thf(1203,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2855_Suc__less__SucD)). 120.83/55.31 thf(9072,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203])). 120.83/55.31 thf(1751,axiom,((! [A:$i]: ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ zero_zero_int)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4661_normalize__denom__zero)). 120.83/55.31 thf(11011,plain,((! [A:$i]: ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ zero_zero_int)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751])). 120.83/55.31 thf(3680,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_rat @ number_number_of_rat @ A))) & ((zero_zero_rat = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3217_of__nat__number__of__lemma)). 120.83/55.31 thf(17703,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_rat @ number_number_of_rat @ A))) & ((zero_zero_rat = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ number_number_of_nat @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3680])). 120.83/55.31 thf(4339,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2455_dvd__mod__imp__dvd)). 120.83/55.31 thf(20185,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4339])). 120.83/55.31 thf(4247,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_fun_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f808647893nt_int @ cOMBC_736024425nt_int @ A) @ B) @ C) = (hAPP_f1356864277nt_int @ (hAPP_i744251628nt_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J)). 120.83/55.31 thf(19822,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_fun_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f808647893nt_int @ cOMBC_736024425nt_int @ A) @ B) @ C) = (hAPP_f1356864277nt_int @ (hAPP_i744251628nt_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4247])). 120.83/55.31 thf(136,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ A) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3601_tan__periodic__n)). 120.83/55.31 thf(5400,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ A) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 120.83/55.31 thf(3359,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1404_power__decreasing)). 120.83/55.31 thf(16612,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3359])). 120.83/55.31 thf(2024,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3906_real__root__less__mono)). 120.83/55.31 thf(11920,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024])). 120.83/55.31 thf(1722,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1272_power__increasing)). 120.83/55.31 thf(10872,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722])). 120.83/55.31 thf(4795,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((zero_zero_int != A) | (zero_zero_int != B)) => (one_one_int = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (legacy_zgcd @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4513_div__zgcd__relprime)). 120.83/55.31 thf(21954,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((~ (zero_zero_int = A) | ~ (zero_zero_int = B)) => (one_one_int = (hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (legacy_zgcd @ B) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (legacy_zgcd @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4795])). 120.83/55.31 thf(4773,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_bin__less__0__simps_I4_J)). 120.83/55.31 thf(21877,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4773])). 120.83/55.31 thf(3090,axiom,((! [A:$i,B:$i]: (((A = B) <=> ((hAPP_int_complex @ number528085621omplex @ A) = (hAPP_int_complex @ number528085621omplex @ B))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_eq__number__of)). 120.83/55.31 thf(15696,plain,((! [A:$i,B:$i]: ((((A = B) => ((hAPP_int_complex @ number528085621omplex @ A) = (hAPP_int_complex @ number528085621omplex @ B))) & (((hAPP_int_complex @ number528085621omplex @ A) = (hAPP_int_complex @ number528085621omplex @ B)) => (A = B))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3090])). 120.83/55.31 thf(84,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3487_minus__real__def)). 120.83/55.31 thf(5241,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 120.83/55.31 thf(2624,axiom,((! [A:$i]: (A = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.31 thf(14072,plain,((! [A:$i]: (A = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2624])). 120.83/55.31 thf(2483,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1399_power__less__imp__less__base)). 120.83/55.31 thf(13559,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483])). 120.83/55.31 thf(4816,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.31 thf(22027,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4816])). 120.83/55.31 thf(356,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_mult__nonneg__nonpos2)). 120.83/55.31 thf(6140,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 120.83/55.31 thf(1749,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4022_coprime__Suc0_H)). 120.83/55.31 thf(11006,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749])). 120.83/55.31 thf(3954,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_zcong__shift)). 120.83/55.31 thf(18663,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3954])). 120.83/55.31 thf(384,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4423_ceiling__le)). 120.83/55.31 thf(6234,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 120.83/55.31 thf(1491,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1995_add__le__imp__le__left)). 120.83/55.31 thf(10068,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491])). 120.83/55.31 thf(4618,axiom,((! [A:$i,B:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2491_mod__mult__self1__is__0)). 120.83/55.31 thf(21304,plain,((! [A:$i,B:$i]: (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4618])). 120.83/55.31 thf(3177,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1919_add__imp__eq)). 120.83/55.31 thf(15998,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3177])). 120.83/55.31 thf(1587,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1654_mult__le__mono1)). 120.83/55.31 thf(10425,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587])). 120.83/55.31 thf(2454,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ C) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.31 thf(13471,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ C) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454])). 120.83/55.31 thf(3532,axiom,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ A) @ (hAPP_i1948725293t_bool @ sRStar @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4055_ResSet__SRStar__prop)). 120.83/55.31 thf(17160,plain,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ A) @ (hAPP_i1948725293t_bool @ sRStar @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3532])). 120.83/55.31 thf(1409,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1767_diff__less__mono)). 120.83/55.31 thf(9798,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409])). 120.83/55.31 thf(2562,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3029_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.31 thf(13832,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2562])). 120.83/55.31 thf(4640,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => ((? [D:$i]: ((is_int @ D) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1314_zcong__iff__lin)). 120.83/55.31 thf(21373,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => (((? [D:$i]: ((is_int @ D) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => (? [D:$i]: ((is_int @ D) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4640])). 120.83/55.31 thf(2923,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2199_add__le__less__mono)). 120.83/55.31 thf(15117,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2923])). 120.83/55.31 thf(460,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4016_coprime__commute)). 120.83/55.31 thf(6468,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 120.83/55.31 thf(3869,axiom,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2847_int__Suc)). 120.83/55.31 thf(18378,plain,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3869])). 120.83/55.31 thf(1155,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))) = (hAPP_real_real @ arctan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3373_arctan__half)). 120.83/55.31 thf(8909,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))) = (hAPP_real_real @ arctan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155])). 120.83/55.31 thf(1927,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1602_nat__mult__assoc)). 120.83/55.31 thf(11633,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927])). 120.83/55.31 thf(2641,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1344_mult__less__imp__less__right)). 120.83/55.31 thf(14146,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2641])). 120.83/55.31 thf(4845,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3235_even__div__2__prop1)). 120.83/55.31 thf(22138,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4845])). 120.83/55.31 thf(1185,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1750_diff__le__mono)). 120.83/55.31 thf(9010,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185])). 120.83/55.31 thf(467,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ real_nat @ B) = (hAPP_nat_real @ real_nat @ A)) <=> (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3636_real__of__nat__inject)). 120.83/55.31 thf(6493,plain,((! [A:$i,B:$i]: ((((hAPP_nat_real @ real_nat @ B) = (hAPP_nat_real @ real_nat @ A)) => (A = B)) & ((A = B) => ((hAPP_nat_real @ real_nat @ B) = (hAPP_nat_real @ real_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 120.83/55.31 thf(3784,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_dvd__mult__left)). 120.83/55.31 thf(18064,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3784])). 120.83/55.31 thf(3551,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_number__of__add)). 120.83/55.31 thf(17231,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3551])). 120.83/55.31 thf(1835,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_int_real @ number267125858f_real @ A) = (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3219_of__nat__number__of__lemma)). 120.83/55.31 thf(11323,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => ((hAPP_int_real @ number267125858f_real @ A) = (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835])). 120.83/55.31 thf(4684,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3164_power__Suc__less__one)). 120.83/55.31 thf(21523,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4684])). 120.83/55.31 thf(967,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2001_add__le__imp__le__right)). 120.83/55.31 thf(8259,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[967])). 120.83/55.31 thf(2741,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_zpower__zdvd__prop2)). 120.83/55.31 thf(14466,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2741])). 120.83/55.31 thf(4574,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1498__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096)). 120.83/55.31 thf(21151,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4574])). 120.83/55.31 thf(4651,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.31 thf(21428,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4651])). 120.83/55.31 thf(3153,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.31 thf(15909,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3153])). 120.83/55.31 thf(1837,axiom,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_mult__zero__right)). 120.83/55.31 thf(11333,plain,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837])). 120.83/55.31 thf(1775,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((A != zero_zero_int) => (B = one_one_int))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2794_self__quotient)). 120.83/55.31 thf(11105,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((~ (A = zero_zero_int)) => (B = one_one_int))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775])). 120.83/55.31 thf(1105,axiom,(((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii) = (of_real_complex @ (hAPP_int_real @ number267125858f_real @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3994_i__mult__eq)). 120.83/55.31 thf(8762,plain,(((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii) = (of_real_complex @ (hAPP_int_real @ number267125858f_real @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105])). 120.83/55.31 thf(582,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3422_pi__ge__zero)). 120.83/55.31 thf(6870,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])). 120.83/55.31 thf(3189,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1789_real__mult__less__iff1)). 120.83/55.31 thf(16033,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3189])). 120.83/55.31 thf(2427,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1246_less__1__mult)). 120.83/55.31 thf(13368,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2427])). 120.83/55.31 thf(3151,axiom,((zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2821_code__numeral__zero__minus__one)). 120.83/55.31 thf(15904,plain,((zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3151])). 120.83/55.31 thf(609,axiom,((one_one_complex != ii)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3976_complex__i__not__one)). 120.83/55.31 thf(6959,plain,((~ (one_one_complex = ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[609])). 120.83/55.31 thf(1730,axiom,((! [A:$i]: ((((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) & ((((zero_zero_int = (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) => ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (normalize @ A))) & (((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))))) <= (zero_zero_int != (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4959_normalize__def)). 120.83/55.31 thf(10906,plain,((! [A:$i]: ((((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) & ((((zero_zero_int = (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) => ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (normalize @ A))) & (((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))))) | (zero_zero_int = (hAPP_P1175774780nt_int @ product_snd_int_int @ A)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730])). 120.83/55.31 thf(165,axiom,(((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ pi)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3589_cos__3over2__pi)). 120.83/55.31 thf(5488,plain,(((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ pi)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 120.83/55.31 thf(2730,axiom,((! [A:$i,B:$i]: (((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (negDivAlg @ A @ B)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)))) & (((negDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))) <= (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2776_negDivAlg_Opsimps)). 120.83/55.31 thf(14434,plain,((! [A:$i,B:$i]: (((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (negDivAlg @ A @ B)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)))) & (((negDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (negDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2730])). 120.83/55.31 thf(755,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ one_one_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3157_realpow__Suc__le__self)). 120.83/55.31 thf(7497,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ one_one_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])). 120.83/55.31 thf(587,axiom,((zero_zero_real = (hAPP_real_real @ arctan @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3376_arctan__zero__zero)). 120.83/55.31 thf(6881,plain,((zero_zero_real = (hAPP_real_real @ arctan @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 120.83/55.31 thf(4867,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2915_of__nat__0__le__iff)). 120.83/55.31 thf(22199,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4867])). 120.83/55.31 thf(1151,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1398_power__less__imp__less__base)). 120.83/55.31 thf(8900,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151])). 120.83/55.31 thf(3504,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4014_coprime__1)). 120.83/55.31 thf(17083,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3504])). 120.83/55.31 thf(4246,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_rel__simps_I22_J)). 120.83/55.31 thf(19817,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit1 @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ (hAPP_int_int @ bit1 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4246])). 120.83/55.31 thf(2786,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3312_real__sqrt__le__mono)). 120.83/55.31 thf(14647,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2786])). 120.83/55.31 thf(410,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.31 thf(6312,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 120.83/55.31 thf(1529,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2391_mod__mult__mult1)). 120.83/55.31 thf(10200,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529])). 120.83/55.31 thf(2900,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2719_div__le__mono2)). 120.83/55.31 thf(15030,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2900])). 120.83/55.31 thf(4923,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)) <=> (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3257_int__int__eq)). 120.83/55.31 thf(22377,plain,((! [A:$i,B:$i]: ((((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)) => (B = A)) & ((B = A) => ((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4923])). 120.83/55.31 thf(993,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ real_nat @ A)) @ B) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3654_power__real__of__nat)). 120.83/55.31 thf(8349,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ real_nat @ A)) @ B) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[993])). 120.83/55.31 thf(818,axiom,((! [A:$i,B:$i]: ((B = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2574_dvd__mult__div__cancel)). 120.83/55.31 thf(7736,plain,((! [A:$i,B:$i]: ((B = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 120.83/55.31 thf(1352,axiom,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1224_zero__less__one)). 120.83/55.31 thf(9602,plain,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352])). 120.83/55.31 thf(3188,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A) = (image_nat_int @ semiri1621563631at_int @ (hAPP_n1699378549t_bool @ ord_lessThan_nat @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4954_image__atLeastZeroLessThan__int)). 120.83/55.31 thf(16030,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A) = (image_nat_int @ semiri1621563631at_int @ (hAPP_n1699378549t_bool @ ord_lessThan_nat @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3188])). 120.83/55.31 thf(679,axiom,((! [A:$i,B:$i]: ((zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) => ((zero_zero_complex = B) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_divisors__zero)). 120.83/55.31 thf(7233,plain,((! [A:$i,B:$i]: ((zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) => ((zero_zero_complex = B) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])). 120.83/55.31 thf(2103,axiom,((! [A:$i]: ((hAPP_nat_nat @ size_size_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ size_size_nat @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4057_nat_Osize_I4_J)). 120.83/55.31 thf(12170,plain,((! [A:$i]: ((hAPP_nat_nat @ size_size_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ size_size_nat @ A)) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103])). 120.83/55.31 thf(2716,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2860_less__SucI)). 120.83/55.31 thf(14394,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2716])). 120.83/55.31 thf(4784,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J)). 120.83/55.31 thf(21926,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4784])). 120.83/55.31 thf(3847,axiom,((! [A:$i]: (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2997_power__0__Suc)). 120.83/55.31 thf(18302,plain,((! [A:$i]: (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3847])). 120.83/55.31 thf(1011,axiom,((! [A:$i]: ((A = zero_zero_complex) <=> ((hAPP_complex_complex @ cnj @ A) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4065_complex__cnj__zero__iff)). 120.83/55.31 thf(8404,plain,((! [A:$i]: (((A = zero_zero_complex) => ((hAPP_complex_complex @ cnj @ A) = zero_zero_complex)) & (((hAPP_complex_complex @ cnj @ A) = zero_zero_complex) => (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])). 120.83/55.31 thf(1740,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)) <=> (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2876_Suc__mult__cancel1)). 120.83/55.31 thf(10963,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)) => (C = B)) & ((C = B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740])). 120.83/55.31 thf(2030,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1875_add__strict__increasing2)). 120.83/55.31 thf(11941,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030])). 120.83/55.31 thf(1950,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ one_on1684967323de_int)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.31 thf(11703,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ one_on1684967323de_int)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950])). 120.83/55.31 thf(2061,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3005_power__Suc2)). 120.83/55.31 thf(12038,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061])). 120.83/55.31 thf(2142,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ prime @ A)) & (one_one_nat = B)) <=> (hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4176_prime__exp)). 120.83/55.31 thf(12317,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ prime @ A)) & (one_one_nat = B)) => (hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ prime @ A)) & (one_one_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142])). 120.83/55.31 thf(4862,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0)). 120.83/55.31 thf(22188,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4862])). 120.83/55.31 thf(3393,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_dvd__power__same)). 120.83/55.31 thf(16723,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3393])). 120.83/55.31 thf(2137,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ D) @ zero_zero_nat))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ A) @ B)) <= (! [D:$i,E:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ D) @ E)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ E) @ (hAPP_nat_nat @ (div_mod_nat @ D) @ E)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4551_gcd__nat__induct)). 120.83/55.31 thf(12301,plain,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ D) @ zero_zero_nat))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ A) @ B)) | ~ (! [D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ D) @ E)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ C @ E) @ (hAPP_nat_nat @ (div_mod_nat @ D) @ E))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137])). 120.83/55.31 thf(3726,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_add__Bit0__Bit0)). 120.83/55.31 thf(17854,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3726])). 120.83/55.31 thf(4137,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_le__number__of__eq__not__less)). 120.83/55.31 thf(19412,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4137])). 120.83/55.31 thf(1984,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ C @ A) = (hAPP_real_real @ C @ B)) <= (! [D:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ C @ D) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3951_DERIV__isconst__all)). 120.83/55.31 thf(11809,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ C @ A) = (hAPP_real_real @ C @ B)) | ~ (! [D:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ C @ D) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984])). 120.83/55.31 thf(3583,axiom,((! [A:$i,B:$i,C:$i]: (((C = B) | (A = zero_zero_nat)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1622_mult__cancel1)). 120.83/55.31 thf(17347,plain,((! [A:$i,B:$i,C:$i]: ((((C = B) | (A = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => ((C = B) | (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3583])). 120.83/55.31 thf(4489,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2207_le__iff__diff__le__0)). 120.83/55.31 thf(20746,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4489])). 120.83/55.31 thf(3436,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => ((comple124823625p_real @ (hAPP_r1134773055l_bool @ (ord_at1496968948n_real @ A) @ B)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4917_Sup__atLeastLessThan)). 120.83/55.31 thf(16855,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => ((comple124823625p_real @ (hAPP_r1134773055l_bool @ (ord_at1496968948n_real @ A) @ B)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3436])). 120.83/55.31 thf(293,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A))) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2353_div__mod__equality2)). 120.83/55.31 thf(5923,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A))) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 120.83/55.31 thf(2581,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3205_Suc__div__eq__add3__div__number__of)). 120.83/55.31 thf(13898,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581])). 120.83/55.31 thf(1090,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_mult__dvd__mono)). 120.83/55.31 thf(8711,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090])). 120.83/55.31 thf(1983,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4030_coprime__exp2)). 120.83/55.31 thf(11804,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983])). 120.83/55.31 thf(3472,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1514_dvd__reduce)). 120.83/55.31 thf(16977,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3472])). 120.83/55.31 thf(4921,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2644_zdiv__leq__prop)). 120.83/55.31 thf(22372,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4921])). 120.83/55.31 thf(2768,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ D) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1631_less__add__eq__less)). 120.83/55.31 thf(14572,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ D) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2768])). 120.83/55.31 thf(822,axiom,((! [A:$i]: ((hAPP_int_int @ fact_fact_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4280_transfer__int__nat__factorial)). 120.83/55.31 thf(7751,plain,((! [A:$i]: ((hAPP_int_int @ fact_fact_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])). 120.83/55.31 thf(740,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_mult__zero__left)). 120.83/55.31 thf(7440,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 120.83/55.31 thf(3525,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_dvd__0__right)). 120.83/55.31 thf(17141,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3525])). 120.83/55.31 thf(4421,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = (hAPP_int_int @ abs_abs_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4993_gcd__proj2__if__dvd__int)). 120.83/55.31 thf(20486,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A) = (hAPP_int_int @ abs_abs_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4421])). 120.83/55.31 thf(298,axiom,((zero_zero_real = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3581_cos__pi__half)). 120.83/55.31 thf(5940,plain,((zero_zero_real = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 120.83/55.31 thf(1385,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3937_real__root__increasing)). 120.83/55.31 thf(9706,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385])). 120.83/55.31 thf(3971,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2615_pos__mod__sign)). 120.83/55.31 thf(18726,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3971])). 120.83/55.31 thf(4891,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1464_convex__bound__le)). 120.83/55.31 thf(22277,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) @ E))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4891])). 120.83/55.31 thf(599,axiom,(((hAPP_real_real @ arctan @ one_one_real) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3472_arctan1__eq__pi4)). 120.83/55.31 thf(6927,plain,(((hAPP_real_real @ arctan @ one_one_real) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])). 120.83/55.31 thf(1123,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ zEven)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3150_odd__minus__one__even)). 120.83/55.31 thf(8809,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123])). 120.83/55.31 thf(4615,axiom,((! [A:$i]: ~ (! [B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) != one_one_int)) <= (A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5026_Rat__cases)). 120.83/55.31 thf(21289,plain,((! [A:$i]: ~ (! [B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C) = one_one_int))) | ~ (A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4615])). 120.83/55.31 thf(4280,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2698_nat__mod__distrib)). 120.83/55.31 thf(19949,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4280])). 120.83/55.31 thf(4567,axiom,(((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ s) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ s) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_s0p)). 120.83/55.31 thf(21122,plain,(((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ s) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ s) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4567])). 120.83/55.31 thf(305,axiom,((zero_zero_real = (hAPP_real_real @ sin @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3637_sin__zero)). 120.83/55.31 thf(5962,plain,((zero_zero_real = (hAPP_real_real @ sin @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 120.83/55.31 thf(4324,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5013_gcd__le1__int)). 120.83/55.31 thf(20105,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4324])). 120.83/55.31 thf(960,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ one_one_nat)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3704_ge__natfloor__plus__one__imp__gt)). 120.83/55.31 thf(8222,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ one_one_nat)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])). 120.83/55.31 thf(271,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ tan @ (hAPP_real_real @ arctan @ A)) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3622_arctan)). 120.83/55.31 thf(5831,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ tan @ (hAPP_real_real @ arctan @ A)) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 120.83/55.31 thf(2336,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1644_trans__le__add2)). 120.83/55.31 thf(13033,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336])). 120.83/55.31 thf(1780,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2395_mod__mult__mult2)). 120.83/55.31 thf(11124,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780])). 120.83/55.31 thf(2106,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = B) => (one_one_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))) & (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) <= (zero_zero_nat != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1833_realpow__num__eq__if)). 120.83/55.31 thf(12184,plain,((! [A:$i,B:$i]: (((zero_zero_nat = B) => (one_one_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))) & (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) | (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106])). 120.83/55.31 thf(2804,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.31 thf(14714,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2804])). 120.83/55.31 thf(3333,axiom,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) = zero_z126310315umeral) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2587_dvd__eq__mod__eq__0__number__of)). 120.83/55.31 thf(16532,plain,((! [A:$i,B:$i]: ((((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) = zero_z126310315umeral) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ B))) => ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ B)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) = zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3333])). 120.83/55.31 thf(3230,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2054_add__strict__left__mono)). 120.83/55.31 thf(16209,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3230])). 120.83/55.31 thf(2364,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ A) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (is_RRset @ C) @ D)) => ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ C)) => (A = B)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4590_RRset__zcong__eq)). 120.83/55.31 thf(13125,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ A) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ D)) => ((hBOOL @ (hAPP_int_bool @ (is_RRset @ C) @ D)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ C)) => (A = B)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364])). 120.83/55.31 thf(2288,axiom,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1761_diff__add__0)). 120.83/55.31 thf(12862,plain,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288])). 120.83/55.31 thf(2536,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2507_mod__mult__self1)). 120.83/55.31 thf(13755,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2536])). 120.83/55.31 thf(2809,axiom,((! [A:$i,B:$i]: ((A != B) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1717_dvd_Oless__imp__neq)). 120.83/55.31 thf(14731,plain,((! [A:$i,B:$i]: (~ (A = B) | ~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2809])). 120.83/55.31 thf(4589,axiom,((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_semiring__norm_I113_J)). 120.83/55.31 thf(21201,plain,((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4589])). 120.83/55.31 thf(1111,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_dvd__mult__left)). 120.83/55.31 thf(8777,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111])). 120.83/55.31 thf(3254,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2090_diff__0__right)). 120.83/55.31 thf(16278,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3254])). 120.83/55.31 thf(2484,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))) @ zero_zero_real)) <=> ((zero_zero_real = A) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sum__squares__le__zero__iff)). 120.83/55.31 thf(13561,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))) @ zero_zero_real)) => ((zero_zero_real = A) & (B = zero_zero_real))) & (((zero_zero_real = A) & (B = zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484])). 120.83/55.31 thf(1237,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4012_coprime__mul__eq)). 120.83/55.31 thf(9189,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237])). 120.83/55.31 thf(4563,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ A)) @ (posDivAlg @ one_one_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ A)))))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2680_posDivAlg__eqn__1__number__of)). 120.83/55.31 thf(21109,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ A)) @ (posDivAlg @ one_one_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ A)))))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (posDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4563])). 120.83/55.31 thf(2426,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2073_add__less__cancel__right)). 120.83/55.31 thf(13363,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426])). 120.83/55.31 thf(313,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_mult__right__mono)). 120.83/55.31 thf(5984,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 120.83/55.31 thf(988,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2913_of__nat__0__le__iff)). 120.83/55.31 thf(8332,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ semiri132038758t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])). 120.83/55.31 thf(44,axiom,((! [A:$i]: ((hAPP_complex_complex @ cnj @ A) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4132_cnj__def)). 120.83/55.31 thf(5097,plain,((! [A:$i]: ((hAPP_complex_complex @ cnj @ A) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 120.83/55.31 thf(420,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3584_cos__60)). 120.83/55.31 thf(6344,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 120.83/55.31 thf(2674,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_int_rat @ number_number_of_rat @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ C))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_int_rat @ number_number_of_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_left__distrib__number__of)). 120.83/55.31 thf(14247,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_int_rat @ number_number_of_rat @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ C))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_int_rat @ number_number_of_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2674])). 120.83/55.31 thf(2913,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1753_Nat_Odiff__diff__eq)). 120.83/55.31 thf(15079,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2913])). 120.83/55.31 thf(2553,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3127_n__less__n__mult__m)). 120.83/55.31 thf(13809,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553])). 120.83/55.31 thf(1062,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) <= (C != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2539_div__mult__mult2)). 120.83/55.31 thf(8581,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) | (C = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062])). 120.83/55.31 thf(3731,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2331_mod__div__trivial)). 120.83/55.31 thf(17882,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3731])). 120.83/55.31 thf(3566,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3331_real__sqrt__le__1__iff)). 120.83/55.31 thf(17273,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3566])). 120.83/55.31 thf(1181,axiom,((! [A:$i]: (A = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.31 thf(8993,plain,((! [A:$i]: (A = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181])). 120.83/55.31 thf(95,axiom,((zero_zero_nat = (hAPP_nat_nat @ size_size_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4060_nat_Osize_I3_J)). 120.83/55.31 thf(5271,plain,((zero_zero_nat = (hAPP_nat_nat @ size_size_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 120.83/55.31 thf(121,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1516_dvd__diff)). 120.83/55.31 thf(5350,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 120.83/55.31 thf(4357,axiom,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ zero_zero_int) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2459_zmod__zero)). 120.83/55.31 thf(20237,plain,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ zero_zero_int) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4357])). 120.83/55.31 thf(2728,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2905_zero__le__imp__of__nat)). 120.83/55.31 thf(14429,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2728])). 120.83/55.31 thf(2990,axiom,((! [A:$i,B:$i]: ((B != zero_zero_rat) => ((zero_zero_rat != (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) <= (zero_zero_rat != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_no__zero__divisors)). 120.83/55.31 thf(15348,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_rat)) => (~ (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) | (zero_zero_rat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2990])). 120.83/55.31 thf(83,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_dvd__mult__right)). 120.83/55.31 thf(5239,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C)) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 120.83/55.31 thf(1424,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_right__distrib__number__of)). 120.83/55.31 thf(9852,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424])). 120.83/55.31 thf(4676,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3237_int__power__div__base)). 120.83/55.31 thf(21497,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4676])). 120.83/55.31 thf(2587,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3190_realpow__two__diff)). 120.83/55.31 thf(13920,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587])). 120.83/55.31 thf(843,axiom,((! [A:$i]: ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ abs_abs_real @ A)) @ zero_zero_real @ sequentially)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5044_LIMSEQ__rabs__realpow__zero)). 120.83/55.31 thf(7828,plain,((! [A:$i]: ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ abs_abs_real @ A)) @ zero_zero_real @ sequentially)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[843])). 120.83/55.31 thf(2462,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1636_le__neq__implies__less)). 120.83/55.31 thf(13492,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2462])). 120.83/55.31 thf(1723,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((B != A) & (C != D)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_crossproduct__noteq)). 120.83/55.31 thf(10874,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (B = A) & ~ (C = D)) => (~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))))) & ((~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))) => (~ (B = A) & ~ (C = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723])). 120.83/55.31 thf(2334,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_complex_complex @ cnj @ B) = (hAPP_complex_complex @ cnj @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4072_complex__cnj__cancel__iff)). 120.83/55.31 thf(13022,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_complex_complex @ cnj @ B) = (hAPP_complex_complex @ cnj @ A))) & (((hAPP_complex_complex @ cnj @ B) = (hAPP_complex_complex @ cnj @ A)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334])). 120.83/55.31 thf(3898,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A)))) @ A) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2235_Int2_Oaux____2)). 120.83/55.31 thf(18477,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_int_int @ (multInv @ B) @ (hAPP_int_int @ (multInv @ B) @ A)))) @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3898])). 120.83/55.31 thf(4245,axiom,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ one_one_int)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5082_card__atLeastAtMost__int)). 120.83/55.31 thf(19814,plain,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ one_one_int)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4245])). 120.83/55.31 thf(4747,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ min)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_rel__simps_I11_J)). 120.83/55.31 thf(21805,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ min)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ min)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4747])). 120.83/55.31 thf(1954,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) = D) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = one_one_nat)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) = C)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4365_gcd__coprime__nat)). 120.83/55.31 thf(11714,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) = D) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = one_one_nat)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D)) = C) | ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954])). 120.83/55.31 thf(4598,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.31 thf(21233,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4598])). 120.83/55.31 thf(2629,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) => ((((A = C) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1483_power__eq__imp__eq__base)). 120.83/55.31 thf(14095,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) => ((A = C) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2629])). 120.83/55.31 thf(530,axiom,((! [A:$i]: ((hAPP_nat_real @ real_nat @ A) = (hAPP_int_real @ real_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4392_real__of__int__of__nat__eq)). 120.83/55.31 thf(6705,plain,((! [A:$i]: ((hAPP_nat_real @ real_nat @ A) = (hAPP_int_real @ real_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 120.83/55.31 thf(4800,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1552_diff__bin__simps_I9_J)). 120.83/55.31 thf(21974,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4800])). 120.83/55.31 thf(4734,axiom,((zero_z891286103de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_zero__power2)). 120.83/55.31 thf(21750,plain,((zero_z891286103de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4734])). 120.83/55.31 thf(4058,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ B) | (hBOOL @ (fdisj @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U)). 120.83/55.31 thf(19071,plain,((! [A:$i,B:$i]: (~ (hBOOL @ B) | (hBOOL @ (fdisj @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4058])). 120.83/55.31 thf(180,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_mult__nonneg__nonpos)). 120.83/55.31 thf(5535,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 120.83/55.31 thf(3673,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2600_neg__imp__zdiv__nonneg__iff)). 120.83/55.31 thf(17669,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3673])). 120.83/55.31 thf(1002,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1738_diff__self__eq__0)). 120.83/55.31 thf(8381,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])). 120.83/55.31 thf(1484,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5191_max__0R)). 120.83/55.31 thf(10044,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484])). 120.83/55.31 thf(832,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) <=> (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2870_not__less__eq__eq)). 120.83/55.31 thf(7795,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) & ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 120.83/55.31 thf(2381,axiom,((! [A:$i]: ((A != zero_zero_nat) => (? [B:$i]: (A = (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3353_not0__implies__Suc)). 120.83/55.31 thf(13197,plain,((! [A:$i]: ((~ (A = zero_zero_nat)) => (? [B:$i]: (A = (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381])). 120.83/55.31 thf(2425,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4442_number__of__less__real__of__int__iff2)). 120.83/55.31 thf(13358,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2425])). 120.83/55.31 thf(2781,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.31 thf(14619,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2781])). 120.83/55.31 thf(983,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_one__dvd)). 120.83/55.31 thf(8318,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[983])). 120.83/55.31 thf(3737,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2184_add__pos__pos)). 120.83/55.31 thf(17905,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3737])). 120.83/55.31 thf(1107,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3178_lemma__realpow__diff)). 120.83/55.31 thf(8767,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107])). 120.83/55.31 thf(2812,axiom,((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1216_not__one__le__zero)). 120.83/55.31 thf(14743,plain,((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2812])). 120.83/55.31 thf(1987,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((zero_zero_nat != E) => (((C = D) & (B != A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ B)) != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_add__scale__eq__noteq)). 120.83/55.31 thf(11819,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (zero_zero_nat = E)) => (((C = D) & ~ (B = A)) => (~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987])). 120.83/55.31 thf(29,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (divmod_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4217_divmod__nat__rel__divmod__nat)). 120.83/55.31 thf(5039,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (divmod_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 120.83/55.31 thf(4138,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J)). 120.83/55.31 thf(19417,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4138])). 120.83/55.31 thf(2413,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1303_power__add)). 120.83/55.31 thf(13319,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2413])). 120.83/55.31 thf(1939,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zOdd))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2488_EvenOdd_Oodd__times__odd)). 120.83/55.31 thf(11671,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zOdd))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939])). 120.83/55.31 thf(3927,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_rel__simps_I23_J)). 120.83/55.31 thf(18573,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3927])). 120.83/55.31 thf(2712,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1584_less__not__refl)). 120.83/55.31 thf(14384,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2712])). 120.83/55.31 thf(4048,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero)). 120.83/55.31 thf(19042,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4048])). 120.83/55.31 thf(27,axiom,((! [A:$i,B:$i]: (A = (hAPP_complex_real @ re @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4113_Re)). 120.83/55.31 thf(5033,plain,((! [A:$i,B:$i]: (A = (hAPP_complex_real @ re @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 120.83/55.31 thf(1365,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.31 thf(9638,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365])). 120.83/55.31 thf(4021,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ E)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ E)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_zcong__eq__trans)). 120.83/55.31 thf(18916,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ E)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4021])). 120.83/55.31 thf(3157,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zOdd)) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2645_power__preserves__odd)). 120.83/55.31 thf(15919,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zOdd)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3157])). 120.83/55.31 thf(4336,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4517_zrelprime__zdvd__zmult)). 120.83/55.31 thf(20173,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4336])). 120.83/55.31 thf(433,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2089_diff__0__right)). 120.83/55.31 thf(6385,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 120.83/55.31 thf(3693,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_mult__pos__neg2)). 120.83/55.31 thf(17744,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3693])). 120.83/55.31 thf(3708,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_power2__eq__square)). 120.83/55.31 thf(17801,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3708])). 120.83/55.31 thf(3851,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_dvd__triv__right)). 120.83/55.31 thf(18314,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3851])). 120.83/55.31 thf(1372,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1370_mult__strict__mono_H)). 120.83/55.31 thf(9659,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372])). 120.83/55.31 thf(2387,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4157_termination__basic__simps_I1_J)). 120.83/55.31 thf(13217,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387])). 120.83/55.31 thf(159,axiom,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4109_Im_Obounded)). 120.83/55.31 thf(5471,plain,((? [A:$i]: ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ norm_norm_real @ (hAPP_complex_real @ im @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 120.83/55.31 thf(423,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3507_arcsin__bounded)). 120.83/55.31 thf(6357,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 120.83/55.31 thf(692,axiom,(((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_one__add__one__is__two)). 120.83/55.31 thf(7270,plain,(((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 120.83/55.31 thf(2529,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.31 thf(13730,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2529])). 120.83/55.31 thf(2070,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_power__even__eq)). 120.83/55.31 thf(12067,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070])). 120.83/55.31 thf(3328,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2686_div__mod__equality_H)). 120.83/55.31 thf(16515,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3328])). 120.83/55.31 thf(1578,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_dvd__add)). 120.83/55.31 thf(10393,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578])). 120.83/55.31 thf(517,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D)) => (((zero_zero_real = D) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => ((hAPP_real_real @ B @ E) = (hAPP_real_real @ B @ C))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3886_DERIV__local__const)). 120.83/55.31 thf(6667,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D)) => ((zero_zero_real = D) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => ((hAPP_real_real @ B @ E) = (hAPP_real_real @ B @ C)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 120.83/55.31 thf(3074,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_dvd__mult__right)). 120.83/55.31 thf(15649,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3074])). 120.83/55.31 thf(1497,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_number__of__mult)). 120.83/55.31 thf(10083,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497])). 120.83/55.31 thf(3533,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.31 thf(17162,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3533])). 120.83/55.31 thf(889,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1547_right__diff__distrib__number__of)). 120.83/55.31 thf(7983,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])). 120.83/55.31 thf(4020,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) => (! [D:$i]: ((is_int @ D) => (((D = A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C) = A)) <= (! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) != D)) <= (is_int @ F)))) <= (is_int @ E))))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5096_aset_I3_J)). 120.83/55.31 thf(18899,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ A) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) => (! [D:$i]: ((is_int @ D) => (((D = A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C) = A)) | ~ (! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) = D))) | ~ (is_int @ F)))) | ~ (is_int @ E))))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4020])). 120.83/55.31 thf(1134,axiom,((! [A:$i]: ((A = zero_zero_nat) <=> (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1895_zero__reorient)). 120.83/55.31 thf(8841,plain,((! [A:$i]: (((A = zero_zero_nat) => (zero_zero_nat = A)) & ((zero_zero_nat = A) => (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134])). 120.83/55.31 thf(766,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3579_cos__two__le__zero)). 120.83/55.31 thf(7534,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])). 120.83/55.31 thf(4829,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_power3__eq__cube)). 120.83/55.31 thf(22081,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4829])). 120.83/55.31 thf(1068,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_even__less__0__iff)). 120.83/55.31 thf(8629,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068])). 120.83/55.31 thf(1326,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1382_mult__le__cancel__left__pos)). 120.83/55.31 thf(9506,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326])). 120.83/55.31 thf(2203,axiom,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4569_div__code__int__def)). 120.83/55.31 thf(12566,plain,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2203])). 120.83/55.31 thf(2936,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1948_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.31 thf(15160,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2936])). 120.83/55.31 thf(276,axiom,((! [A:$i]: (((hAPP_real_real @ sin @ A) = zero_zero_real) <=> (? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3753_sin__zero__iff)). 120.83/55.31 thf(5859,plain,((! [A:$i]: ((((hAPP_real_real @ sin @ A) = zero_zero_real) => (? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)))) & ((? [B:$i]: (((hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))) => ((hAPP_real_real @ sin @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 120.83/55.31 thf(3974,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3158_realpow__Suc__le__self)). 120.83/55.31 thf(18748,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3974])). 120.83/55.31 thf(1059,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.31 thf(8566,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059])). 120.83/55.31 thf(1885,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1442_power__strict__increasing)). 120.83/55.31 thf(11502,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885])). 120.83/55.31 thf(1145,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2068_add__less__cancel__left)). 120.83/55.31 thf(8877,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145])). 120.83/55.31 thf(1077,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2254_pinf_I10_J)). 120.83/55.31 thf(8665,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077])). 120.83/55.31 thf(3652,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2766_Euler__part2)). 120.83/55.31 thf(17590,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3652])). 120.83/55.31 thf(99,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.31 thf(5282,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 120.83/55.31 thf(2684,axiom,((! [A:$i,B:$i]: (((B != zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A)))) & ((B = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1804_mult__eq__if)). 120.83/55.31 thf(14275,plain,((! [A:$i,B:$i]: (((~ (B = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A)))) & ((B = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2684])). 120.83/55.31 thf(3704,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2696_nat__div__distrib)). 120.83/55.31 thf(17789,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3704])). 120.83/55.31 thf(3043,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.31 thf(15517,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3043])). 120.83/55.31 thf(2431,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2300_mult__left_Odiff)). 120.83/55.31 thf(13380,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431])). 120.83/55.31 thf(3618,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) @ zero_zero_int)) <=> ((A = zero_zero_int) & (zero_zero_int = B))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__squares__le__zero__iff)). 120.83/55.31 thf(17458,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) @ zero_zero_int)) => ((A = zero_zero_int) & (zero_zero_int = B))) & (((A = zero_zero_int) & (zero_zero_int = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) @ zero_zero_int)))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3618])). 120.83/55.31 thf(1803,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2113_mult__1)). 120.83/55.31 thf(11201,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ one_one_nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803])). 120.83/55.31 thf(561,axiom,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3688_tan__npi)). 120.83/55.31 thf(6794,plain,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 120.83/55.31 thf(1936,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1601_nat__mult__commute)). 120.83/55.31 thf(11662,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936])). 120.83/55.31 thf(1862,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1304_power__add)). 120.83/55.31 thf(11423,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862])). 120.83/55.31 thf(4125,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ fact_fact_int @ A) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4278_fact__nonzero__int)). 120.83/55.31 thf(19376,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (~ ((hAPP_int_int @ fact_fact_int @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4125])). 120.83/55.31 thf(3324,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4156_termination__basic__simps_I4_J)). 120.83/55.31 thf(16503,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3324])). 120.83/55.31 thf(2637,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.31 thf(14134,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2637])). 120.83/55.31 thf(2176,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2519_dvd__eq__mod__eq__0)). 120.83/55.31 thf(12451,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ B) @ A))) & ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176])). 120.83/55.31 thf(3543,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1259_less__add__one)). 120.83/55.31 thf(17209,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3543])). 120.83/55.31 thf(43,axiom,((! [A:$i,B:$i,C:$i]: (((A = C) & (B = zero_zero_real)) <=> ((of_real_complex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3987_complex__eq__cancel__iff2)). 120.83/55.31 thf(5086,plain,((! [A:$i,B:$i,C:$i]: ((((A = C) & (B = zero_zero_real)) => ((of_real_complex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B))) & (((of_real_complex @ C) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) => ((A = C) & (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 120.83/55.31 thf(3955,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f1448486952t_bool @ (hAPP_f696844121t_bool @ cOMBB_nat_bool_int @ A) @ B) @ C) = (hAPP_nat_bool @ A @ (hAPP_int_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__HOL__Obool_000tc__Int__Oint_U)). 120.83/55.31 thf(18665,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_bool @ (hAPP_f1448486952t_bool @ (hAPP_f696844121t_bool @ cOMBB_nat_bool_int @ A) @ B) @ C) = (hAPP_nat_bool @ A @ (hAPP_int_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3955])). 120.83/55.31 thf(1829,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2851_Suc__not__Zero)). 120.83/55.31 thf(11291,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829])). 120.83/55.31 thf(3222,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_power2__eq__square__number__of)). 120.83/55.31 thf(16167,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3222])). 120.83/55.31 thf(1848,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1401_power__less__imp__less__base)). 120.83/55.31 thf(11370,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848])). 120.83/55.31 thf(3013,axiom,((! [A:$i,B:$i]: (((quickcheck_int_of @ A) = (quickcheck_int_of @ B)) <=> (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4255_Quickcheck__Narrowing_Oint__of__inject)). 120.83/55.31 thf(15428,plain,((! [A:$i,B:$i]: ((((quickcheck_int_of @ A) = (quickcheck_int_of @ B)) => (B = A)) & ((B = A) => ((quickcheck_int_of @ A) = (quickcheck_int_of @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3013])). 120.83/55.31 thf(1332,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A) = (hAPP_nat_nat @ suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3081_power__Suc__0)). 120.83/55.31 thf(9538,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A) = (hAPP_nat_nat @ suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332])). 120.83/55.31 thf(4765,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_power__strict__mono)). 120.83/55.31 thf(21859,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4765])). 120.83/55.31 thf(2039,axiom,((! [A:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3723_fact__lemma)). 120.83/55.31 thf(11968,plain,((! [A:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039])). 120.83/55.31 thf(1405,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2274_pinf_I9_J)). 120.83/55.31 thf(9776,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405])). 120.83/55.31 thf(1942,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2204_add__less__le__mono)). 120.83/55.31 thf(11678,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942])). 120.83/55.31 thf(2260,axiom,((! [A:$i]: ((hAPP_nat_complex @ semiri2020571505omplex @ A) = (hAPP_complex_complex @ cnj @ (hAPP_nat_complex @ semiri2020571505omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4075_complex__cnj__of__nat)). 120.83/55.31 thf(12748,plain,((! [A:$i]: ((hAPP_nat_complex @ semiri2020571505omplex @ A) = (hAPP_complex_complex @ cnj @ (hAPP_nat_complex @ semiri2020571505omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260])). 120.83/55.31 thf(3553,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_P1975530577nt_int @ (adjust @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) = (hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4730_adjust__eq)). 120.83/55.31 thf(17236,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_P1975530577nt_int @ (adjust @ A) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)) = (hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3553])). 120.83/55.31 thf(871,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.31 thf(7924,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])). 120.83/55.31 thf(2264,axiom,((! [A:$i,B:$i]: (((one_one_nat = A) & (one_one_nat = B)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1813_nat__mult__eq__one)). 120.83/55.31 thf(12759,plain,((! [A:$i,B:$i]: ((((one_one_nat = A) & (one_one_nat = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat) => ((one_one_nat = A) & (one_one_nat = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264])). 120.83/55.31 thf(1674,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3179_Suc__pred_H)). 120.83/55.31 thf(10728,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674])). 120.83/55.31 thf(2309,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2002_add__le__imp__le__right)). 120.83/55.31 thf(12936,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309])). 120.83/55.31 thf(833,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3919_real__root__gt__0__iff)). 120.83/55.31 thf(7800,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 120.83/55.31 thf(2654,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) @ (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1843_mult__sum2sq)). 120.83/55.31 thf(14183,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) @ (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2654])). 120.83/55.31 thf(508,axiom,((! [A:$i,B:$i]: (B = (hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ fFalse) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__RealDef__Oreal_T)). 120.83/55.31 thf(6638,plain,((! [A:$i,B:$i]: (B = (hAPP_real_real @ (hAPP_r1250527377l_real @ (hAPP_b646336293l_real @ if_real @ fFalse) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 120.83/55.31 thf(1323,axiom,((! [A:$i,B:$i]: ((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ fFalse) @ A) @ B)) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Int__Oint_T)). 120.83/55.31 thf(9496,plain,((! [A:$i,B:$i]: ((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ fFalse) @ A) @ B)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323])). 120.83/55.31 thf(2603,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1392_zero__less__two)). 120.83/55.31 thf(13984,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2603])). 120.83/55.31 thf(2739,axiom,((! [A:$i,B:$i]: (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1802_realpow__minus__mult)). 120.83/55.31 thf(14461,plain,((! [A:$i,B:$i]: (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2739])). 120.83/55.31 thf(654,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_int_complex @ number528085621omplex @ A))) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_number__of__Bit1)). 120.83/55.31 thf(7145,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_int_complex @ number528085621omplex @ A))) @ (hAPP_int_complex @ number528085621omplex @ A)) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])). 120.83/55.31 thf(2041,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1612_Nat_Oadd__0__right)). 120.83/55.31 thf(11973,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041])). 120.83/55.31 thf(2143,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5124_min__Suc__Suc)). 120.83/55.31 thf(12327,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143])). 120.83/55.31 thf(4876,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1402_power__decreasing)). 120.83/55.31 thf(22227,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4876])). 120.83/55.31 thf(3799,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ fact_fact_int @ A)) = (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4287_fact__plus__one__int)). 120.83/55.31 thf(18124,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ fact_fact_int @ A)) = (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3799])). 120.83/55.31 thf(2965,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1523_zdiff__zmult__distrib2)). 120.83/55.31 thf(15244,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2965])). 120.83/55.31 thf(2096,axiom,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ one_on1684967323de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1394_zero__less__two)). 120.83/55.31 thf(12146,plain,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ one_on1684967323de_int) @ one_on1684967323de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096])). 120.83/55.31 thf(3537,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1447_power__less__imp__less__exp)). 120.83/55.31 thf(17173,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3537])). 120.83/55.31 thf(2501,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_mult__nonneg__nonneg)). 120.83/55.31 thf(13638,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501])). 120.83/55.31 thf(2984,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3661_real__of__nat__Suc__gt__zero)). 120.83/55.31 thf(15329,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2984])). 120.83/55.31 thf(2836,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1596_le__antisym)). 120.83/55.31 thf(14820,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2836])). 120.83/55.31 thf(1478,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2914_of__nat__0__le__iff)). 120.83/55.31 thf(10024,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478])). 120.83/55.31 thf(3028,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1368_mult__strict__mono_H)). 120.83/55.31 thf(15470,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3028])). 120.83/55.31 thf(1378,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1874_add__strict__increasing)). 120.83/55.31 thf(9681,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378])). 120.83/55.31 thf(3132,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3191_realpow__two__diff)). 120.83/55.31 thf(15842,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3132])). 120.83/55.31 thf(389,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4455_real__of__int__floor__ge__diff__one)). 120.83/55.31 thf(6248,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 120.83/55.31 thf(1813,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3344_real__sqrt__sum__squares__triangle__ineq)). 120.83/55.31 thf(11237,plain,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ D)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813])). 120.83/55.31 thf(1047,axiom,((! [A:$i]: ((A = one_one_nat) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1515_nat__dvd__1__iff__1)). 120.83/55.31 thf(8524,plain,((! [A:$i]: (((A = one_one_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) => (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047])). 120.83/55.31 thf(4383,axiom,((! [A:$i,B:$i,C:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)) & ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_zcong__zprime__prod__zero__contra)). 120.83/55.31 thf(20330,plain,((! [A:$i,B:$i,C:$i]: (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C)) | ~ (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)) & ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4383])). 120.83/55.31 thf(3339,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_real) <=> ((A = zero_zero_real) & ((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_power__eq__0__iff__number__of)). 120.83/55.31 thf(16553,plain,((! [A:$i,B:$i]: ((((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_real) => ((A = zero_zero_real) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat))) & (((A = zero_zero_real) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat)) => ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3339])). 120.83/55.31 thf(3409,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3366_real__average__minus__second)). 120.83/55.31 thf(16782,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3409])). 120.83/55.31 thf(1632,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (tendsto_nat_real @ B @ C @ sequentially)) => ((? [D:$i]: ! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ E)) @ A)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5035_LIMSEQ__le__const2)). 120.83/55.31 thf(10596,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (tendsto_nat_real @ B @ C @ sequentially)) => ((? [D:$i]: ! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ B @ E)) @ A)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632])). 120.83/55.31 thf(2102,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2576_dvd__mult__div__cancel)). 120.83/55.31 thf(12167,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102])). 120.83/55.31 thf(4404,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_split__mult__pos__le)). 120.83/55.31 thf(20426,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4404])). 120.83/55.31 thf(4900,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2697_Divides_Otransfer__nat__int__functions_I1_J)). 120.83/55.31 thf(22309,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4900])). 120.83/55.31 thf(1411,axiom,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))) = (hAPP_nat_nat @ fact_fact_nat @ A)) <= (A != zero_zero_nat)) & (((hAPP_nat_nat @ fact_fact_nat @ A) = one_one_nat) <= (zero_zero_nat = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3815_fact__num__eq__if__nat)). 120.83/55.31 thf(9803,plain,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat))) = (hAPP_nat_nat @ fact_fact_nat @ A)) | (A = zero_zero_nat)) & (((hAPP_nat_nat @ fact_fact_nat @ A) = one_one_nat) | ~ (zero_zero_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411])). 120.83/55.31 thf(3100,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) | (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2901_even__odd__disj)). 120.83/55.31 thf(15733,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) | (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3100])). 120.83/55.31 thf(3224,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2308_gcd__lcm__complete__lattice__nat_Otop__greatest)). 120.83/55.31 thf(16174,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3224])). 120.83/55.31 thf(255,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3508_arcsin__lbound)). 120.83/55.31 thf(5784,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 120.83/55.31 thf(1921,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5159_isCont__real__root)). 120.83/55.31 thf(11618,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921])). 120.83/55.31 thf(2016,axiom,((! [A:$i]: ((A = zero_z126310315umeral) <=> (A = zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1897_zero__reorient)). 120.83/55.31 thf(11900,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016])). 120.83/55.31 thf(953,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1847_nat__mult__less__cancel1)). 120.83/55.31 thf(8202,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[953])). 120.83/55.31 thf(3329,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2042_add__less__imp__less__right)). 120.83/55.31 thf(16518,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3329])). 120.83/55.31 thf(1004,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1208_pos__add__strict)). 120.83/55.31 thf(8387,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])). 120.83/55.31 thf(3878,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_number__of__Bit0)). 120.83/55.31 thf(18399,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3878])). 120.83/55.31 thf(4821,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__eq__int__code_I13_J)). 120.83/55.31 thf(22045,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4821])). 120.83/55.31 thf(3281,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (? [C:$i]: (! [D:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ (hAPP_i1948725293t_bool @ norRRset @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ D) @ B))) => (D = C)) <= (is_int @ D)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ norRRset @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B)) & (is_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4586_norR__mem__unique)). 120.83/55.31 thf(16370,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (? [C:$i]: (! [D:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ (hAPP_i1948725293t_bool @ norRRset @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ D) @ B))) => (D = C)) | ~ (is_int @ D)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ C) @ (hAPP_i1948725293t_bool @ norRRset @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B)) & (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3281])). 120.83/55.31 thf(1269,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ semiri132038758t_real @ B) = (hAPP_nat_real @ semiri132038758t_real @ A)) <=> (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2832_of__nat__eq__iff)). 120.83/55.31 thf(9307,plain,((! [A:$i,B:$i]: ((((hAPP_nat_real @ semiri132038758t_real @ B) = (hAPP_nat_real @ semiri132038758t_real @ A)) => (B = A)) & ((B = A) => ((hAPP_nat_real @ semiri132038758t_real @ B) = (hAPP_nat_real @ semiri132038758t_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269])). 120.83/55.31 thf(3562,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3180_Suc__diff__1)). 120.83/55.31 thf(17260,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3562])). 120.83/55.31 thf(4194,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1870_add__strict__increasing)). 120.83/55.31 thf(19609,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4194])). 120.83/55.31 thf(820,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_times__numeral__code_I5_J)). 120.83/55.31 thf(7746,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 120.83/55.31 thf(3887,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((((comple219730294t_bool @ (setS @ A @ B)) = (hAPP_i1948725293t_bool @ sRStar @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3306_MultInvPair__prop2)). 120.83/55.31 thf(18431,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((comple219730294t_bool @ (setS @ A @ B)) = (hAPP_i1948725293t_bool @ sRStar @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3887])). 120.83/55.31 thf(4275,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1311_zcong__not__zero)). 120.83/55.31 thf(19930,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4275])). 120.83/55.31 thf(4110,axiom,((! [A:$i,B:$i]: ((((A = zero_zero_int) & (B = zero_zero_int)) <=> (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B)))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_sum__squares__eq__zero__iff)). 120.83/55.31 thf(19321,plain,((! [A:$i,B:$i]: (((((A = zero_zero_int) & (B = zero_zero_int)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B)))) & ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) => ((A = zero_zero_int) & (B = zero_zero_int)))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4110])). 120.83/55.31 thf(3597,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ D @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ F) @ G))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A) @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ C)) @ E))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ C)) @ E)))) <= (zero_zero_int != E)))) <= (is_int @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2800_zadd1__lemma)). 120.83/55.31 thf(17392,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ D @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ F) @ G))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A) @ E) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ C)) @ E))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ C)) @ E)))) | (zero_zero_int = E)))) | ~ (is_int @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3597])). 120.83/55.31 thf(1892,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2485_div__dvd__div)). 120.83/55.31 thf(11525,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892])). 120.83/55.31 thf(4920,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => (((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4525_zcong__cancel)). 120.83/55.31 thf(22367,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => (((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4920])). 120.83/55.31 thf(1320,axiom,((! [A:$i,B:$i]: ((((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) <= (B != zero_zero_nat)) & ((B = zero_zero_nat) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = one_on1684967323de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1834_realpow__num__eq__if)). 120.83/55.31 thf(9483,plain,((! [A:$i,B:$i]: ((((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) | (B = zero_zero_nat)) & ((B = zero_zero_nat) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = one_on1684967323de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320])). 120.83/55.31 thf(2583,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != B) & (A = zero_zero_complex)) <=> (zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1293_power__eq__0__iff)). 120.83/55.31 thf(13903,plain,((! [A:$i,B:$i]: (((~ (zero_zero_nat = B) & (A = zero_zero_complex)) => (zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B))) & ((zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) => (~ (zero_zero_nat = B) & (A = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2583])). 120.83/55.31 thf(1514,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ C))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_int_complex @ number528085621omplex @ C))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_int_complex @ number528085621omplex @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_left__distrib__number__of)). 120.83/55.31 thf(10140,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ C))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ (hAPP_int_complex @ number528085621omplex @ C))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_int_complex @ number528085621omplex @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514])). 120.83/55.31 thf(1460,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4307_gcd__semilattice__nat_Oinf_Oleft__idem)). 120.83/55.31 thf(9967,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460])). 120.83/55.31 thf(4672,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (B = A))) <= ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_power2__eq__imp__eq)). 120.83/55.31 thf(21484,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (B = A))) | ~ ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4672])). 120.83/55.31 thf(3323,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4334_gcd__mult__distrib__nat)). 120.83/55.31 thf(16500,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3323])). 120.83/55.31 thf(2474,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2381_mod__mult__left__eq)). 120.83/55.31 thf(13531,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2474])). 120.83/55.31 thf(2458,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)) => (? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3413_lemma__interval__lt)). 120.83/55.31 thf(13482,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)) => (? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2458])). 120.83/55.31 thf(186,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2208_le__iff__diff__le__0)). 120.83/55.31 thf(5556,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 120.83/55.31 thf(3815,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.31 thf(18167,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ one_one_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3815])). 120.83/55.31 thf(2199,axiom,((! [A:$i]: ((((hAPP_nat_real @ real_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_real @ number267125858f_real @ A)) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_nat_real @ real_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_real) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3700_real__of__nat__number__of)). 120.83/55.31 thf(12547,plain,((! [A:$i]: ((((hAPP_nat_real @ real_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_real @ number267125858f_real @ A)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & (((hAPP_nat_real @ real_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_real) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199])). 120.83/55.31 thf(1376,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1412_power__le__imp__le__exp)). 120.83/55.31 thf(9670,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376])). 120.83/55.31 thf(4837,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4281_fact__gt__zero__int)). 120.83/55.31 thf(22103,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4837])). 120.83/55.31 thf(1420,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2181_add__neg__neg)). 120.83/55.31 thf(9835,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420])). 120.83/55.31 thf(1248,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2932_of__nat__less__imp__less)). 120.83/55.31 thf(9224,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248])). 120.83/55.31 thf(331,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (log @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3864_Log_Olog__def)). 120.83/55.31 thf(6048,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (log @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 120.83/55.31 thf(4222,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1348_mult__right__less__imp__less)). 120.83/55.31 thf(19715,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4222])). 120.83/55.31 thf(336,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.31 thf(6061,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 120.83/55.31 thf(4881,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3031_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J)). 120.83/55.31 thf(22244,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4881])). 120.83/55.31 thf(2440,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1379_mult__le__cancel__left__neg)). 120.83/55.31 thf(13417,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2440])). 120.83/55.31 thf(4642,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ A)) @ (big_co1548731110nt_int @ cOMBI_int @ B)) @ C)) <= (hBOOL @ (hAPP_f1469637905l_bool @ (hAPP_P1681069257l_bool @ member308914164t_bool @ (hAPP_f538843494t_bool @ (hAPP_f1418982953t_bool @ produc713279741t_bool @ A) @ B)) @ (bijR_int_int @ (zcongm @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5155_bijzcong__zcong__prod)). 120.83/55.31 thf(21388,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ A)) @ (big_co1548731110nt_int @ cOMBI_int @ B)) @ C)) | ~ (hBOOL @ (hAPP_f1469637905l_bool @ (hAPP_P1681069257l_bool @ member308914164t_bool @ (hAPP_f538843494t_bool @ (hAPP_f1418982953t_bool @ produc713279741t_bool @ A) @ B)) @ (bijR_int_int @ (zcongm @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4642])). 120.83/55.31 thf(659,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (expi @ A)) @ (expi @ B)) = (expi @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4000_expi__add)). 120.83/55.31 thf(7158,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (expi @ A)) @ (expi @ B)) = (expi @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])). 120.83/55.31 thf(3449,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2043_add__less__imp__less__right)). 120.83/55.31 thf(16900,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3449])). 120.83/55.31 thf(771,axiom,((! [A:$i]: (((A = zero_z126310315umeral) => (zero_zero_int = (code_int_of @ A))) & ((A != zero_z126310315umeral) => (((zero_z126310315umeral != (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((code_int_of @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (code_int_of @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (code_int_of @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (code_int_of @ A)) <= ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_z126310315umeral))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2806_Code__Numeral_Oint__of__code)). 120.83/55.31 thf(7546,plain,((! [A:$i]: (((A = zero_z126310315umeral) => (zero_zero_int = (code_int_of @ A))) & ((~ (A = zero_z126310315umeral)) => (((~ (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((code_int_of @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (code_int_of @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (code_int_of @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (code_int_of @ A)) | ~ ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ (hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_z126310315umeral))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 120.83/55.31 thf(3906,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2740_nat__le__eq__zle)). 120.83/55.31 thf(18516,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3906])). 120.83/55.31 thf(1018,axiom,((! [A:$i]: (A = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_power__one__right)). 120.83/55.31 thf(8436,plain,((! [A:$i]: (A = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018])). 120.83/55.31 thf(907,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3896_real__root__Suc__0)). 120.83/55.31 thf(8042,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])). 120.83/55.31 thf(3615,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4980_dvd__gcd__D2__int)). 120.83/55.31 thf(17448,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3615])). 120.83/55.31 thf(463,axiom,((! [A:$i]: (is_int @ (archim856651990g_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Oceiling_000tc__RealDef__Oreal)). 120.83/55.31 thf(6478,plain,((! [A:$i]: (is_int @ (archim856651990g_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 120.83/55.31 thf(3214,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3469_pi__half__ge__zero)). 120.83/55.31 thf(16133,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3214])). 120.83/55.31 thf(3335,axiom,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1226_zero__less__one)). 120.83/55.31 thf(16542,plain,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3335])). 120.83/55.31 thf(4354,axiom,((min != pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_rel__simps_I37_J)). 120.83/55.31 thf(20228,plain,((~ (min = pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4354])). 120.83/55.31 thf(1276,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4252_less__eq__code__int__def)). 120.83/55.31 thf(9344,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276])). 120.83/55.31 thf(2075,axiom,((is_int @ pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OPls)). 120.83/55.31 thf(12082,plain,((is_int @ pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075])). 120.83/55.31 thf(2081,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1331_mult__less__imp__less__left)). 120.83/55.31 thf(12096,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081])). 120.83/55.31 thf(3391,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1998_add__le__imp__le__right)). 120.83/55.31 thf(16718,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3391])). 120.83/55.31 thf(542,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ real_nat @ (natceiling @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3656_real__natceiling__ge)). 120.83/55.31 thf(6742,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_nat_real @ real_nat @ (natceiling @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])). 120.83/55.31 thf(1023,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_mult__less__cancel__left__neg)). 120.83/55.31 thf(8452,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023])). 120.83/55.31 thf(971,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3932_real__root__pos__mult__exp)). 120.83/55.31 thf(8276,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])). 120.83/55.31 thf(3397,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_power2__sum)). 120.83/55.31 thf(16735,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3397])). 120.83/55.31 thf(4181,axiom,((! [A:$i]: ((is_int @ A) => (((((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) != A) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))) <= (A != (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_prime__g__5)). 120.83/55.31 thf(19555,plain,((! [A:$i]: ((is_int @ A) => (((~ ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))) | (A = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4181])). 120.83/55.31 thf(3445,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = B) <=> (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C)))) <= (zero_zero_nat != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2643_dvd__div__eq__mult)). 120.83/55.31 thf(16883,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) => ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = B) => (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) & ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C) = B)))) | (zero_zero_nat = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3445])). 120.83/55.31 thf(2216,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_mult__pos__pos)). 120.83/55.31 thf(12604,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216])). 120.83/55.31 thf(1945,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.31 thf(11686,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945])). 120.83/55.31 thf(490,axiom,((! [A:$i]: ((zero_zero_nat = A) <=> ((hAPP_nat_real @ real_nat @ A) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3645_real__of__nat__zero__iff)). 120.83/55.31 thf(6572,plain,((! [A:$i]: (((zero_zero_nat = A) => ((hAPP_nat_real @ real_nat @ A) = zero_zero_real)) & (((hAPP_nat_real @ real_nat @ A) = zero_zero_real) => (zero_zero_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 120.83/55.31 thf(2573,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1187_mult__pos__pos)). 120.83/55.31 thf(13871,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2573])). 120.83/55.31 thf(603,axiom,((! [A:$i]: ((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & (A = (hAPP_real_real @ tan @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3625_tan__total__pi4)). 120.83/55.31 thf(6942,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & (A = (hAPP_real_real @ tan @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])). 120.83/55.31 thf(1613,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ zero_z891286103de_int) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.31 thf(10532,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ zero_z891286103de_int) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613])). 120.83/55.31 thf(2393,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3763_odd__pos)). 120.83/55.31 thf(13240,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393])). 120.83/55.31 thf(874,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1810_add__diff__add)). 120.83/55.31 thf(7933,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ B) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])). 120.83/55.31 thf(828,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3900_odd__real__root__pow)). 120.83/55.31 thf(7783,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])). 120.83/55.31 thf(1589,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))) <=> (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1585_nat__neq__iff)). 120.83/55.31 thf(10429,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))) => (~ (B = A))) & ((~ (B = A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589])). 120.83/55.31 thf(1593,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1643_trans__le__add1)). 120.83/55.31 thf(10448,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593])). 120.83/55.31 thf(219,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2445_mod__mod__cancel)). 120.83/55.31 thf(5671,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 120.83/55.31 thf(4713,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zmult__commute)). 120.83/55.31 thf(21664,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4713])). 120.83/55.31 thf(3235,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) <= ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4963_invertible__coprime__int)). 120.83/55.31 thf(16226,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) | ~ ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3235])). 120.83/55.31 thf(3024,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4302_gcd__exp__nat)). 120.83/55.31 thf(15460,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3024])). 120.83/55.31 thf(2886,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3729_sin__cos__squared__add2)). 120.83/55.31 thf(14989,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2886])). 120.83/55.31 thf(1277,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B) = A) <= (zero_zero_int != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2541_div__mult__self1__is__id)). 120.83/55.31 thf(9349,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ B) = A) | (zero_zero_int = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277])). 120.83/55.31 thf(1781,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4170_prime__divprod)). 120.83/55.31 thf(11127,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781])). 120.83/55.31 thf(794,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (? [C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3953_le__Suc__ex)). 120.83/55.31 thf(7643,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (? [C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])). 120.83/55.31 thf(4193,axiom,((! [A:$i]: ((hAPP_int_int @ pred @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4040_pred__Bit1)). 120.83/55.31 thf(19606,plain,((! [A:$i]: ((hAPP_int_int @ pred @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4193])). 120.83/55.31 thf(4365,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = B) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4509_zgcd__zmult__eq__self)). 120.83/55.31 thf(20260,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = B) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4365])). 120.83/55.31 thf(1284,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4312_gcd__semilattice__nat_Oinf__assoc)). 120.83/55.31 thf(9375,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284])). 120.83/55.31 thf(1310,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_power2__sum)). 120.83/55.31 thf(9454,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310])). 120.83/55.31 thf(596,axiom,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ A) = (archim856651990g_real @ (hAPP_nat_real @ real_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4363_ceiling__real__of__nat)). 120.83/55.31 thf(6920,plain,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ A) = (archim856651990g_real @ (hAPP_nat_real @ real_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 120.83/55.31 thf(1092,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((B != A) & (C != D)) <=> ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ A)) != (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_crossproduct__noteq)). 120.83/55.31 thf(8715,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (B = A) & ~ (C = D)) => (~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B))))) & ((~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)))) => (~ (B = A) & ~ (C = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092])). 120.83/55.31 thf(85,axiom,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ tan @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3596_tan__minus)). 120.83/55.31 thf(5244,plain,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ tan @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 120.83/55.31 thf(2114,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B)) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_combine__common__factor)). 120.83/55.31 thf(12214,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)) @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114])). 120.83/55.31 thf(1429,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2564_dvd__div__mult)). 120.83/55.31 thf(9867,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429])). 120.83/55.31 thf(1120,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4444_number__of__le__real__of__int__iff2)). 120.83/55.31 thf(8799,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120])). 120.83/55.31 thf(3161,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat) <=> (! [C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) <=> (C = (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4372_coprime__Suc__0__nat)). 120.83/55.31 thf(15929,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat) => (! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) => (C = (hAPP_nat_nat @ suc @ zero_zero_nat))) & ((C = (hAPP_nat_nat @ suc @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))))))) & ((! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) => (C = (hAPP_nat_nat @ suc @ zero_zero_nat))) & ((C = (hAPP_nat_nat @ suc @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3161])). 120.83/55.31 thf(2118,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.31 thf(12227,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118])). 120.83/55.31 thf(174,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi))) = (hAPP_real_real @ tan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3691_tan__periodic__nat)). 120.83/55.31 thf(5520,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi))) = (hAPP_real_real @ tan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 120.83/55.31 thf(2635,axiom,((! [A:$i,B:$i]: (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_complex) <=> ((zero_zero_complex = A) & ((hAPP_int_nat @ number_number_of_nat @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_power__eq__0__iff__number__of)). 120.83/55.31 thf(14119,plain,((! [A:$i,B:$i]: ((((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_complex) => ((zero_zero_complex = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat))) & (((zero_zero_complex = A) & ~ ((hAPP_int_nat @ number_number_of_nat @ B) = zero_zero_nat)) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2635])). 120.83/55.31 thf(865,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_mult__nonneg__nonneg)). 120.83/55.31 thf(7907,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[865])). 120.83/55.31 thf(452,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_complex_real @ re @ (cis @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4146_Re__cis)). 120.83/55.31 thf(6443,plain,((! [A:$i]: ((hAPP_real_real @ cos @ A) = (hAPP_complex_real @ re @ (cis @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 120.83/55.31 thf(2981,axiom,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_power__even__eq)). 120.83/55.31 thf(15316,plain,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2981])). 120.83/55.31 thf(3020,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (A = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_power2__eq__imp__eq)). 120.83/55.31 thf(15452,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (A = B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3020])). 120.83/55.31 thf(846,axiom,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ inverse_inverse_real @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3855_real__inv__sqrt__pow2)). 120.83/55.31 thf(7837,plain,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ inverse_inverse_real @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[846])). 120.83/55.31 thf(3919,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1882_add__neg__nonpos)). 120.83/55.31 thf(18551,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3919])). 120.83/55.31 thf(3966,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ A) @ B) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Nat__Onat_000tc__Int__Oint_U)). 120.83/55.31 thf(18708,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_nat_fun_int_int @ (hAPP_f2105620693nt_int @ cOMBC_int_nat_int @ A) @ B) @ C) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3966])). 120.83/55.31 thf(4691,axiom,((! [A:$i]: (((? [B:$i]: ((is_int @ B) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int) = A))) <=> (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3243_odd__equiv__def)). 120.83/55.31 thf(21548,plain,((! [A:$i]: ((((? [B:$i]: ((is_int @ B) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int) = A))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (? [B:$i]: ((is_int @ B) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) @ one_one_int) = A))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4691])). 120.83/55.31 thf(1172,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3214_of__nat__less__two__power)). 120.83/55.31 thf(8970,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172])). 120.83/55.31 thf(3758,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((one_one_int != (hAPP_int_int @ (inv @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2129_inv__not__1)). 120.83/55.31 thf(17971,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (~ (one_one_int = (hAPP_int_int @ (inv @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3758])). 120.83/55.31 thf(3262,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((B != A) & (C != D)) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ A)) != (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_crossproduct__noteq)). 120.83/55.31 thf(16306,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (B = A) & ~ (C = D)) => (~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))))) & ((~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)))) => (~ (B = A) & ~ (C = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3262])). 120.83/55.31 thf(2346,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B)) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_combine__common__factor)). 120.83/55.31 thf(13064,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346])). 120.83/55.31 thf(4166,axiom,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_int)) => (zero_zero_int = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_even__power__le__0__imp__0)). 120.83/55.31 thf(19506,plain,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_int)) => (zero_zero_int = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4166])). 120.83/55.31 thf(468,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3502_arctan__bounded)). 120.83/55.31 thf(6500,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 120.83/55.31 thf(3663,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (nat_tsub @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3188_tsub__eq)). 120.83/55.31 thf(17643,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (nat_tsub @ B) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3663])). 120.83/55.31 thf(1949,axiom,((! [A:$i]: (((min = (hAPP_int_int @ bit1 @ A)) <=> (A = min)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_rel__simps_I47_J)). 120.83/55.31 thf(11697,plain,((! [A:$i]: ((((min = (hAPP_int_int @ bit1 @ A)) => (A = min)) & ((A = min) => (min = (hAPP_int_int @ bit1 @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949])). 120.83/55.31 thf(2007,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1358_mult__le__less__imp__less)). 120.83/55.31 thf(11878,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007])). 120.83/55.31 thf(4278,axiom,((hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_p)). 120.83/55.31 thf(19945,plain,((hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4278])). 120.83/55.31 thf(726,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4696_number__of__real__code)). 120.83/55.31 thf(7379,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ A) = (ratreal @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 120.83/55.31 thf(1404,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3045_zdvd__int)). 120.83/55.31 thf(9771,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404])). 120.83/55.31 thf(373,axiom,((! [A:$i]: (((zero_zero_real != (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ tan @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ tan @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))) <= ((hAPP_real_real @ cos @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3594_tan__double)). 120.83/55.31 thf(6197,plain,((! [A:$i]: (((~ (zero_zero_real = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ tan @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ tan @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))) | ((hAPP_real_real @ cos @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 120.83/55.31 thf(349,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3616_tan__monotone)). 120.83/55.31 thf(6112,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 120.83/55.31 thf(4865,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_dvd__power__le)). 120.83/55.31 thf(22195,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4865])). 120.83/55.31 thf(3263,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_mult__left__mono)). 120.83/55.31 thf(16317,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3263])). 120.83/55.31 thf(4510,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: (((! [E:$i]: (((! [F:$i]: (((D != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B))) <= (is_int @ F))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C)))) <= (is_int @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))))) <= (is_int @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5090_aset_I8_J)). 120.83/55.31 thf(20833,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: (((! [E:$i]: (! [F:$i]: (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) | ~ (is_int @ F)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) | ~ (is_int @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))))) | ~ (is_int @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4510])). 120.83/55.31 thf(2710,axiom,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_lessThan_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_n1699378549t_bool @ ord_atMost_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5187_lessThan__Suc__atMost)). 120.83/55.31 thf(14379,plain,((! [A:$i]: ((hAPP_n1699378549t_bool @ ord_lessThan_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_n1699378549t_bool @ ord_atMost_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2710])). 120.83/55.31 thf(739,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4298_gcd__dvd2__nat)). 120.83/55.31 thf(7438,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 120.83/55.31 thf(712,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4342_gcd__red__nat)). 120.83/55.31 thf(7328,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])). 120.83/55.31 thf(2826,axiom,((! [A:$i,B:$i]: (((A = one_one_nat) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1572_dvd__mult__cancel1)). 120.83/55.31 thf(14788,plain,((! [A:$i,B:$i]: ((((A = one_one_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ B)) => (A = one_one_nat))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2826])). 120.83/55.31 thf(1727,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_mult__neg__pos)). 120.83/55.31 thf(10898,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727])). 120.83/55.31 thf(3696,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2921_of__nat__less__0__iff)). 120.83/55.31 thf(17754,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3696])). 120.83/55.31 thf(4419,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3152_zmult__zless__mono2__lemma)). 120.83/55.31 thf(20482,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4419])). 120.83/55.31 thf(3779,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i]: (((! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: ((is_int @ G) => ((E != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)))))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D)) @ A))))) <= (is_int @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5105_aset_I9_J)). 120.83/55.31 thf(18045,plain,((! [A:$i,B:$i,C:$i,D:$i]: (! [E:$i]: (((! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: ((is_int @ G) => (~ (E = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)))))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D)) @ A))))) | ~ (is_int @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3779])). 120.83/55.31 thf(1959,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (natfloor @ B)) @ (natfloor @ A))) @ (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3403_le__mult__natfloor)). 120.83/55.31 thf(11735,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (natfloor @ B)) @ (natfloor @ A))) @ (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959])). 120.83/55.31 thf(2480,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ one_one_complex) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__special_I3_J)). 120.83/55.31 thf(13546,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ one_one_complex) = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2480])). 120.83/55.31 thf(945,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1591_nat__add__commute)). 120.83/55.31 thf(8171,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[945])). 120.83/55.31 thf(1623,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__numeral__1__right)). 120.83/55.31 thf(10564,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623])). 120.83/55.31 thf(4036,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ d22set @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2265_d22set__le__swap)). 120.83/55.31 thf(18966,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ d22set @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4036])). 120.83/55.31 thf(4170,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5147_transfer__int__nat__factorial__closure)). 120.83/55.31 thf(19520,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ fact_fact_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4170])). 120.83/55.31 thf(2150,axiom,((~ (hBOOL @ (hAPP_nat_bool @ prime @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4163_prime__0)). 120.83/55.31 thf(12354,plain,((~ (hBOOL @ (hAPP_nat_bool @ prime @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150])). 120.83/55.31 thf(2775,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1339_mult__left__less__imp__less)). 120.83/55.31 thf(14595,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2775])). 120.83/55.31 thf(1958,axiom,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_number__of__Pls)). 120.83/55.31 thf(11733,plain,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958])). 120.83/55.31 thf(2830,axiom,((one_one_complex != zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_one__neq__zero)). 120.83/55.31 thf(14803,plain,((~ (one_one_complex = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2830])). 120.83/55.31 thf(1844,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1967_add_Ocomm__neutral)). 120.83/55.31 thf(11355,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844])). 120.83/55.31 thf(1559,axiom,((! [A:$i]: ((one_one_nat != A) <=> (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2314_gcd__lcm__complete__lattice__nat_Obot__less)). 120.83/55.31 thf(10316,plain,((! [A:$i]: (((~ (one_one_nat = A)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))) & ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A))) => (~ (one_one_nat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559])). 120.83/55.31 thf(4855,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2447_mod__mod__cancel)). 120.83/55.31 thf(22170,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4855])). 120.83/55.31 thf(1784,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2060_add__strict__right__mono)). 120.83/55.31 thf(11134,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784])). 120.83/55.31 thf(981,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1325_mult__right__le__imp__le)). 120.83/55.31 thf(8313,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])). 120.83/55.31 thf(4401,axiom,(((hAPP_n546711566l_real @ root @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = sqrt)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3939_sqrt__def)). 120.83/55.31 thf(20407,plain,(((hAPP_n546711566l_real @ root @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = sqrt)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4401])). 120.83/55.31 thf(3964,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ D) @ B) = one_one_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ A) = one_one_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4972_coprime__divisors__nat)). 120.83/55.31 thf(18702,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ D) @ B) = one_one_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ A) = one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3964])). 120.83/55.31 thf(4309,axiom,((~ (hBOOL @ (trivial_limit_nat @ sequentially)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5116_trivial__limit__sequentially)). 120.83/55.31 thf(20048,plain,((~ (hBOOL @ (trivial_limit_nat @ sequentially)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4309])). 120.83/55.31 thf(2125,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ real_int @ A)) @ B) = (hAPP_int_real @ real_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4390_power__real__of__int)). 120.83/55.31 thf(12263,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ real_int @ A)) @ B) = (hAPP_int_real @ real_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125])). 120.83/55.31 thf(622,axiom,((! [A:$i,B:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2349_mod__div__equality)). 120.83/55.31 thf(7001,plain,((! [A:$i,B:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])). 120.83/55.31 thf(4714,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_semiring__mult__number__of)). 120.83/55.31 thf(21667,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4714])). 120.83/55.31 thf(2743,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4727_one__le__Fract__iff)). 120.83/55.31 thf(14471,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ one_one_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2743])). 120.83/55.31 thf(3721,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4502_zgcd__zadd__zmult)). 120.83/55.31 thf(17841,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ B) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3721])). 120.83/55.31 thf(3926,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2508_mod__mult__self2)). 120.83/55.31 thf(18570,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3926])). 120.83/55.31 thf(201,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C))) <= (! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B)))) <= (D != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3892_DERIV__const__ratio__const)). 120.83/55.31 thf(5610,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C))) | ~ (! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B))) | (D = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 120.83/55.31 thf(2442,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ suc @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3137_diff__Suc__diff__eq1)). 120.83/55.31 thf(13422,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ suc @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442])). 120.83/55.31 thf(722,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3843_exp__less__one__iff)). 120.83/55.31 thf(7360,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])). 120.83/55.31 thf(2696,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2842_of__nat__Suc)). 120.83/55.31 thf(14322,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2696])). 120.83/55.31 thf(4914,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1414_power__increasing__iff)). 120.83/55.31 thf(22350,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4914])). 120.83/55.31 thf(401,axiom,(((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3586_cos__45)). 120.83/55.31 thf(6289,plain,(((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 120.83/55.31 thf(1033,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1625_not__add__less2)). 120.83/55.31 thf(8485,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033])). 120.83/55.31 thf(1555,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3140_mod__mult__self4)). 120.83/55.31 thf(10296,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555])). 120.83/55.31 thf(4722,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3517_zminus__zadd__distrib)). 120.83/55.31 thf(21699,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4722])). 120.83/55.31 thf(2820,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2304_mult__right_Odiff)). 120.83/55.31 thf(14767,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2820])). 120.83/55.31 thf(4180,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3522_zdiv__zminus2)). 120.83/55.31 thf(19552,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4180])). 120.83/55.31 thf(1040,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4725_Fract__le__zero__iff)). 120.83/55.31 thf(8502,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ zero_zero_rat)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040])). 120.83/55.31 thf(747,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_power2__eq__square__number__of)). 120.83/55.31 thf(7470,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 120.83/55.31 thf(1502,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.31 thf(10098,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502])). 120.83/55.31 thf(792,axiom,((! [A:$i]: ((one_one_nat = A) <=> (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1951_one__reorient)). 120.83/55.31 thf(7632,plain,((! [A:$i]: (((one_one_nat = A) => (A = one_one_nat)) & ((A = one_one_nat) => (one_one_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 120.83/55.31 thf(499,axiom,((! [A:$i]: ((archim1246769320r_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_int_real @ real_int @ A))) = (hAPP_int_int @ uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4428_floor__minus__real__of__int)). 120.83/55.31 thf(6604,plain,((! [A:$i]: ((archim1246769320r_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_int_real @ real_int @ A))) = (hAPP_int_int @ uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 120.83/55.31 thf(3021,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_le__imp__power__dvd)). 120.83/55.31 thf(15455,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3021])). 120.83/55.31 thf(129,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.31 thf(5381,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 120.83/55.31 thf(260,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & ((hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A)) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3624_arccos)). 120.83/55.31 thf(5795,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & ((hAPP_real_real @ cos @ (hAPP_real_real @ arccos @ A)) = A) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 120.83/55.31 thf(4536,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_int_bool @ A @ B)) | (hBOOL @ (hAPP_f448129468l_bool @ fEx_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_fEx_000tc__Int__Oint_U)). 120.83/55.31 thf(20943,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_int_bool @ A @ B)) | (hBOOL @ (hAPP_f448129468l_bool @ fEx_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4536])). 120.83/55.31 thf(4338,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ C))) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2846_zless__iff__Suc__zadd)). 120.83/55.31 thf(20179,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ C))) = B))) & ((? [C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ C))) = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4338])). 120.83/55.31 thf(4748,axiom,((! [A:$i,B:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (B = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_power2__eq__imp__eq)). 120.83/55.31 thf(21810,plain,((! [A:$i,B:$i]: (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4748])). 120.83/55.31 thf(1894,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1321_mult__left__le__imp__le)). 120.83/55.31 thf(11531,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894])). 120.83/55.31 thf(4165,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hAPP_int_int @ (legacy_zgcd @ A) @ C) = one_one_int) => (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ A) @ B)) @ (rsetR @ C))))) <= (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ B) @ (rsetR @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4788_RsetR__zmult__mono)). 120.83/55.31 thf(19503,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hAPP_int_int @ (legacy_zgcd @ A) @ C) = one_one_int) => (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ A) @ B)) @ (rsetR @ C))))) | ~ (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ B) @ (rsetR @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4165])). 120.83/55.31 thf(4318,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096)). 120.83/55.31 thf(20083,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4318])). 120.83/55.31 thf(1118,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3039_zadd__int)). 120.83/55.31 thf(8794,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118])). 120.83/55.31 thf(4940,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) <=> (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2589_dvd__eq__mod__eq__0__number__of)). 120.83/55.31 thf(22439,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)))) & ((zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4940])). 120.83/55.31 thf(757,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3238_even__prod__div__2)). 120.83/55.31 thf(7502,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])). 120.83/55.31 thf(1867,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.31 thf(11438,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867])). 120.83/55.31 thf(3076,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1991_add__0__left)). 120.83/55.31 thf(15654,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3076])). 120.83/55.31 thf(4361,axiom,((! [A:$i]: (((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_nat) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2771_mod__exhaust__less__4)). 120.83/55.31 thf(20250,plain,((! [A:$i]: (((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_nat) | ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4361])). 120.83/55.31 thf(4840,axiom,((! [A:$i]: ((quickcheck_nat_of @ A) = (hAPP_int_nat @ nat @ (quickcheck_int_of @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4269_nat__of__def)). 120.83/55.31 thf(22120,plain,((! [A:$i]: ((quickcheck_nat_of @ A) = (hAPP_int_nat @ nat @ (quickcheck_int_of @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4840])). 120.83/55.31 thf(2268,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_one__neq__zero)). 120.83/55.31 thf(12780,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268])). 120.83/55.31 thf(2762,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2313_gcd__lcm__complete__lattice__nat_Obot__least)). 120.83/55.31 thf(14555,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2762])). 120.83/55.31 thf(1437,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2325_mod__mod__trivial)). 120.83/55.31 thf(9890,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437])). 120.83/55.31 thf(1912,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3316_real__sqrt__less__mono)). 120.83/55.31 thf(11586,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912])). 120.83/55.31 thf(2850,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) => ((A != B) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_order__le__neq__implies__less)). 120.83/55.31 thf(14865,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) => ((~ (A = B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2850])). 120.83/55.31 thf(1832,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5003_Fract__coprime)). 120.83/55.31 thf(11306,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832])). 120.83/55.31 thf(1663,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.31 thf(10696,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663])). 120.83/55.31 thf(457,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_dvd__mult__left)). 120.83/55.31 thf(6460,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 120.83/55.31 thf(1858,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1278_one__le__power)). 120.83/55.31 thf(11406,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858])). 120.83/55.31 thf(816,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2063_add__strict__right__mono)). 120.83/55.31 thf(7731,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 120.83/55.31 thf(3883,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_q__neg__lemma)). 120.83/55.31 thf(18414,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3883])). 120.83/55.31 thf(3208,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)) @ A) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_power3__eq__cube)). 120.83/55.31 thf(16107,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)) @ A) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3208])). 120.83/55.31 thf(93,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3633_real__of__nat__ge__zero)). 120.83/55.31 thf(5267,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 120.83/55.31 thf(3186,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4182_prime__nd__one)). 120.83/55.31 thf(16025,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3186])). 120.83/55.31 thf(2784,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_mult__le__0__iff)). 120.83/55.31 thf(14632,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2784])). 120.83/55.31 thf(4418,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_zadd__zmult__distrib)). 120.83/55.31 thf(20479,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4418])). 120.83/55.31 thf(3686,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_mult__less__cancel__left__pos)). 120.83/55.31 thf(17725,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3686])). 120.83/55.31 thf(1056,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_real @ number267125858f_real @ B) = (hAPP_int_real @ number267125858f_real @ A)) <=> (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_eq__number__of)). 120.83/55.31 thf(8556,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((hAPP_int_real @ number267125858f_real @ B) = (hAPP_int_real @ number267125858f_real @ A)) => (B = A)) & ((B = A) => ((hAPP_int_real @ number267125858f_real @ B) = (hAPP_int_real @ number267125858f_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056])). 120.83/55.31 thf(4026,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.31 thf(18931,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4026])). 120.83/55.31 thf(1548,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) <=> (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1618_le__0__eq)). 120.83/55.31 thf(10265,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (zero_zero_nat = A)) & ((zero_zero_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548])). 120.83/55.31 thf(1771,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = zero_zero_nat) <=> ((B != zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1290_power__eq__0__iff)). 120.83/55.31 thf(11078,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = zero_zero_nat) => (~ (B = zero_zero_nat) & (A = zero_zero_nat))) & ((~ (B = zero_zero_nat) & (A = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771])). 120.83/55.31 thf(188,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D)) => ((A = B) <=> (D = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1958_diff__eq__diff__eq)). 120.83/55.31 thf(5563,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ D)) => (((A = B) => (D = C)) & ((D = C) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 120.83/55.31 thf(3921,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ B)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_zprime__power__zdvd__cancel__left)). 120.83/55.31 thf(18558,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ D) @ A)) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3921])). 120.83/55.31 thf(2666,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ E) @ B)) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ D)) <= ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ D))) <= ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ E) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2404_mod__mult__cong)). 120.83/55.31 thf(14223,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ E) @ B)) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ D)) | ~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ D)) | ~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ E) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2666])). 120.83/55.31 thf(3563,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1320_mult__left__le__imp__le)). 120.83/55.31 thf(17263,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3563])). 120.83/55.31 thf(1594,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.31 thf(10450,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594])). 120.83/55.31 thf(50,axiom,(((hAPP_complex_complex @ invers1449016382omplex @ ii) = (hAPP_complex_complex @ uminus473333897omplex @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3979_inverse__i)). 120.83/55.31 thf(5114,plain,(((hAPP_complex_complex @ invers1449016382omplex @ ii) = (hAPP_complex_complex @ uminus473333897omplex @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 120.83/55.31 thf(552,axiom,((! [A:$i,B:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2676_mod__div__decomp)). 120.83/55.31 thf(6769,plain,((! [A:$i,B:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 120.83/55.31 thf(3248,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1798_realpow__minus__mult)). 120.83/55.31 thf(16263,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3248])). 120.83/55.31 thf(1650,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_dvdI)). 120.83/55.31 thf(10645,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ A)) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650])). 120.83/55.31 thf(3795,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ E))) <= (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ E)))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2783_negDivAlg_Opinduct)). 120.83/55.31 thf(18105,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ E))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ negDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3795])). 120.83/55.31 thf(3298,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1357_mult__le__less__imp__less)). 120.83/55.31 thf(16422,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3298])). 120.83/55.31 thf(2700,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2569_div__mult__swap)). 120.83/55.31 thf(14337,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2700])). 120.83/55.31 thf(1242,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) @ C)) <= (C != zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2627_div__mult__self2)). 120.83/55.31 thf(9206,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) @ C)) | (C = zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242])). 120.83/55.31 thf(1096,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_zero__neq__one)). 120.83/55.31 thf(8735,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096])). 120.83/55.31 thf(343,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3360_real__0__le__divide__iff)). 120.83/55.31 thf(6087,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 120.83/55.31 thf(266,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4464_real__of__int__div2)). 120.83/55.31 thf(5816,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 120.83/55.31 thf(4267,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ abs_abs_int @ B)) @ (hAPP_int_int @ abs_abs_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3430_abs__div)). 120.83/55.31 thf(19898,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ abs_abs_int @ B)) @ (hAPP_int_int @ abs_abs_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4267])). 120.83/55.31 thf(1426,axiom,((! [A:$i,B:$i]: ((B != A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1589_less__not__refl3)). 120.83/55.31 thf(9857,plain,((! [A:$i,B:$i]: (~ (B = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426])). 120.83/55.31 thf(4148,axiom,((! [A:$i]: ((one_one_int = (hAPP_int_int @ abs_abs_int @ A)) <=> ((hAPP_int_int @ (legacy_zgcd @ zero_zero_int) @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4519_zgcd__0__1__iff)). 120.83/55.31 thf(19449,plain,((! [A:$i]: (((one_one_int = (hAPP_int_int @ abs_abs_int @ A)) => ((hAPP_int_int @ (legacy_zgcd @ zero_zero_int) @ A) = one_one_int)) & (((hAPP_int_int @ (legacy_zgcd @ zero_zero_int) @ A) = one_one_int) => (one_one_int = (hAPP_int_int @ abs_abs_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4148])). 120.83/55.31 thf(4315,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) <=> ((hAPP_int_int @ (div_mod_int @ B) @ C) = (hAPP_int_int @ (div_mod_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2616_zcong__zmod__eq)). 120.83/55.31 thf(20068,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => ((hAPP_int_int @ (div_mod_int @ B) @ C) = (hAPP_int_int @ (div_mod_int @ A) @ C))) & (((hAPP_int_int @ (div_mod_int @ B) @ C) = (hAPP_int_int @ (div_mod_int @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4315])). 120.83/55.31 thf(4192,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((A != B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_zless__le)). 120.83/55.31 thf(19599,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((~ (A = B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (~ (A = B) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4192])). 120.83/55.31 thf(4473,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_fun_int_int @ (hAPP_f1935805932nt_int @ (hAPP_f125788821nt_int @ cOMBB_859312247nt_nat @ A) @ B) @ C) = (hAPP_int_fun_int_int @ A @ (hAPP_nat_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_001)). 120.83/55.31 thf(20696,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_fun_int_int @ (hAPP_f1935805932nt_int @ (hAPP_f125788821nt_int @ cOMBB_859312247nt_nat @ A) @ B) @ C) = (hAPP_int_fun_int_int @ A @ (hAPP_nat_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4473])). 120.83/55.31 thf(2342,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.31 thf(13050,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ D)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342])). 120.83/55.31 thf(3592,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3768_real__of__nat__fact__gt__zero)). 120.83/55.31 thf(17379,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3592])). 120.83/55.31 thf(4424,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2602_div__nonneg__neg__le0)). 120.83/55.31 thf(20497,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4424])). 120.83/55.31 thf(292,axiom,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ zero_z891286103de_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2375_mod__0)). 120.83/55.31 thf(5920,plain,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ zero_z891286103de_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 120.83/55.31 thf(2842,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.31 thf(14839,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2842])). 120.83/55.31 thf(3066,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3835_not__exp__less__zero)). 120.83/55.31 thf(15626,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3066])). 120.83/55.31 thf(694,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3933_real__root__pos2)). 120.83/55.31 thf(7275,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])). 120.83/55.31 thf(4011,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3531_not__int__zless__negative)). 120.83/55.31 thf(18876,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4011])). 120.83/55.31 thf(2589,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_not__sum__squares__lt__zero)). 120.83/55.31 thf(13930,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2589])). 120.83/55.31 thf(1572,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ one_one_rat)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1825_real__squared__diff__one__factored)). 120.83/55.31 thf(10375,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ one_one_rat)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572])). 120.83/55.31 thf(1923,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_le__special_I3_J)). 120.83/55.31 thf(11623,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923])). 120.83/55.31 thf(4941,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2591_StandardRes__ubound)). 120.83/55.31 thf(22446,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4941])). 120.83/55.31 thf(4872,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4973_coprime__exp__int)). 120.83/55.31 thf(22212,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4872])). 120.83/55.31 thf(4215,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zEven)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2897_EvenOdd_Oeven__plus__even)). 120.83/55.31 thf(19691,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zEven)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4215])). 120.83/55.31 thf(1544,axiom,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ zero_z891286103de_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_mult__zero__left)). 120.83/55.31 thf(10253,plain,((! [A:$i]: (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ zero_z891286103de_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544])). 120.83/55.31 thf(1699,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B)) @ D) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_combine__common__factor)). 120.83/55.31 thf(10810,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B)) @ D) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699])). 120.83/55.31 thf(939,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.31 thf(8156,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[939])). 120.83/55.31 thf(2608,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = C) => (? [D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2786_mod__eqD)). 120.83/55.31 thf(14016,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = C) => (? [D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2608])). 120.83/55.31 thf(284,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (rcis @ A @ B)) @ (rcis @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4265_rcis__divide)). 120.83/55.31 thf(5894,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (rcis @ A @ B)) @ (rcis @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 120.83/55.31 thf(1980,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_mult__neg__neg)). 120.83/55.31 thf(11796,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980])). 120.83/55.31 thf(2182,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1486_one__less__power)). 120.83/55.31 thf(12477,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182])). 120.83/55.31 thf(2707,axiom,((! [A:$i,B:$i,C:$i]: (((A = zero_zero_rat) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1265_dvd__mult__cancel__left)). 120.83/55.31 thf(14365,plain,((! [A:$i,B:$i,C:$i]: ((((A = zero_zero_rat) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((A = zero_zero_rat) | (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2707])). 120.83/55.31 thf(2692,axiom,((! [A:$i,B:$i]: ((frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4645_Frct__code__post_I6_J)). 120.83/55.31 thf(14311,plain,((! [A:$i,B:$i]: ((frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2692])). 120.83/55.31 thf(1206,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_left__distrib__number__of)). 120.83/55.31 thf(9079,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206])). 120.83/55.31 thf(2064,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2692_div__mult2__eq)). 120.83/55.31 thf(12049,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064])). 120.83/55.31 thf(3458,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.31 thf(16926,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3458])). 120.83/55.31 thf(3038,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2958_of__nat__add)). 120.83/55.31 thf(15497,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3038])). 120.83/55.31 thf(2439,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B))) <=> (~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_le__number__of__eq__not__less)). 120.83/55.31 thf(13412,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B))) => (~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A))))) & ((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ B)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_i1732201573de_int @ number1226105091de_int @ A)) @ (hAPP_i1732201573de_int @ number1226105091de_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439])). 120.83/55.31 thf(2567,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.31 thf(13856,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567])). 120.83/55.31 thf(3271,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1762_diff__is__0__eq_H)). 120.83/55.31 thf(16338,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3271])). 120.83/55.31 thf(2013,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3708_sin__gt__zero)). 120.83/55.31 thf(11893,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013])). 120.83/55.31 thf(3012,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = zero_zero_int) <=> ((A = zero_zero_int) & (B = zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4490_zgcd0)). 120.83/55.31 thf(15420,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((((hAPP_int_int @ (legacy_zgcd @ A) @ B) = zero_zero_int) => ((A = zero_zero_int) & (B = zero_zero_int))) & (((A = zero_zero_int) & (B = zero_zero_int)) => ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3012])). 120.83/55.31 thf(1418,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_mult__mono_H)). 120.83/55.31 thf(9830,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) => (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418])). 120.83/55.31 thf(775,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_dvd__0__left)). 120.83/55.31 thf(7566,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])). 120.83/55.31 thf(2063,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3766_even__nat__def)). 120.83/55.31 thf(12044,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ semiri1621563631at_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063])). 120.83/55.31 thf(1644,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2572_div__mult__swap)). 120.83/55.31 thf(10628,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644])). 120.83/55.31 thf(618,axiom,((! [A:$i]: (((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ cos @ A)) = one_one_real) <= (zero_zero_real = (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3681_sin__zero__abs__cos__one)). 120.83/55.31 thf(6989,plain,((! [A:$i]: (((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ cos @ A)) = one_one_real) | ~ (zero_zero_real = (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 120.83/55.31 thf(1853,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C))) <= (zero_zero_nat != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2625_div__mult__self2)). 120.83/55.31 thf(11392,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C))) | (zero_zero_nat = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853])). 120.83/55.31 thf(2205,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4448_int__le__real__less)). 120.83/55.31 thf(12572,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ B)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205])). 120.83/55.31 thf(4586,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) => (B = zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1458_Int2_Ozcong__zero)). 120.83/55.31 thf(21190,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) => (B = zero_zero_int))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4586])). 120.83/55.31 thf(2401,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2350_div__mod__equality2)). 120.83/55.31 thf(13272,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401])). 120.83/55.31 thf(1798,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2505_mod__mult__self1)). 120.83/55.31 thf(11188,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798])). 120.83/55.31 thf(150,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3503_arctan__lbound)). 120.83/55.31 thf(5439,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arctan @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 120.83/55.31 thf(4119,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_power2__le__imp__le)). 120.83/55.31 thf(19357,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4119])). 120.83/55.31 thf(2194,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_real = (hAPP_int_real @ real_int @ A)) <=> (zero_zero_int = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4387_real__of__int__zero__cancel)). 120.83/55.31 thf(12528,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_real = (hAPP_int_real @ real_int @ A)) => (zero_zero_int = A)) & ((zero_zero_int = A) => (zero_zero_real = (hAPP_int_real @ real_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194])). 120.83/55.31 thf(2322,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ one_one_int) = (hAPP_nat_rat @ semiri151668891at_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4676_of__nat__rat)). 120.83/55.31 thf(12973,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ one_one_int) = (hAPP_nat_rat @ semiri151668891at_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322])). 120.83/55.31 thf(614,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4101_Im_Odiff)). 120.83/55.31 thf(6974,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 120.83/55.31 thf(805,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2682_div__add1__eq)). 120.83/55.31 thf(7685,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 120.83/55.31 thf(4157,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hAPP_P1175774780nt_int @ product_snd_int_int @ (posDivAlg @ B @ A)) = (hAPP_int_int @ (div_mod_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4235_mod__pos__pos)). 120.83/55.31 thf(19483,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hAPP_P1175774780nt_int @ product_snd_int_int @ (posDivAlg @ B @ A)) = (hAPP_int_int @ (div_mod_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4157])). 120.83/55.31 thf(3241,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3845_exp__ge__add__one__self)). 120.83/55.31 thf(16241,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3241])). 120.83/55.31 thf(4254,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ sRStar @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3363_SRStar__finite)). 120.83/55.31 thf(19848,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ sRStar @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4254])). 120.83/55.31 thf(13,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ A)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3996_i__complex__of__real)). 120.83/55.31 thf(4985,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ A)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 120.83/55.31 thf(4241,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ A)) <=> (! [B:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => ((B = A) | (one_one_int = B)))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_zprime__def)). 120.83/55.31 thf(19785,plain,((! [A:$i]: ((((hBOOL @ (hAPP_int_bool @ zprime @ A)) => (! [B:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => ((B = A) | (one_one_int = B)))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)))) & ((! [B:$i]: ((is_int @ B) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => ((B = A) | (one_one_int = B)))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))) => (hBOOL @ (hAPP_int_bool @ zprime @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4241])). 120.83/55.31 thf(4633,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1215_not__one__le__zero)). 120.83/55.31 thf(21346,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4633])). 120.83/55.31 thf(2638,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mult__2)). 120.83/55.31 thf(14137,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2638])). 120.83/55.31 thf(4679,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) @ E)) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_convex__bound__lt)). 120.83/55.31 thf(21508,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) @ E)) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4679])). 120.83/55.31 thf(1961,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2378_mod__mult__right__eq)). 120.83/55.31 thf(11746,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961])). 120.83/55.31 thf(2540,axiom,((! [A:$i,B:$i]: (((B = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1830_realpow__num__eq__if)). 120.83/55.31 thf(13766,plain,((! [A:$i,B:$i]: (((B = zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2540])). 120.83/55.31 thf(1689,axiom,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_semiring__numeral__0__eq__0)). 120.83/55.31 thf(10778,plain,(((hAPP_int_real @ number267125858f_real @ pls) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689])). 120.83/55.31 thf(3844,axiom,((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2881_even__zero__int)). 120.83/55.31 thf(18270,plain,((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3844])). 120.83/55.31 thf(3741,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2011_add__left__mono)). 120.83/55.31 thf(17914,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3741])). 120.83/55.31 thf(4544,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((B = A) <=> (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2080_eq__iff__diff__eq__0)). 120.83/55.31 thf(21010,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((B = A) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) & ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4544])). 120.83/55.31 thf(3936,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_t__l__p)). 120.83/55.31 thf(18612,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ t) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3936])). 120.83/55.31 thf(4200,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_fun_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ A) @ B) @ C) = (hAPP_int_fun_int_int @ A @ (hAPP_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J)). 120.83/55.31 thf(19634,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_fun_int_int @ (hAPP_f1760145644nt_int @ (hAPP_f1629352853nt_int @ cOMBB_1496585939nt_int @ A) @ B) @ C) = (hAPP_int_fun_int_int @ A @ (hAPP_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4200])). 120.83/55.31 thf(887,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_mult__nonneg__nonpos2)). 120.83/55.31 thf(7978,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])). 120.83/55.31 thf(1400,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2032_add__le__cancel__right)). 120.83/55.31 thf(9756,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B)))) & ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400])). 120.83/55.31 thf(1713,axiom,((! [A:$i,B:$i]: ((zero_zero_nat != B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2629_div__add__self1)). 120.83/55.31 thf(10847,plain,((! [A:$i,B:$i]: ((~ (zero_zero_nat = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713])). 120.83/55.31 thf(3451,axiom,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ sqrt @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3402_real__sqrt__abs)). 120.83/55.31 thf(16905,plain,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ sqrt @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3451])). 120.83/55.31 thf(3165,axiom,((! [A:$i,B:$i]: ((((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_semiring__mult__number__of)). 120.83/55.31 thf(15961,plain,((! [A:$i,B:$i]: (((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3165])). 120.83/55.31 thf(1335,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.31 thf(9553,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335])). 120.83/55.31 thf(1533,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3068_mult__Suc__right)). 120.83/55.31 thf(10219,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533])). 120.83/55.31 thf(1890,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3771_odd__nat__plus__one__div__two)). 120.83/55.31 thf(11519,plain,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890])). 120.83/55.31 thf(133,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_zero__le__square)). 120.83/55.31 thf(5392,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 120.83/55.31 thf(3059,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) <=> (! [C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) <=> (one_one_nat = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4028_coprime)). 120.83/55.31 thf(15575,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (one_one_nat = C)) & ((one_one_nat = C) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))))))) & ((! [C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (one_one_nat = C)) & ((one_one_nat = C) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3059])). 120.83/55.31 thf(797,axiom,((! [A:$i,B:$i]: (((A = zero_zero_rat) & (B = zero_zero_rat)) <=> (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_sum__squares__eq__zero__iff)). 120.83/55.31 thf(7654,plain,((! [A:$i,B:$i]: ((((A = zero_zero_rat) & (B = zero_zero_rat)) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B)))) & ((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) => ((A = zero_zero_rat) & (B = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 120.83/55.31 thf(4070,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_zadd__power2)). 120.83/55.31 thf(19157,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4070])). 120.83/55.31 thf(2225,axiom,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)) @ (hAPP_int_rat @ number_number_of_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_double__number__of__Bit0)). 120.83/55.31 thf(12631,plain,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ A)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)) @ (hAPP_int_rat @ number_number_of_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225])). 120.83/55.31 thf(3598,axiom,(((quotient_of @ zero_zero_rat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4663_rat__zero__code)). 120.83/55.31 thf(17396,plain,(((quotient_of @ zero_zero_rat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3598])). 120.83/55.31 thf(999,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3746_sin__arccos__lemma1)). 120.83/55.31 thf(8372,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])). 120.83/55.31 thf(447,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4705_real__times__code)). 120.83/55.31 thf(6429,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 120.83/55.31 thf(1183,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A)) <=> (! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4614_nat__set__def)). 120.83/55.31 thf(8998,plain,((! [A:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A)) => (! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))) & ((! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))) => (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183])). 120.83/55.31 thf(778,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) = one_one_nat) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = B) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = A))) <= (zero_zero_nat != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4373_gcd__coprime__exists__nat)). 120.83/55.31 thf(7575,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) = one_one_nat) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = B) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) = A)) | (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])). 120.83/55.31 thf(3557,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2911_of__nat__0__le__iff)). 120.83/55.31 thf(17248,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3557])). 120.83/55.31 thf(4859,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1378_mult__le__cancel__left__neg)). 120.83/55.31 thf(22180,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4859])). 120.83/55.31 thf(3781,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_zcong__zmult)). 120.83/55.31 thf(18057,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ D) @ E)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3781])). 120.83/55.31 thf(904,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ zero_z891286103de_int)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_mult__pos__neg2)). 120.83/55.31 thf(8032,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ zero_z891286103de_int)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[904])). 120.83/55.31 thf(3891,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_less__special_I3_J)). 120.83/55.31 thf(18448,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3891])). 120.83/55.31 thf(4333,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_rel__simps_I10_J)). 120.83/55.31 thf(20164,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4333])). 120.83/55.31 thf(1911,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (zero_zero_nat != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3233_lemma__Suc__Suc__4n__diff__2)). 120.83/55.31 thf(11583,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911])). 120.83/55.31 thf(4018,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_bin__less__0__simps_I1_J)). 120.83/55.31 thf(18895,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4018])). 120.83/55.31 thf(1925,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1446_power__less__imp__less__exp)). 120.83/55.31 thf(11630,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925])). 120.83/55.31 thf(3220,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) <= (zero_zero_nat != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2534_div__mult__mult1)). 120.83/55.31 thf(16162,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) | (zero_zero_nat = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3220])). 120.83/55.31 thf(1523,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_sum__power2__ge__zero)). 120.83/55.31 thf(10172,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523])). 120.83/55.31 thf(2049,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_mult__strict__right__mono)). 120.83/55.31 thf(12000,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049])). 120.83/55.31 thf(563,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.31 thf(6802,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 120.83/55.31 thf(3759,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) <=> ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) & (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5000_coprime__mul__eq__int)). 120.83/55.31 thf(17974,plain,((! [A:$i,B:$i,C:$i]: (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) & (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))) & (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) & (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) => (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3759])). 120.83/55.31 thf(4234,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((hBOOL @ (hAPP_f448129468l_bool @ (resSet @ C) @ (image_int_int @ A @ B))) <= (! [D:$i]: ((is_int @ D) => ((! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ A @ D)) @ (hAPP_int_int @ A @ E)) @ C)) => (D = E))) <= (is_int @ E))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ B)))))) <= (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4599_ResSet__image)). 120.83/55.31 thf(19747,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (resSet @ C) @ (image_int_int @ A @ B))) | ~ (! [D:$i]: ((is_int @ D) => (! [E:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ A @ D)) @ (hAPP_int_int @ A @ E)) @ C)) => (D = E))) | ~ (is_int @ E)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ D) @ B))))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (resSet @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4234])). 120.83/55.31 thf(3206,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ one_on1645066479umeral) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2501_mod__by__1)). 120.83/55.31 thf(16101,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ one_on1645066479umeral) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3206])). 120.83/55.31 thf(4314,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_le__nat__number__of)). 120.83/55.31 thf(20061,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4314])). 120.83/55.31 thf(3856,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ D))) @ D)) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ D))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2221_aux______1)). 120.83/55.31 thf(18326,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ D))) @ D)) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ D))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3856])). 120.83/55.31 thf(744,axiom,((! [A:$i,B:$i]: (((((B = zero_zero_nat) & (A = zero_zero_nat)) <=> (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2161_add__nonneg__eq__0__iff)). 120.83/55.31 thf(7450,plain,((! [A:$i,B:$i]: (((((B = zero_zero_nat) & (A = zero_zero_nat)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))) & ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) => ((B = zero_zero_nat) & (A = zero_zero_nat)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])). 120.83/55.31 thf(1204,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1244_zero__le__power)). 120.83/55.31 thf(9074,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204])). 120.83/55.31 thf(2244,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ C) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_power__mult)). 120.83/55.31 thf(12697,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ C) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2244])). 120.83/55.31 thf(1574,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <= (A != B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_order__le__neq__implies__less)). 120.83/55.31 thf(10380,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | (A = B) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574])). 120.83/55.31 thf(453,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ exp_real @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3846_exp__real__of__nat__mult)). 120.83/55.31 thf(6446,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ exp_real @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 120.83/55.31 thf(21,axiom,((! [A:$i,B:$i]: (((A = zero_zero_real) & (zero_zero_real = B)) <=> ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3957_Complex__eq__0)). 120.83/55.31 thf(5007,plain,((! [A:$i,B:$i]: ((((A = zero_zero_real) & (zero_zero_real = B)) => ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = zero_zero_complex)) & (((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = zero_zero_complex) => ((A = zero_zero_real) & (zero_zero_real = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 120.83/55.31 thf(3168,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4023_coprime__Suc0)). 120.83/55.31 thf(15968,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3168])). 120.83/55.31 thf(483,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ one_one_real) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1823_real__squared__diff__one__factored)). 120.83/55.31 thf(6553,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ one_one_real) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 120.83/55.31 thf(635,axiom,(((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3605_tan__60)). 120.83/55.31 thf(7066,plain,(((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 120.83/55.31 thf(2160,axiom,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) <= (~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2900_not__odd__impl__even)). 120.83/55.31 thf(12381,plain,((! [A:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) | (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160])). 120.83/55.31 thf(2074,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2444_dvd__mod__iff)). 120.83/55.31 thf(12079,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074])). 120.83/55.31 thf(3167,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4319_gcd__semilattice__nat_Oinf__greatest)). 120.83/55.31 thf(15966,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3167])). 120.83/55.32 thf(1470,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2109_mult__1__right)). 120.83/55.32 thf(10004,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470])). 120.83/55.32 thf(2348,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3493_real__0__less__add__iff)). 120.83/55.32 thf(13069,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348])). 120.83/55.32 thf(2459,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2006_add__mono)). 120.83/55.32 thf(13486,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459])). 120.83/55.32 thf(2916,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (ratreal @ A)) @ (ratreal @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4700_real__less__eq__code)). 120.83/55.32 thf(15094,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (ratreal @ A)) @ (ratreal @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (ratreal @ A)) @ (ratreal @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2916])). 120.83/55.32 thf(608,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) <= (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_split__mult__neg__le)). 120.83/55.32 thf(6956,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)) | ~ (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])). 120.83/55.32 thf(2129,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_mult__less__cancel__left__neg)). 120.83/55.32 thf(12274,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129])). 120.83/55.32 thf(2795,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2355_div__mod__equality)). 120.83/55.32 thf(14682,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2795])). 120.83/55.32 thf(2997,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ real_nat @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3671_real__of__nat__diff)). 120.83/55.32 thf(15378,plain,((! [A:$i,B:$i]: (((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_nat_real @ real_nat @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2997])). 120.83/55.32 thf(3385,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2568_dvd__div__mult__self)). 120.83/55.32 thf(16703,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3385])). 120.83/55.32 thf(1741,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3761_even__product__nat)). 120.83/55.32 thf(10970,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741])). 120.83/55.32 thf(3812,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3786_even__even__mod__4__iff)). 120.83/55.32 thf(18156,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3812])). 120.83/55.32 thf(2473,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1335_mult__less__imp__less__left)). 120.83/55.32 thf(13529,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2473])). 120.83/55.32 thf(1581,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ E) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C) = E) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1540_eq__add__iff1)). 120.83/55.32 thf(10402,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ E) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C) = E) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C) = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581])). 120.83/55.32 thf(896,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_mult__dvd__mono)). 120.83/55.32 thf(8007,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])). 120.83/55.32 thf(1431,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_dvd__refl)). 120.83/55.32 thf(9873,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431])). 120.83/55.32 thf(2571,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ B)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1386_mult__left__le__one__le)). 120.83/55.32 thf(13867,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571])). 120.83/55.32 thf(392,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_complex_real @ im @ A)))) @ ii)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4090_complex__diff__cnj)). 120.83/55.32 thf(6255,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_complex_real @ im @ A)))) @ ii)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 120.83/55.32 thf(2961,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1600_le__refl)). 120.83/55.32 thf(15233,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2961])). 120.83/55.32 thf(3649,axiom,((~ (! [A:$i]: ((is_int @ A) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_)). 120.83/55.32 thf(17576,plain,((~ (! [A:$i]: ((is_int @ A) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3649])). 120.83/55.32 thf(4440,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4527_zrelprime__zdvd__zmult__aux)). 120.83/55.32 thf(20558,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4440])). 120.83/55.32 thf(1654,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3454_ln__mult)). 120.83/55.32 thf(10660,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654])). 120.83/55.32 thf(784,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((B = A) <=> ((hAPP_real_real @ ln @ A) = (hAPP_real_real @ ln @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3428_ln__inj__iff)). 120.83/55.32 thf(7603,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((B = A) => ((hAPP_real_real @ ln @ A) = (hAPP_real_real @ ln @ B))) & (((hAPP_real_real @ ln @ A) = (hAPP_real_real @ ln @ B)) => (B = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 120.83/55.32 thf(3798,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2838_of__nat__Suc)). 120.83/55.32 thf(18121,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3798])). 120.83/55.32 thf(242,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2285_mult__left_Ozero)). 120.83/55.32 thf(5742,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 120.83/55.32 thf(2329,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) => ((A = (archim1246769320r_real @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4467_floor__eq2)). 120.83/55.32 thf(13010,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) => ((A = (archim1246769320r_real @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329])). 120.83/55.32 thf(4644,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ (hAPP_P230595783nt_int @ (hAPP_P941956607nt_int @ produc883642259nt_int @ A) @ B)) @ ratrel)) <=> ((zero_zero_int != (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))) & ((hAPP_P1175774780nt_int @ product_snd_int_int @ B) != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4666_ratrel__iff)). 120.83/55.32 thf(21392,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ (hAPP_P230595783nt_int @ (hAPP_P941956607nt_int @ produc883642259nt_int @ A) @ B)) @ ratrel)) => (~ (zero_zero_int = (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))) & ~ ((hAPP_P1175774780nt_int @ product_snd_int_int @ B) = zero_zero_int))) & ((~ (zero_zero_int = (hAPP_P1175774780nt_int @ product_snd_int_int @ A)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ A)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ A))) & ~ ((hAPP_P1175774780nt_int @ product_snd_int_int @ B) = zero_zero_int)) => (hBOOL @ (hAPP_f526364711l_bool @ (hAPP_P1062890741l_bool @ member2143287562nt_int @ (hAPP_P230595783nt_int @ (hAPP_P941956607nt_int @ produc883642259nt_int @ A) @ B)) @ ratrel)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4644])). 120.83/55.32 thf(2233,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2745_transfer__nat__int__relations_I4_J)). 120.83/55.32 thf(12655,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233])). 120.83/55.32 thf(3925,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3193_realpow__two__diff)). 120.83/55.32 thf(18567,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3925])). 120.83/55.32 thf(2146,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1742_less__imp__diff__less)). 120.83/55.32 thf(12336,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146])). 120.83/55.32 thf(2945,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)))) => ((hAPP_int_nat @ nat @ (archim1246769320r_real @ B)) = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4032_floor__eq3)). 120.83/55.32 thf(15188,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)))) => ((hAPP_int_nat @ nat @ (archim1246769320r_real @ B)) = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2945])). 120.83/55.32 thf(2488,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2944_of__nat__less__iff)). 120.83/55.32 thf(13578,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488])). 120.83/55.32 thf(1591,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3851_inv__real__of__nat__fact__gt__zero)). 120.83/55.32 thf(10444,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591])). 120.83/55.32 thf(4674,axiom,((! [A:$i]: ((is_int @ A) => ((? [B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) & (is_int @ B))) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3221_even__equiv__def)). 120.83/55.32 thf(21489,plain,((! [A:$i]: ((is_int @ A) => (((? [B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) & (is_int @ B))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (? [B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) & (is_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4674])). 120.83/55.32 thf(4470,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((B = A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zle__antisym)). 120.83/55.32 thf(20682,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((B = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4470])). 120.83/55.32 thf(3386,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_dvd__add)). 120.83/55.32 thf(16706,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3386])). 120.83/55.32 thf(296,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1782_real__mult__1)). 120.83/55.32 thf(5931,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 120.83/55.32 thf(933,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2292_mult_Oadd__right)). 120.83/55.32 thf(8131,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[933])). 120.83/55.32 thf(2755,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_power__mult__distrib)). 120.83/55.32 thf(14525,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2755])). 120.83/55.32 thf(2325,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2091_diff__0__right)). 120.83/55.32 thf(13000,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325])). 120.83/55.32 thf(3223,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A) = B) <= ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C) = A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3935_real__root__pos__unique)). 120.83/55.32 thf(16170,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A) = B) | ~ ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C) = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3223])). 120.83/55.32 thf(127,axiom,((! [A:$i,B:$i,C:$i]: ((zero_zero_real != C) => ((A = B) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1787_real__mult__right__cancel)). 120.83/55.32 thf(5372,plain,((! [A:$i,B:$i,C:$i]: ((~ (zero_zero_real = C)) => (((A = B) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 120.83/55.32 thf(454,axiom,((! [A:$i,B:$i]: ((hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ fFalse) @ A) @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_T)). 120.83/55.32 thf(6449,plain,((! [A:$i,B:$i]: ((hAPP_P1975530577nt_int @ (hAPP_P1145851913nt_int @ (hAPP_b40753821nt_int @ if_Pro1731782967nt_int @ fFalse) @ A) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 120.83/55.32 thf(4178,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_mult__pos__neg)). 120.83/55.32 thf(19548,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4178])). 120.83/55.32 thf(4283,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1661_power2__diff)). 120.83/55.32 thf(19957,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4283])). 120.83/55.32 thf(1064,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) <=> (((hBOOL @ (hAPP_nat_bool @ A @ B)) <= (C = zero_zero_nat)) & ((zero_zero_nat != C) => (! [D:$i,E:$i]: (((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E)) => (hBOOL @ (hAPP_nat_bool @ A @ E))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2735_split__mod)). 120.83/55.32 thf(8588,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) => (((hBOOL @ (hAPP_nat_bool @ A @ B)) | ~ (C = zero_zero_nat)) & ((~ (zero_zero_nat = C)) => (! [D:$i,E:$i]: (((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E)) => (hBOOL @ (hAPP_nat_bool @ A @ E))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C))))))) & ((((hBOOL @ (hAPP_nat_bool @ A @ B)) | ~ (C = zero_zero_nat)) & ((~ (zero_zero_nat = C)) => (! [D:$i,E:$i]: (((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) @ E)) => (hBOOL @ (hAPP_nat_bool @ A @ E))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C)))))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064])). 120.83/55.32 thf(3240,axiom,((! [A:$i]: (one_one_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4408_powr__zero__eq__one)). 120.83/55.32 thf(16238,plain,((! [A:$i]: (one_one_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3240])). 120.83/55.32 thf(501,axiom,((! [A:$i,B:$i]: (A = (hAPP_f957591787ol_nat @ (cOMBK_1643584600t_bool @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_)). 120.83/55.32 thf(6609,plain,((! [A:$i,B:$i]: (A = (hAPP_f957591787ol_nat @ (cOMBK_1643584600t_bool @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 120.83/55.32 thf(4134,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ C))) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2503_zmod__zmult2__eq)). 120.83/55.32 thf(19404,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ C))) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4134])). 120.83/55.32 thf(1557,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_zero__le__mult__iff)). 120.83/55.32 thf(10301,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557])). 120.83/55.32 thf(3097,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_semiring__mult__2__right)). 120.83/55.32 thf(15725,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3097])). 120.83/55.32 thf(2661,axiom,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ one_on1645066479umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1393_zero__less__two)). 120.83/55.32 thf(14207,plain,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ one_on1645066479umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2661])). 120.83/55.32 thf(1061,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2078_right__minus__eq)). 120.83/55.32 thf(8573,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex)) & (((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B) = zero_zero_complex) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061])). 120.83/55.32 thf(2195,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1671_mult__less__mono1)). 120.83/55.32 thf(12534,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195])). 120.83/55.32 thf(3114,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_n522471361de_int @ semiri1424489471de_int @ B) = (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2828_of__nat__eq__iff)). 120.83/55.32 thf(15782,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_n522471361de_int @ semiri1424489471de_int @ B) = (hAPP_n522471361de_int @ semiri1424489471de_int @ A))) & (((hAPP_n522471361de_int @ semiri1424489471de_int @ B) = (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3114])). 120.83/55.32 thf(1550,axiom,((zero_zero_rat = (hAPP_int_rat @ number_number_of_rat @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_semiring__norm_I112_J)). 120.83/55.32 thf(10275,plain,((zero_zero_rat = (hAPP_int_rat @ number_number_of_rat @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550])). 120.83/55.32 thf(3320,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_mult__dvd__mono)). 120.83/55.32 thf(16493,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3320])). 120.83/55.32 thf(4167,axiom,((! [A:$i,B:$i]: (((B = A) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ zero_zero_int))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_IntPrimes_Ozcong__zero)). 120.83/55.32 thf(19510,plain,((! [A:$i,B:$i]: ((((B = A) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ zero_zero_int)) => (B = A))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4167])). 120.83/55.32 thf(2854,axiom,((! [A:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2307_gcd__lcm__complete__lattice__nat_Onot__top__less)). 120.83/55.32 thf(14876,plain,((! [A:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2854])). 120.83/55.32 thf(979,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_mult__strict__left__mono__neg)). 120.83/55.32 thf(8308,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[979])). 120.83/55.32 thf(1267,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat))) <=> (zero_zero_nat != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2309_gcd__lcm__complete__lattice__nat_Oless__top)). 120.83/55.32 thf(9294,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat))) => (~ (zero_zero_nat = A))) & ((~ (zero_zero_nat = A)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267])). 120.83/55.32 thf(4248,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5129_is__nat__def)). 120.83/55.32 thf(19825,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4248])). 120.83/55.32 thf(1476,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1334_mult__less__imp__less__left)). 120.83/55.32 thf(10020,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476])). 120.83/55.32 thf(1618,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_int_nat @ number_number_of_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3208_Suc__mod__eq__add3__mod__number__of)). 120.83/55.32 thf(10549,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_int_nat @ number_number_of_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618])). 120.83/55.32 thf(1607,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2200_add__le__less__mono)). 120.83/55.32 thf(10514,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607])). 120.83/55.32 thf(2983,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ sqrt @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3319_real__sqrt__power)). 120.83/55.32 thf(15326,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ sqrt @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2983])). 120.83/55.32 thf(2722,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2302_mult_Odiff__left)). 120.83/55.32 thf(14412,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2722])). 120.83/55.32 thf(2236,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ D))) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2736_mod__lemma)). 120.83/55.32 thf(12672,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ D))) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236])). 120.83/55.32 thf(4742,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1354_mult__le__less__imp__less)). 120.83/55.32 thf(21776,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4742])). 120.83/55.32 thf(2077,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ fequal_nat @ A) @ B)) | (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T)). 120.83/55.32 thf(12086,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ fequal_nat @ A) @ B)) | (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077])). 120.83/55.32 thf(1394,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3349_real__sqrt__sum__squares__mult__squared__eq)). 120.83/55.32 thf(9741,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394])). 120.83/55.32 thf(4478,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ one_one_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1473_power__strict__decreasing)). 120.83/55.32 thf(20717,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4478])). 120.83/55.32 thf(3859,axiom,(((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ min)))) => (one_one_int != (hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1503__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_)). 120.83/55.32 thf(18335,plain,(((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ min)))) => (~ (one_one_int = (hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3859])). 120.83/55.32 thf(4925,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2174_zero__le__double__add__iff__zero__le__single__add)). 120.83/55.32 thf(22387,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4925])). 120.83/55.32 thf(1970,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2141_add__nonpos__nonpos)). 120.83/55.32 thf(11775,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970])). 120.83/55.32 thf(4130,axiom,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t)). 120.83/55.32 thf(19389,plain,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4130])). 120.83/55.32 thf(1322,axiom,((! [A:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (~ (! [B:$i]: ((is_int @ B) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B) != A))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3248_zEvenE)). 120.83/55.32 thf(9492,plain,((! [A:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (~ (! [B:$i]: ((is_int @ B) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B) = A)))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322])). 120.83/55.32 thf(1691,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((zero_zero_real = (hAPP_real_real @ sqrt @ A)) => (zero_zero_real = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3322_real__sqrt__eq__zero__cancel)). 120.83/55.32 thf(10782,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((zero_zero_real = (hAPP_real_real @ sqrt @ A)) => (zero_zero_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691])). 120.83/55.32 thf(1463,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3807_fact__less__mono__nat)). 120.83/55.32 thf(9975,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463])). 120.83/55.32 thf(2152,axiom,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_number__of__add)). 120.83/55.32 thf(12358,plain,((! [A:$i,B:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152])). 120.83/55.32 thf(395,axiom,((! [A:$i]: ((~ (! [B:$i]: (A != (code_S1047413653umeral @ B)))) <= (A != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4091_code__numeral_Oexhaust)). 120.83/55.32 thf(6270,plain,((! [A:$i]: (~ (! [B:$i]: ~ (A = (code_S1047413653umeral @ B))) | (A = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 120.83/55.32 thf(2513,axiom,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ A) = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4641_Frct__code__post_I4_J)). 120.83/55.32 thf(13666,plain,((! [A:$i]: ((hAPP_int_rat @ number_number_of_rat @ A) = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513])). 120.83/55.32 thf(4257,axiom,((! [A:$i,B:$i]: ((zero_zero_int != (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) => ((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3533_zmod__zminus1__not__zero)). 120.83/55.32 thf(19866,plain,((! [A:$i,B:$i]: ((~ (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B))) => (~ ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4257])). 120.83/55.32 thf(1255,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1749_diff__le__mono2)). 120.83/55.32 thf(9249,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255])). 120.83/55.32 thf(4095,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4767_zpower__number__of__even)). 120.83/55.32 thf(19257,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4095])). 120.83/55.32 thf(380,axiom,((! [A:$i,B:$i]: ((rcis @ A @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (cis @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4266_rcis__def)). 120.83/55.32 thf(6223,plain,((! [A:$i,B:$i]: ((rcis @ A @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (cis @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 120.83/55.32 thf(1286,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2182_add__neg__neg)). 120.83/55.32 thf(9381,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286])). 120.83/55.32 thf(1817,axiom,((! [A:$i,B:$i]: ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) = (pdivmod @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3946_pdivmod__def)). 120.83/55.32 thf(11245,plain,((! [A:$i,B:$i]: ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))) = (pdivmod @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817])). 120.83/55.32 thf(4481,axiom,((one_on1684967323de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ one_on1684967323de_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_one__power2)). 120.83/55.32 thf(20731,plain,((one_on1684967323de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ one_on1684967323de_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4481])). 120.83/55.32 thf(4295,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ C) = one_one_int) <= ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4504_zgcd__1__power__left__distrib)). 120.83/55.32 thf(20000,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ C) = one_one_int) | ~ ((hAPP_int_int @ (legacy_zgcd @ B) @ C) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4295])). 120.83/55.32 thf(3134,axiom,((! [A:$i]: (((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_on1684967323de_int)) & (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_z891286103de_int) <= (zero_zero_nat != (hAPP_int_nat @ number_number_of_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_power__0__left__number__of)). 120.83/55.32 thf(15849,plain,((! [A:$i]: (((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_on1684967323de_int)) & (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_z891286103de_int) | (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3134])). 120.83/55.32 thf(2005,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1211_zero__le__one)). 120.83/55.32 thf(11874,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005])). 120.83/55.32 thf(1851,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ A))))) <=> (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3211_split__div__lemma)). 120.83/55.32 thf(11380,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ A))))) => (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) & ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ suc @ A))))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851])). 120.83/55.32 thf(2359,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3041_Nat__Transfer_Otransfer__int__nat__functions_I1_J)). 120.83/55.32 thf(13112,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359])). 120.83/55.32 thf(4585,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) != D)) <= (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))))) <= (is_int @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5093_aset_I7_J)). 120.83/55.32 thf(21183,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i]: (((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) = D))) | ~ (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))))) | ~ (is_int @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4585])). 120.83/55.32 thf(2052,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2394_mod__mult__mult2)). 120.83/55.32 thf(12006,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052])). 120.83/55.32 thf(4075,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ B) & (is_int @ C)) => (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int))))) => ((B != zero_zero_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = C))) <= (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2653_divmod__int__rel__div__eq)). 120.83/55.32 thf(19179,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ B) & (is_int @ C)) => (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ zero_zero_int))))) => ((~ (B = zero_zero_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = C))) | ~ (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4075])). 120.83/55.32 thf(567,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2085_diff__self)). 120.83/55.32 thf(6816,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])). 120.83/55.32 thf(3006,axiom,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3006_power__Suc2)). 120.83/55.32 thf(15405,plain,((! [A:$i,B:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3006])). 120.83/55.32 thf(1445,axiom,((! [A:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2826_number__of__int)). 120.83/55.32 thf(9916,plain,((! [A:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445])). 120.83/55.32 thf(3574,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_semiring__mult__2)). 120.83/55.32 thf(17313,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3574])). 120.83/55.32 thf(2157,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ zero_z891286103de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_mult__nonneg__nonpos2)). 120.83/55.32 thf(12373,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ zero_z891286103de_int))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157])). 120.83/55.32 thf(4163,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_mult__nonneg__nonpos2)). 120.83/55.32 thf(19499,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4163])). 120.83/55.32 thf(2686,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3452_ln__ge__zero__imp__ge__one)). 120.83/55.32 thf(14287,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2686])). 120.83/55.32 thf(4337,axiom,((! [A:$i,B:$i]: ((((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (div_mod_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4237_mod__pos__neg)). 120.83/55.32 thf(20176,plain,((! [A:$i,B:$i]: (((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A)))) = (hAPP_int_int @ (div_mod_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4337])). 120.83/55.32 thf(3743,axiom,((! [A:$i,B:$i,C:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (multInvPair @ B @ C) @ A)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3301_MultInvPair__card__two)). 120.83/55.32 thf(17921,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (multInvPair @ B @ C) @ A)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3743])). 120.83/55.32 thf(4168,axiom,(((hAPP_int_nat @ number_number_of_nat @ pls) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_nat__number__of__Pls)). 120.83/55.32 thf(19516,plain,(((hAPP_int_nat @ number_number_of_nat @ pls) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4168])). 120.83/55.32 thf(3124,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2497_mod__mult__self2__is__0)). 120.83/55.32 thf(15814,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3124])). 120.83/55.32 thf(3512,axiom,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_semiring__numeral__1__eq__1)). 120.83/55.32 thf(17102,plain,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3512])). 120.83/55.32 thf(3746,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D)) => (((hAPP_int_int @ (div_mod_int @ A) @ D) = (hAPP_int_int @ (div_mod_int @ B) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ B)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2405_mod__add__cong)). 120.83/55.32 thf(17940,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D)) => (((hAPP_int_int @ (div_mod_int @ A) @ D) = (hAPP_int_int @ (div_mod_int @ B) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ B)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3746])). 120.83/55.32 thf(2229,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1587_less__irrefl__nat)). 120.83/55.32 thf(12644,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229])). 120.83/55.32 thf(2908,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_mult__right__mono)). 120.83/55.32 thf(15063,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2908])). 120.83/55.32 thf(3056,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.32 thf(15566,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3056])). 120.83/55.32 thf(2976,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1863_add__nonneg__pos)). 120.83/55.32 thf(15291,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2976])). 120.83/55.32 thf(1973,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1346_mult__less__imp__less__right)). 120.83/55.32 thf(11781,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973])). 120.83/55.32 thf(1020,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3490_real__0__le__add__iff)). 120.83/55.32 thf(8441,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020])). 120.83/55.32 thf(1231,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2506_mod__mult__self1)). 120.83/55.32 thf(9165,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231])). 120.83/55.32 thf(4328,axiom,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_double__number__of__Bit0)). 120.83/55.32 thf(20154,plain,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4328])). 120.83/55.32 thf(1083,axiom,((! [A:$i,B:$i]: (((archim1246769320r_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (archim1246769320r_real @ B)) @ A)) <= ((hAPP_int_real @ real_int @ (archim1246769320r_real @ B)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4425_floor__power)). 120.83/55.32 thf(8676,plain,((! [A:$i,B:$i]: (((archim1246769320r_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (archim1246769320r_real @ B)) @ A)) | ~ ((hAPP_int_real @ real_int @ (archim1246769320r_real @ B)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083])). 120.83/55.32 thf(3840,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (legacy_zgcd @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) @ B) = one_one_int) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4811_Bnor__prod__zgcd)). 120.83/55.32 thf(18254,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (legacy_zgcd @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) @ B) = one_one_int) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3840])). 120.83/55.32 thf(1190,axiom,((! [A:$i]: ((one_one_nat = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4013_coprime__refl)). 120.83/55.32 thf(9033,plain,((! [A:$i]: (((one_one_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ A)) => (one_one_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190])). 120.83/55.32 thf(4820,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_less__eq__int__code_I14_J)). 120.83/55.32 thf(22040,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4820])). 120.83/55.32 thf(4,axiom,(((hAPP_complex_complex @ cnj @ ii) = (hAPP_complex_complex @ uminus473333897omplex @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4084_complex__cnj__i)). 120.83/55.32 thf(4954,plain,(((hAPP_complex_complex @ cnj @ ii) = (hAPP_complex_complex @ uminus473333897omplex @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 120.83/55.32 thf(3494,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_le__special_I1_J)). 120.83/55.32 thf(17051,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_int_rat @ number_number_of_rat @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3494])). 120.83/55.32 thf(2184,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4327_gcd__semilattice__nat_Ole__inf__iff)). 120.83/55.32 thf(12482,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184])). 120.83/55.32 thf(105,axiom,((! [A:$i]: (A = (hAPP_real_real @ tan @ (hAPP_real_real @ arctan @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3598_tan__arctan)). 120.83/55.32 thf(5299,plain,((! [A:$i]: (A = (hAPP_real_real @ tan @ (hAPP_real_real @ arctan @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 120.83/55.32 thf(4789,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_zcong__scalar2)). 120.83/55.32 thf(21938,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4789])). 120.83/55.32 thf(368,axiom,((! [A:$i]: (((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) & (A = (hAPP_real_real @ sin @ B)) & ! [C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (A = (hAPP_real_real @ sin @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ C))) => (B = C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3747_sin__total)). 120.83/55.32 thf(6180,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) & (A = (hAPP_real_real @ sin @ B)) & ! [C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (A = (hAPP_real_real @ sin @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ C))) => (B = C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 120.83/55.32 thf(4199,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.32 thf(19631,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4199])). 120.83/55.32 thf(2658,axiom,((! [A:$i]: (((A != zero_zero_nat) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ A) = zero_zero_rat)) & (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ A) = one_one_rat) <= (zero_zero_nat = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1438_power__0__left)). 120.83/55.32 thf(14194,plain,((! [A:$i]: (((~ (A = zero_zero_nat)) => ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ A) = zero_zero_rat)) & (((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ A) = one_one_rat) | ~ (zero_zero_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2658])). 120.83/55.32 thf(1447,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2961_of__nat__mult)). 120.83/55.32 thf(9921,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B)) = (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447])). 120.83/55.32 thf(2148,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4431_powr__mult)). 120.83/55.32 thf(12341,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148])). 120.83/55.32 thf(4047,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1817_mult__diff__mult)). 120.83/55.32 thf(19039,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4047])). 120.83/55.32 thf(137,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4383_powr__powr)). 120.83/55.32 thf(5403,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 120.83/55.32 thf(3438,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ B))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) & (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ A)) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3286_Suc__nat__number__of__add)). 120.83/55.32 thf(16860,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ B))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3438])). 120.83/55.32 thf(503,axiom,((! [A:$i]: ((A = zero_zero_nat) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3659_real__of__nat__le__zero__cancel__iff)). 120.83/55.32 thf(6614,plain,((! [A:$i]: (((A = zero_zero_nat) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ zero_zero_real)) => (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 120.83/55.32 thf(4830,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4964_gcd__non__0__int)). 120.83/55.32 thf(22084,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4830])). 120.83/55.32 thf(2417,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) <=> (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1933_add__right__cancel)). 120.83/55.32 thf(13330,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) => (A = C)) & ((A = C) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417])). 120.83/55.32 thf(975,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J)). 120.83/55.32 thf(8291,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[975])). 120.83/55.32 thf(2789,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1652_le__square)). 120.83/55.32 thf(14656,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2789])). 120.83/55.32 thf(225,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ (code_S1047413653umeral @ A)) @ one_on1645066479umeral) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4085_Suc__code__numeral__minus__one)). 120.83/55.32 thf(5693,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ minus_1690775515umeral @ (code_S1047413653umeral @ A)) @ one_on1645066479umeral) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 120.83/55.32 thf(3293,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3631_cos__pi__eq__zero)). 120.83/55.32 thf(16408,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3293])). 120.83/55.32 thf(1507,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_right__distrib__number__of)). 120.83/55.32 thf(10119,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507])). 120.83/55.32 thf(2989,axiom,((! [A:$i]: ((one_on1684967323de_int = A) <=> (A = one_on1684967323de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1955_one__reorient)). 120.83/55.32 thf(15340,plain,((! [A:$i]: (((one_on1684967323de_int = A) => (A = one_on1684967323de_int)) & ((A = one_on1684967323de_int) => (one_on1684967323de_int = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2989])). 120.83/55.32 thf(1294,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1448_power__less__imp__less__exp)). 120.83/55.32 thf(9398,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294])). 120.83/55.32 thf(168,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1545_right__diff__distrib__number__of)). 120.83/55.32 thf(5495,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 120.83/55.32 thf(2860,axiom,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1210_zero__le__one)). 120.83/55.32 thf(14898,plain,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2860])). 120.83/55.32 thf(1800,axiom,((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1219_not__one__le__zero)). 120.83/55.32 thf(11193,plain,((~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ one_on1684967323de_int) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800])). 120.83/55.32 thf(54,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = D) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ A))) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4215_divmod__nat__rel__unique)). 120.83/55.32 thf(5139,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((A = D) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ A)) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 120.83/55.32 thf(4597,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2323_pos__zmod__mult__2)). 120.83/55.32 thf(21230,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4597])). 120.83/55.32 thf(759,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((hAPP_nat_complex @ semiri2020571505omplex @ B) = (hAPP_nat_complex @ semiri2020571505omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2833_of__nat__eq__iff)). 120.83/55.32 thf(7507,plain,((! [A:$i,B:$i]: (((B = A) => ((hAPP_nat_complex @ semiri2020571505omplex @ B) = (hAPP_nat_complex @ semiri2020571505omplex @ A))) & (((hAPP_nat_complex @ semiri2020571505omplex @ B) = (hAPP_nat_complex @ semiri2020571505omplex @ A)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])). 120.83/55.32 thf(2874,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_dvd__triv__left)). 120.83/55.32 thf(14947,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2874])). 120.83/55.32 thf(4849,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4283_fact__mono__int__aux)). 120.83/55.32 thf(22152,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4849])). 120.83/55.32 thf(1180,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2438_mod__diff__eq)). 120.83/55.32 thf(8990,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180])). 120.83/55.32 thf(3735,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: (((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (D != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E))) <= (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) @ A)))) <= (is_int @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5091_bset_I6_J)). 120.83/55.32 thf(17896,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: (((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)))) | ~ (is_int @ F)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) @ A)))) | ~ (is_int @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3735])). 120.83/55.32 thf(466,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((E = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1541_eq__add__iff1)). 120.83/55.32 thf(6485,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((E = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) => (E = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 120.83/55.32 thf(378,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_mult__left__mono__neg)). 120.83/55.32 thf(6212,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 120.83/55.32 thf(860,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.32 thf(7884,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[860])). 120.83/55.32 thf(4442,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) = (big_co1548731110nt_int @ cOMBI_int @ (comple219730294t_bool @ (setS @ A @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4815_Union__SetS__setprod__prop2)). 120.83/55.32 thf(20564,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) = (big_co1548731110nt_int @ cOMBI_int @ (comple219730294t_bool @ (setS @ A @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4442])). 120.83/55.32 thf(745,axiom,((! [A:$i,B:$i]: (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) => (((hAPP_int_int @ number_number_of_int @ min) = A) | (A = one_one_int))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_pos__zmult__eq__1__iff__lemma)). 120.83/55.32 thf(7458,plain,((! [A:$i,B:$i]: (((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) => (((hAPP_int_int @ number_number_of_int @ min) = A) | (A = one_one_int))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 120.83/55.32 thf(1846,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4333_gcd__add1__nat)). 120.83/55.32 thf(11361,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846])). 120.83/55.32 thf(2617,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2877_diff__Suc__Suc)). 120.83/55.32 thf(14049,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2617])). 120.83/55.32 thf(1025,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => (((C != zero_zero_int) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C)))))) <= (D != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4718_le__rat)). 120.83/55.32 thf(8457,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => (((~ (C = zero_zero_int)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ C)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C)))))) | (D = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])). 120.83/55.32 thf(557,axiom,((! [A:$i,B:$i]: ((ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (ratreal @ A)) @ (ratreal @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4702_real__minus__code)). 120.83/55.32 thf(6785,plain,((! [A:$i,B:$i]: ((ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (ratreal @ A)) @ (ratreal @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])). 120.83/55.32 thf(3711,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ bit0 @ A)) @ B) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mult__Bit0)). 120.83/55.32 thf(17809,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ bit0 @ A)) @ B) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3711])). 120.83/55.32 thf(2107,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1362_mult__less__le__imp__less)). 120.83/55.32 thf(12192,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107])). 120.83/55.32 thf(1683,axiom,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_nat_nat @ suc @ A)) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2994_power__0__Suc)). 120.83/55.32 thf(10762,plain,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ (hAPP_nat_nat @ suc @ A)) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683])). 120.83/55.32 thf(3048,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1568_less__add__iff2)). 120.83/55.32 thf(15534,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3048])). 120.83/55.32 thf(1662,axiom,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => ((hAPP_int_int @ (standardRes @ B) @ A) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2702_StandardRes__SRStar__prop3)). 120.83/55.32 thf(10692,plain,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => ((hAPP_int_int @ (standardRes @ B) @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662])). 120.83/55.32 thf(2552,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_power__mult__distrib)). 120.83/55.32 thf(13806,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2552])). 120.83/55.32 thf(4782,axiom,((! [A:$i]: (((pls = (hAPP_int_int @ bit0 @ A)) <=> (A = pls)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_rel__simps_I38_J)). 120.83/55.32 thf(21918,plain,((! [A:$i]: ((((pls = (hAPP_int_int @ bit0 @ A)) => (A = pls)) & ((A = pls) => (pls = (hAPP_int_int @ bit0 @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4782])). 120.83/55.32 thf(575,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))) <=> ((A = C) | (D = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_crossproduct__eq)). 120.83/55.32 thf(6838,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))) => ((A = C) | (D = B))) & (((A = C) | (D = B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 120.83/55.32 thf(4128,axiom,((! [A:$i]: ((hAPP_int_int @ bit0 @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_Bit0__def)). 120.83/55.32 thf(19384,plain,((! [A:$i]: ((hAPP_int_int @ bit0 @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4128])). 120.83/55.32 thf(1217,axiom,((! [A:$i,B:$i]: (((zero_zero_real = B) & (zero_zero_real = A)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_sum__squares__eq__zero__iff)). 120.83/55.32 thf(9111,plain,((! [A:$i,B:$i]: ((((zero_zero_real = B) & (zero_zero_real = A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)) = zero_zero_real) => ((zero_zero_real = B) & (zero_zero_real = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217])). 120.83/55.32 thf(4183,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4524_zless__zprime__imp__zrelprime)). 120.83/55.32 thf(19563,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4183])). 120.83/55.32 thf(2511,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ D))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1377_mult__strict__mono)). 120.83/55.32 thf(13662,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ D)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2511])). 120.83/55.32 thf(1596,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1868_add__nonneg__pos)). 120.83/55.32 thf(10456,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596])). 120.83/55.32 thf(949,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2858_less__trans__Suc)). 120.83/55.32 thf(8180,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ B)) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])). 120.83/55.32 thf(1649,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1254_zero__less__power)). 120.83/55.32 thf(10643,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649])). 120.83/55.32 thf(1195,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_mult__pos__neg)). 120.83/55.32 thf(9054,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195])). 120.83/55.32 thf(2884,axiom,((! [A:$i,B:$i]: ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)) = (quotient_of @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4711_quotient__of__Fract)). 120.83/55.32 thf(14983,plain,((! [A:$i,B:$i]: ((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)) = (quotient_of @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2884])). 120.83/55.32 thf(578,axiom,((! [A:$i,B:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2675_mod__div__decomp)). 120.83/55.32 thf(6858,plain,((! [A:$i,B:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 120.83/55.32 thf(185,axiom,((! [A:$i,B:$i]: ((B = A) <=> ((image_nat_int @ semiri1621563631at_int @ B) = (image_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4602_transfer__nat__int__set__relations_I3_J)). 120.83/55.32 thf(5548,plain,((! [A:$i,B:$i]: (((B = A) => ((image_nat_int @ semiri1621563631at_int @ B) = (image_nat_int @ semiri1621563631at_int @ A))) & (((image_nat_int @ semiri1621563631at_int @ B) = (image_nat_int @ semiri1621563631at_int @ A)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 120.83/55.32 thf(1640,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1332_mult__less__imp__less__left)). 120.83/55.32 thf(10617,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640])). 120.83/55.32 thf(2090,axiom,((! [A:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) <= (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3774_even__nat__mod__two__eq__zero)). 120.83/55.32 thf(12120,plain,((! [A:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090])). 120.83/55.32 thf(2919,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.32 thf(15107,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2919])). 120.83/55.32 thf(4697,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3124_zless__nat__eq__int__zless)). 120.83/55.32 thf(21578,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4697])). 120.83/55.32 thf(2403,axiom,((! [A:$i,B:$i]: (((B = zero_zero_rat) | (zero_zero_rat = A)) <=> (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_mult__eq__0__iff)). 120.83/55.32 thf(13278,plain,((! [A:$i,B:$i]: ((((B = zero_zero_rat) | (zero_zero_rat = A)) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B))) & ((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) => ((B = zero_zero_rat) | (zero_zero_rat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403])). 120.83/55.32 thf(1165,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1234_power__mono)). 120.83/55.32 thf(8954,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165])). 120.83/55.32 thf(1584,axiom,((! [A:$i,B:$i]: ((((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)) = (divmod_nat @ A @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4206_divmod__nat__step)). 120.83/55.32 thf(10417,plain,((! [A:$i,B:$i]: (((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)) = (divmod_nat @ A @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584])). 120.83/55.32 thf(3216,axiom,((is_int @ m)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_m)). 120.83/55.32 thf(16143,plain,((is_int @ m)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3216])). 120.83/55.32 thf(4934,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4983_gcd__greatest__iff__int)). 120.83/55.32 thf(22414,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4934])). 120.83/55.32 thf(3476,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 120.83/55.32 thf(16991,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3476])). 120.83/55.32 thf(2370,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != B) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) & (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B) = one_one_int) <= (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1829_realpow__num__eq__if)). 120.83/55.32 thf(13144,plain,((! [A:$i,B:$i]: (((~ (zero_zero_nat = B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) & (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B) = one_one_int) | ~ (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370])). 120.83/55.32 thf(2858,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4629_finite__greaterThanLessThan__int)). 120.83/55.32 thf(14887,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2858])). 120.83/55.32 thf(1704,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_le__imp__power__dvd)). 120.83/55.32 thf(10824,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704])). 120.83/55.32 thf(1937,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.32 thf(11665,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937])). 120.83/55.32 thf(1233,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ C) @ A) @ B))) <= (~ (hBOOL @ C))) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ C) @ A) @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ A)) <= (hBOOL @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3255_int__if__cong)). 120.83/55.32 thf(9170,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_int @ semiri1621563631at_int @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ C) @ A) @ B))) | (hBOOL @ C)) & (((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ C) @ A) @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ A)) | ~ (hBOOL @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233])). 120.83/55.32 thf(3489,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3112_power__le__imp__le__base)). 120.83/55.32 thf(17038,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3489])). 120.83/55.32 thf(4917,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2324_pos__zdiv__mult__2)). 120.83/55.32 thf(22359,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4917])). 120.83/55.32 thf(4571,axiom,(((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ one_one_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_one__power2)). 120.83/55.32 thf(21141,plain,(((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ one_one_int) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4571])). 120.83/55.32 thf(3077,axiom,(((hAPP_nat_nat @ fact @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4565_fact_Osimps_I1_J)). 120.83/55.32 thf(15657,plain,(((hAPP_nat_nat @ fact @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3077])). 120.83/55.32 thf(1296,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2392_mod__mult__mult1)). 120.83/55.32 thf(9403,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296])). 120.83/55.32 thf(4016,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1313_zdvd__bounds)). 120.83/55.32 thf(18891,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4016])). 120.83/55.32 thf(615,axiom,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_real @ re @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4115_complex__Re__cnj)). 120.83/55.32 thf(6977,plain,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ cnj @ A)) = (hAPP_complex_real @ re @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])). 120.83/55.32 thf(3001,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2028_add__le__cancel__right)). 120.83/55.32 thf(15390,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3001])). 120.83/55.32 thf(2248,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3134_Suc__pred)). 120.83/55.32 thf(12708,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (A = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248])). 120.83/55.32 thf(4842,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_mult__neg__neg)). 120.83/55.32 thf(22125,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4842])). 120.83/55.32 thf(764,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_le__special_I2_J)). 120.83/55.32 thf(7526,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 120.83/55.32 thf(4879,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((negDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ A)) @ (negDivAlg @ one_one_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ A)))) = (negDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2321_negDivAlg__eqn__1__number__of)). 120.83/55.32 thf(22234,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))) => ((negDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))) & (((hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ A)) @ (negDivAlg @ one_one_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ A)))) = (negDivAlg @ one_one_int @ (hAPP_int_int @ number_number_of_int @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4879])). 120.83/55.32 thf(650,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3679_real__of__nat__gt__zero__cancel__iff)). 120.83/55.32 thf(7117,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ real_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])). 120.83/55.32 thf(1934,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2031_add__le__cancel__right)). 120.83/55.32 thf(11654,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934])). 120.83/55.32 thf(281,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2449_dvd__mod)). 120.83/55.32 thf(5886,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 120.83/55.32 thf(177,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3699_real__of__nat__div2)). 120.83/55.32 thf(5528,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B))) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 120.83/55.32 thf(2311,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1854_nat__le__add__iff1)). 120.83/55.32 thf(12941,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311])). 120.83/55.32 thf(518,axiom,((! [A:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ one_one_real)) = (hAPP_real_real @ tan @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3630_tan__half)). 120.83/55.32 thf(6672,plain,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ one_one_real)) = (hAPP_real_real @ tan @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])). 120.83/55.32 thf(2833,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2354_div__mod__equality)). 120.83/55.32 thf(14813,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2833])). 120.83/55.32 thf(2132,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2040_add__less__imp__less__right)). 120.83/55.32 thf(12288,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132])). 120.83/55.32 thf(701,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2102_mult_Ocomm__neutral)). 120.83/55.32 thf(7296,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 120.83/55.32 thf(279,axiom,(((of_real_complex @ (hAPP_real_real @ uminus_uminus_real @ one_one_real)) = (hAPP_complex_complex @ uminus473333897omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3997_complex__of__real__minus__one)). 120.83/55.32 thf(5881,plain,(((of_real_complex @ (hAPP_real_real @ uminus_uminus_real @ one_one_real)) = (hAPP_complex_complex @ uminus473333897omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 120.83/55.32 thf(397,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3439_ln__ge__zero)). 120.83/55.32 thf(6276,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ ln @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 120.83/55.32 thf(4549,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_power__commutes)). 120.83/55.32 thf(21031,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4549])). 120.83/55.32 thf(4403,axiom,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int) = A) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1962_add_Ocomm__neutral)). 120.83/55.32 thf(20423,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ zero_zero_int) = A) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4403])). 120.83/55.32 thf(3000,axiom,((! [A:$i,B:$i]: (((A != zero_zero_nat) | (B != zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4370_div__gcd__coprime__nat)). 120.83/55.32 thf(15385,plain,((! [A:$i,B:$i]: ((~ (A = zero_zero_nat) | ~ (B = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A))) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3000])). 120.83/55.32 thf(2410,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.32 thf(13310,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410])). 120.83/55.32 thf(1629,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (bseq_real @ (hAPP_r474017924t_real @ power_power_real @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4750_Bseq__realpow)). 120.83/55.32 thf(10589,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (bseq_real @ (hAPP_r474017924t_real @ power_power_real @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629])). 120.83/55.32 thf(1682,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.32 thf(10759,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682])). 120.83/55.32 thf(3916,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ (hAPP_i1948725293t_bool @ sRStar @ B))) <=> (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2764_StandardRes__SRStar__prop1)). 120.83/55.32 thf(18541,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ A)) @ (hAPP_i1948725293t_bool @ sRStar @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3916])). 120.83/55.32 thf(1339,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2700_div__less)). 120.83/55.32 thf(9563,plain,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339])). 120.83/55.32 thf(1305,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_power2__eq__square__number__of)). 120.83/55.32 thf(9430,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305])). 120.83/55.32 thf(2675,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2689_div__le__mono)). 120.83/55.32 thf(14250,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2675])). 120.83/55.32 thf(3376,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1522_zdiff__zmult__distrib)). 120.83/55.32 thf(16674,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3376])). 120.83/55.32 thf(1382,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_comm__mult__left__mono)). 120.83/55.32 thf(9695,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382])). 120.83/55.32 thf(2921,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2087_diff__self)). 120.83/55.32 thf(15112,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2921])). 120.83/55.32 thf(4596,axiom,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4045_pred__def)). 120.83/55.32 thf(21227,plain,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4596])). 120.83/55.32 thf(2416,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.32 thf(13327,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416])). 120.83/55.32 thf(1121,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1262_less__add__one)). 120.83/55.32 thf(8804,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121])). 120.83/55.32 thf(1720,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3023_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.32 thf(10867,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720])). 120.83/55.32 thf(2214,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_add__number__of__eq)). 120.83/55.32 thf(12599,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2214])). 120.83/55.32 thf(3203,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ pls)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_add__numeral__0__right)). 120.83/55.32 thf(16089,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_int_rat @ number_number_of_rat @ pls)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3203])). 120.83/55.32 thf(2478,axiom,((! [A:$i]: (((hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ A)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3743_sin__arccos__abs)). 120.83/55.32 thf(13540,plain,((! [A:$i]: (((hAPP_real_real @ sin @ (hAPP_real_real @ arccos @ A)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2478])). 120.83/55.32 thf(2604,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2016_add__right__mono)). 120.83/55.32 thf(13985,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2604])). 120.83/55.32 thf(515,axiom,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A)) = (hAPP_real_real @ (log @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (C != one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3874_log__divide)). 120.83/55.32 thf(6659,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (log @ C) @ B)) @ (hAPP_real_real @ (log @ C) @ A)) = (hAPP_real_real @ (log @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) | (C = one_one_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 120.83/55.32 thf(1161,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ D) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2558_div__mult__div__if__dvd)). 120.83/55.32 thf(8936,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ D) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161])). 120.83/55.32 thf(1368,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_998_dvd__power__le)). 120.83/55.32 thf(9646,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368])). 120.83/55.32 thf(3018,axiom,(((hAPP_int_nat @ nat @ zero_zero_int) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2705_nat__0)). 120.83/55.32 thf(15447,plain,(((hAPP_int_nat @ nat @ zero_zero_int) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3018])). 120.83/55.32 thf(4681,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4272_fact__mono__int)). 120.83/55.32 thf(21512,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4681])). 120.83/55.32 thf(1406,axiom,((! [A:$i,B:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) <= (zero_zero_nat != B)) & ((B = zero_zero_nat) => (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1835_realpow__num__eq__if)). 120.83/55.32 thf(9777,plain,((! [A:$i,B:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) | (zero_zero_nat = B)) & ((B = zero_zero_nat) => (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406])). 120.83/55.32 thf(2680,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1365_mult__less__le__imp__less)). 120.83/55.32 thf(14265,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2680])). 120.83/55.32 thf(2892,axiom,((! [A:$i,B:$i]: ((B != zero_z891286103de_int) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ one_on1684967323de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2635_div__add__self2)). 120.83/55.32 thf(15004,plain,((! [A:$i,B:$i]: ((~ (B = zero_z891286103de_int)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ one_on1684967323de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2892])). 120.83/55.32 thf(3888,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4969_gcd__add2__int)). 120.83/55.32 thf(18434,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3888])). 120.83/55.32 thf(4464,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_zadd__left__commute)). 120.83/55.32 thf(20653,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4464])). 120.83/55.32 thf(4516,axiom,((! [A:$i]: (((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) | (A = zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3225_less__2__cases)). 120.83/55.32 thf(20856,plain,((! [A:$i]: ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) | (A = zero_zero_nat) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4516])). 120.83/55.32 thf(370,axiom,((zero_zero_real = (ratreal @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4695_zero__real__code)). 120.83/55.32 thf(6191,plain,((zero_zero_real = (ratreal @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 120.83/55.32 thf(4243,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2596_zdiv__mono1)). 120.83/55.32 thf(19806,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4243])). 120.83/55.32 thf(610,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ uminus_uminus_rat @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4656_diff__rat__def)). 120.83/55.32 thf(6962,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ uminus_uminus_rat @ B)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])). 120.83/55.32 thf(2543,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ one_one_rat)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.32 thf(13781,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ one_one_rat)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2543])). 120.83/55.32 thf(3192,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3084_Nat__Transfer_Otransfer__int__nat__functions_I4_J)). 120.83/55.32 thf(16042,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3192])). 120.83/55.32 thf(656,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1333_mult__less__imp__less__left)). 120.83/55.32 thf(7151,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 120.83/55.32 thf(3351,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ arctan @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3879_DERIV__arctan)). 120.83/55.32 thf(16589,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ arctan @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3351])). 120.83/55.32 thf(1041,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (div_mod_nat @ E) @ D) = (hAPP_nat_nat @ (div_mod_nat @ C) @ D)) => (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ D) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ B)) @ D)) <= ((hAPP_nat_nat @ (div_mod_nat @ B) @ D) = (hAPP_nat_nat @ (div_mod_nat @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2402_mod__mult__cong)). 120.83/55.32 thf(8505,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (div_mod_nat @ E) @ D) = (hAPP_nat_nat @ (div_mod_nat @ C) @ D)) => (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ D) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ B)) @ D)) | ~ ((hAPP_nat_nat @ (div_mod_nat @ B) @ D) = (hAPP_nat_nat @ (div_mod_nat @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041])). 120.83/55.32 thf(1116,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2723_div__less__dividend)). 120.83/55.32 thf(8789,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116])). 120.83/55.32 thf(2650,axiom,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ pi) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3423_pi__not__less__zero)). 120.83/55.32 thf(14175,plain,((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ pi) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2650])). 120.83/55.32 thf(2720,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1688_real__sum__squared__expand)). 120.83/55.32 thf(14406,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2720])). 120.83/55.32 thf(4123,axiom,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) = (hAPP_int_int @ abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3426_int__nat__abs)). 120.83/55.32 thf(19367,plain,((! [A:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) = (hAPP_int_int @ abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4123])). 120.83/55.32 thf(334,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3849_inv__real__of__nat__fact__ge__zero)). 120.83/55.32 thf(6056,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ fact_fact_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 120.83/55.32 thf(985,axiom,((! [A:$i,B:$i,C:$i]: ((B = C) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1928_add__left__imp__eq)). 120.83/55.32 thf(8323,plain,((! [A:$i,B:$i,C:$i]: ((B = C) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[985])). 120.83/55.32 thf(3117,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1411_power__le__imp__le__exp)). 120.83/55.32 thf(15797,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3117])). 120.83/55.32 thf(2935,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E) = C) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1539_eq__add__iff2)). 120.83/55.32 thf(15152,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E) = C) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) & (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E)) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ A)) @ B)) @ E) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2935])). 120.83/55.32 thf(221,axiom,((! [A:$i]: (((hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sgn_sgn_real @ A)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ arctan @ A))) <= (zero_zero_real != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3558_arctan__inverse)). 120.83/55.32 thf(5678,plain,((! [A:$i]: (((hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sgn_sgn_real @ A)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ arctan @ A))) | (zero_zero_real = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 120.83/55.32 thf(1370,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_dvd__trans)). 120.83/55.32 thf(9656,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370])). 120.83/55.32 thf(4635,axiom,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3417_abs__int__eq)). 120.83/55.32 thf(21350,plain,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4635])). 120.83/55.32 thf(4810,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ B) & (is_int @ D) & (is_int @ C) & (is_int @ A)) => (((C != D) & (B != A)) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_crossproduct__noteq)). 120.83/55.32 thf(22002,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ B) & (is_int @ D) & (is_int @ C) & (is_int @ A)) => (((~ (C = D) & ~ (B = A)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))))) & ((~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)))) => (~ (C = D) & ~ (B = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4810])). 120.83/55.32 thf(1946,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <= (! [D:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3253_dvd_Olift__Suc__mono__le)). 120.83/55.32 thf(11689,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (! [D:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946])). 120.83/55.32 thf(924,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1345_mult__less__imp__less__right)). 120.83/55.32 thf(8106,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[924])). 120.83/55.32 thf(4116,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_mult__neg__pos)). 120.83/55.32 thf(19344,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4116])). 120.83/55.32 thf(3049,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) <=> (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1940_add__left__cancel)). 120.83/55.32 thf(15539,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) => (C = B)) & ((C = B) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3049])). 120.83/55.32 thf(1706,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.32 thf(10829,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706])). 120.83/55.32 thf(4660,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2226_wset__less)). 120.83/55.32 thf(21452,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (wset @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ one_one_int))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4660])). 120.83/55.32 thf(735,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ fact_fact_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3801_fact__nonzero__nat)). 120.83/55.32 thf(7420,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ fact_fact_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])). 120.83/55.32 thf(651,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__number__of)). 120.83/55.32 thf(7122,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])). 120.83/55.32 thf(487,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4403_powr__ge__pzero)). 120.83/55.32 thf(6564,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 120.83/55.32 thf(3568,axiom,((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1228_not__one__less__zero)). 120.83/55.32 thf(17281,plain,((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3568])). 120.83/55.32 thf(3464,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2875_Suc__leD)). 120.83/55.32 thf(16948,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3464])). 120.83/55.32 thf(1951,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3748_reals__Archimedean6)). 120.83/55.32 thf(11706,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ B))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951])). 120.83/55.32 thf(4533,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))) <= (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2888_odd__plus__even)). 120.83/55.32 thf(20936,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4533])). 120.83/55.32 thf(4623,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4286_fact__less__mono__int__aux)). 120.83/55.32 thf(21318,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ fact_fact_int @ A)) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4623])). 120.83/55.32 thf(229,axiom,((! [A:$i,B:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2333_mod__div__trivial)). 120.83/55.32 thf(5710,plain,((! [A:$i,B:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 120.83/55.32 thf(1693,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3444_ln__less__zero)). 120.83/55.32 thf(10788,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ ln @ A)) @ zero_zero_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693])). 120.83/55.32 thf(1251,axiom,((! [A:$i]: (A = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.32 thf(9232,plain,((! [A:$i]: (A = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251])). 120.83/55.32 thf(214,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3832_not__exp__le__zero)). 120.83/55.32 thf(5652,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 120.83/55.32 thf(3279,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)) @ (hAPP_int_real @ number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_double__number__of__Bit0)). 120.83/55.32 thf(16362,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real)) @ (hAPP_int_real @ number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3279])). 120.83/55.32 thf(2968,axiom,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3341_real__sqrt__pow2)). 120.83/55.32 thf(15252,plain,((! [A:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = A) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2968])). 120.83/55.32 thf(249,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (natfloor @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3698_less__natfloor)). 120.83/55.32 thf(5763,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (natfloor @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_nat_real @ real_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 120.83/55.32 thf(4617,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2583_div__power)). 120.83/55.32 thf(21301,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4617])). 120.83/55.32 thf(4607,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.32 thf(21263,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4607])). 120.83/55.32 thf(1147,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3895_real__root__zero)). 120.83/55.32 thf(8885,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147])). 120.83/55.32 thf(4628,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_power2__less__imp__less)). 120.83/55.32 thf(21328,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4628])). 120.83/55.32 thf(813,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A) = zero_z126310315umeral) <=> ((A = zero_z126310315umeral) & (B = zero_z126310315umeral)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2159_add__nonneg__eq__0__iff)). 120.83/55.32 thf(7718,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => ((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A) = zero_z126310315umeral) => ((A = zero_z126310315umeral) & (B = zero_z126310315umeral))) & (((A = zero_z126310315umeral) & (B = zero_z126310315umeral)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A) = zero_z126310315umeral)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])). 120.83/55.32 thf(2672,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3451_int__dvd__iff)). 120.83/55.32 thf(14240,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2672])). 120.83/55.32 thf(319,axiom,((! [A:$i]: ((! [B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ A @ D)) @ (hAPP_nat_real @ A @ E)))) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))))))))) <=> (hBOOL @ (cauchy_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4375_Cauchy__iff2)). 120.83/55.32 thf(6008,plain,((! [A:$i]: (((! [B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ A @ D)) @ (hAPP_nat_real @ A @ E)))) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))))))))) => (hBOOL @ (cauchy_real @ A))) & ((hBOOL @ (cauchy_real @ A)) => (! [B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (! [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_nat_real @ A @ D)) @ (hAPP_nat_real @ A @ E)))) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 120.83/55.32 thf(451,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3707_cos__expansion__lemma)). 120.83/55.32 thf(6440,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B))) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ pi)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 120.83/55.32 thf(621,axiom,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3383_real__sqrt__abs2)). 120.83/55.32 thf(6998,plain,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 120.83/55.32 thf(3411,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4027_coprime__divprod)). 120.83/55.32 thf(16787,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3411])). 120.83/55.32 thf(3455,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2957_of__nat__add)). 120.83/55.32 thf(16917,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ semiri132038758t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3455])). 120.83/55.32 thf(2243,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4463_lemma__floor)). 120.83/55.32 thf(12695,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ B)) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243])). 120.83/55.32 thf(3960,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2196_add__le__less__mono)). 120.83/55.32 thf(18686,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3960])). 120.83/55.32 thf(4896,axiom,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5145_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J)). 120.83/55.32 thf(22292,plain,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4896])). 120.83/55.32 thf(1635,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <= (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1705_dvd_Oeq__refl)). 120.83/55.32 thf(10604,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635])). 120.83/55.32 thf(4352,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_rel__simps_I17_J)). 120.83/55.32 thf(20221,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4352])). 120.83/55.32 thf(4086,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1277_one__le__power)). 120.83/55.32 thf(19228,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4086])). 120.83/55.32 thf(509,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_dvd__mult__left)). 120.83/55.32 thf(6641,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 120.83/55.32 thf(4320,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_comm__mult__left__mono)). 120.83/55.32 thf(20089,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4320])). 120.83/55.32 thf(141,axiom,((! [A:$i]: ((is_int @ A) => ((archim1246769320r_real @ (hAPP_int_real @ real_int @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4381_floor__real__of__int)). 120.83/55.32 thf(5414,plain,((! [A:$i]: ((is_int @ A) => ((archim1246769320r_real @ (hAPP_int_real @ real_int @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 120.83/55.32 thf(4894,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_zero__le__square)). 120.83/55.32 thf(22285,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4894])). 120.83/55.32 thf(853,axiom,((! [A:$i]: (one_on1684967323de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1301_power__0)). 120.83/55.32 thf(7864,plain,((! [A:$i]: (one_on1684967323de_int = (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])). 120.83/55.32 thf(3530,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ one_one_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4015_coprime__1_H)). 120.83/55.32 thf(17156,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ one_one_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3530])). 120.83/55.32 thf(2897,axiom,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_dvdI)). 120.83/55.32 thf(15021,plain,((! [A:$i,B:$i,C:$i]: ((A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2897])). 120.83/55.32 thf(152,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ E)) => (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ A) @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ F) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ G) @ C)) @ E))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ G) @ C)) @ E)))))) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ D @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ F) @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4214_divmod__nat__rel__add1__eq)). 120.83/55.32 thf(5446,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ B) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ E)) => (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ A) @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ F) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ G) @ C)) @ E))) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ G) @ C)) @ E)))))) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ D @ E) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ F) @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 120.83/55.32 thf(2980,axiom,((! [A:$i,B:$i]: (((B = zero_zero_nat) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) = (hAPP_nat_nat @ fact_fact_nat @ A))) & ((B != zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A))) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3799_fact__add__num__eq__if2__nat)). 120.83/55.32 thf(15308,plain,((! [A:$i,B:$i]: (((B = zero_zero_nat) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) = (hAPP_nat_nat @ fact_fact_nat @ A))) & ((~ (B = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A))) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2980])). 120.83/55.32 thf(2395,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (((B != zero_zero_real) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) <= (zero_zero_real = B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4475_powr__realpow2)). 120.83/55.32 thf(13246,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (((~ (B = zero_zero_real)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) | ~ (zero_zero_real = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395])). 120.83/55.32 thf(787,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2949_of__nat__le__iff)). 120.83/55.32 thf(7615,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ (hAPP_nat_nat @ semiri984289939at_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 120.83/55.32 thf(189,axiom,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4104_complex__In__mult__cnj__zero)). 120.83/55.32 thf(5570,plain,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ cnj @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 120.83/55.32 thf(1153,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3500_m2pi__less__pi)). 120.83/55.32 thf(8905,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))) @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153])). 120.83/55.32 thf(3426,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_mult__strict__right__mono__neg)). 120.83/55.32 thf(16828,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3426])). 120.83/55.32 thf(4051,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3231_power__odd__eq)). 120.83/55.32 thf(19050,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4051])). 120.83/55.32 thf(3125,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1655_mult__le__mono2)). 120.83/55.32 thf(15817,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3125])). 120.83/55.32 thf(783,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3912_real__root__divide)). 120.83/55.32 thf(7600,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 120.83/55.32 thf(2685,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2070_add__less__cancel__right)). 120.83/55.32 thf(14282,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2685])). 120.83/55.32 thf(3178,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ A) = (hAPP_rat_rat @ inverse_inverse_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4684_inverse__rat)). 120.83/55.32 thf(16001,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ A) = (hAPP_rat_rat @ inverse_inverse_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3178])). 120.83/55.32 thf(3398,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2720_nat__mult__div__cancel1)). 120.83/55.32 thf(16738,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3398])). 120.83/55.32 thf(2632,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_neg @ A)) => (zero_zero_nat = (hAPP_int_nat @ nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3275_neg__nat)). 120.83/55.32 thf(14111,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ nat_neg @ A)) => (zero_zero_nat = (hAPP_int_nat @ nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2632])). 120.83/55.32 thf(2126,axiom,((! [A:$i]: ((! [B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ A @ D))) @ B)))))) => (hBOOL @ (vanishes @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5152_vanishesI)). 120.83/55.32 thf(12266,plain,((! [A:$i]: ((! [B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => (? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ abs_abs_rat @ (hAPP_nat_rat @ A @ D))) @ B)))))) => (hBOOL @ (vanishes @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126])). 120.83/55.32 thf(231,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1784_real__mult__assoc)). 120.83/55.32 thf(5716,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 120.83/55.32 thf(4587,axiom,((~ (! [A:$i]: ((is_int @ A) => (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440__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_)). 120.83/55.32 thf(21193,plain,((~ (! [A:$i]: ((is_int @ A) => (~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ s1) @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4587])). 120.83/55.32 thf(2659,axiom,((! [A:$i,B:$i]: ((A != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => (((hAPP_nat_nat @ suc @ zero_zero_nat) != A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3132_one__less__m)). 120.83/55.32 thf(14201,plain,((! [A:$i,B:$i]: ((~ (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((~ ((hAPP_nat_nat @ suc @ zero_zero_nat) = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2659])). 120.83/55.32 thf(3546,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => ((archim1246769320r_real @ B) = A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4453_floor__eq)). 120.83/55.32 thf(17217,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) => ((archim1246769320r_real @ B) = A))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3546])). 120.83/55.32 thf(642,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2201_add__less__le__mono)). 120.83/55.32 thf(7087,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])). 120.83/55.32 thf(2446,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1241_zero__le__power)). 120.83/55.32 thf(13450,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446])). 120.83/55.32 thf(1060,axiom,((! [A:$i]: (A != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2836_Suc__n__not__n)). 120.83/55.32 thf(8569,plain,((! [A:$i]: ~ (A = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060])). 120.83/55.32 thf(1762,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_dvd__0__right)). 120.83/55.32 thf(11045,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762])). 120.83/55.32 thf(3645,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3038_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.32 thf(17564,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3645])). 120.83/55.32 thf(3641,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_le__number__of)). 120.83/55.32 thf(17551,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3641])). 120.83/55.32 thf(2898,axiom,((! [A:$i,B:$i]: (is_int @ (hAPP_f659380387ol_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Int__Oint)). 120.83/55.32 thf(15026,plain,((! [A:$i,B:$i]: (is_int @ (hAPP_f659380387ol_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2898])). 120.83/55.32 thf(662,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_dvd__mult__left)). 120.83/55.32 thf(7166,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 120.83/55.32 thf(3369,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3082_int__power)). 120.83/55.32 thf(16653,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3369])). 120.83/55.32 thf(2313,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2013_add__left__mono)). 120.83/55.32 thf(12947,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313])). 120.83/55.32 thf(386,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_dvd__triv__left)). 120.83/55.32 thf(6238,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 120.83/55.32 thf(200,axiom,((! [A:$i]: (A = (hAPP_real_real @ ln @ (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3822_ln__exp)). 120.83/55.32 thf(5607,plain,((! [A:$i]: (A = (hAPP_real_real @ ln @ (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 120.83/55.32 thf(2708,axiom,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1973_add__0__right)). 120.83/55.32 thf(14374,plain,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2708])). 120.83/55.32 thf(4854,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1200_not__square__less__zero)). 120.83/55.32 thf(22167,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4854])). 120.83/55.32 thf(4944,axiom,((! [A:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ fact_fact_int @ A)) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_int_nat @ nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4285_transfer__nat__int__factorial)). 120.83/55.32 thf(22451,plain,((! [A:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ fact_fact_int @ A)) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_int_nat @ nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4944])). 120.83/55.32 thf(1615,axiom,((one_one_nat = (hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2972_of__nat__1)). 120.83/55.32 thf(10540,plain,((one_one_nat = (hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615])). 120.83/55.32 thf(1226,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3088_divides__rexp)). 120.83/55.32 thf(9153,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226])). 120.83/55.32 thf(1449,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (hBOOL @ (hAPP_C24501650l_bool @ A @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)))) <=> (? [C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ A @ C)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ zero_z126310315umeral)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1675_unity__coeff__ex)). 120.83/55.32 thf(9926,plain,((! [A:$i,B:$i]: (((? [C:$i]: (hBOOL @ (hAPP_C24501650l_bool @ A @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ A @ C)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ zero_z126310315umeral)))))) & ((? [C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ A @ C)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ zero_z126310315umeral))))) => (? [C:$i]: (hBOOL @ (hAPP_C24501650l_bool @ A @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449])). 120.83/55.32 thf(3752,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_plus__numeral__code_I9_J)). 120.83/55.32 thf(17953,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3752])). 120.83/55.32 thf(4502,axiom,((! [A:$i]: (((hAPP_int_int @ number_number_of_int @ min) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2646_div__eq__minus1)). 120.83/55.32 thf(20796,plain,((! [A:$i]: (((hAPP_int_int @ number_number_of_int @ min) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4502])). 120.83/55.32 thf(198,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2291_mult_Oadd__right)). 120.83/55.32 thf(5602,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 120.83/55.32 thf(1354,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1905_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.32 thf(9606,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354])). 120.83/55.32 thf(2986,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_comm__mult__left__mono)). 120.83/55.32 thf(15333,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2986])). 120.83/55.32 thf(1873,axiom,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2472_div__by__0)). 120.83/55.32 thf(11460,plain,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873])). 120.83/55.32 thf(2631,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) <=> ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3757_even__sum__nat)). 120.83/55.32 thf(14101,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) => ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))) & (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) | ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) & (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2631])). 120.83/55.32 thf(4040,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ norRRset @ B)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (noXRRset @ B) @ A))) <= (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4587_card__nor__eq__noX)). 120.83/55.32 thf(18979,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ norRRset @ B)) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (noXRRset @ B) @ A))) | ~ (one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4040])). 120.83/55.32 thf(1222,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_power__mult__distrib)). 120.83/55.32 thf(9138,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222])). 120.83/55.32 thf(3259,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.32 thf(16298,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3259])). 120.83/55.32 thf(4005,axiom,((one_one_nat = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_semiring__numeral__1__eq__1)). 120.83/55.32 thf(18848,plain,((one_one_nat = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4005])). 120.83/55.32 thf(87,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3356_real__sqrt__divide)). 120.83/55.32 thf(5250,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 120.83/55.32 thf(3197,axiom,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_nat) <= (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A))) & (((hAPP_int_nat @ number_number_of_nat @ A) != zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_power__0__left__number__of)). 120.83/55.32 thf(16064,plain,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_nat) | ~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A))) & ((~ ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3197])). 120.83/55.32 thf(3051,axiom,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3239_even__div__2__prop2)). 120.83/55.32 thf(15549,plain,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3051])). 120.83/55.32 thf(2456,axiom,((! [A:$i,B:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_add__number__of__eq)). 120.83/55.32 thf(13477,plain,((! [A:$i,B:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2456])). 120.83/55.32 thf(332,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (log @ A) @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ ln @ A)) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4791_DERIV__log)). 120.83/55.32 thf(6051,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ (log @ A) @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ ln @ A)) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 120.83/55.32 thf(2996,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2306_mult_Odiff__right)). 120.83/55.32 thf(15375,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2996])). 120.83/55.32 thf(3506,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_zero__less__mult__pos)). 120.83/55.32 thf(17087,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3506])). 120.83/55.32 thf(4084,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2677_zfact__prop)). 120.83/55.32 thf(19221,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4084])). 120.83/55.32 thf(3757,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) => ((hAPP_int_int @ (div_mod_int @ A) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2617_zmod__zdvd__zmod)). 120.83/55.32 thf(17968,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) => ((hAPP_int_int @ (div_mod_int @ A) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3757])). 120.83/55.32 thf(49,axiom,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ uminus473333897omplex @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ re @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4124_Re_Ominus)). 120.83/55.32 thf(5111,plain,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ uminus473333897omplex @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ re @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 120.83/55.32 thf(4637,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4976_gcd__exp__int)). 120.83/55.32 thf(21361,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4637])). 120.83/55.32 thf(4539,axiom,((! [A:$i,B:$i]: (((((((A = B) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) & (((hAPP_int_int @ number_number_of_int @ A) = zero_zero_int) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ B)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))) <=> ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_int_nat @ number_number_of_nat @ B))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3279_eq__nat__number__of)). 120.83/55.32 thf(20951,plain,((! [A:$i,B:$i]: ((((((((A = B) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_int_int @ number_number_of_int @ A) = zero_zero_int) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ B)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))) => ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_int_nat @ number_number_of_nat @ B))) & (((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_int_nat @ number_number_of_nat @ B)) => (((((A = B) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_int_int @ number_number_of_int @ A) = zero_zero_int) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ B)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))))))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4539])). 120.83/55.32 thf(1906,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3163_power__Suc__less__one)). 120.83/55.32 thf(11562,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ one_one_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906])). 120.83/55.32 thf(161,axiom,((one_one_complex = (cis @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4149_cis__zero)). 120.83/55.32 thf(5478,plain,((one_one_complex = (cis @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 120.83/55.32 thf(2766,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = A) <= (B = zero_zero_nat)) & ((zero_zero_nat != B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3181_add__eq__if)). 120.83/55.32 thf(14562,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = A) | ~ (B = zero_zero_nat)) & ((~ (zero_zero_nat = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2766])). 120.83/55.32 thf(1028,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 120.83/55.32 thf(8466,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028])). 120.83/55.32 thf(2084,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (rcis @ A @ B)) @ (rcis @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4264_rcis__mult)). 120.83/55.32 thf(12103,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rcis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (rcis @ A @ B)) @ (rcis @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084])). 120.83/55.32 thf(2341,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2511_mod__mult__self2)). 120.83/55.32 thf(13047,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C))) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341])). 120.83/55.32 thf(3578,axiom,((! [A:$i,B:$i,C:$i]: (((zero_zero_nat != C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((zero_zero_nat = C) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2701_nat__mult__div__cancel__disj)). 120.83/55.32 thf(17324,plain,((! [A:$i,B:$i,C:$i]: (((~ (zero_zero_nat = C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)))) & ((zero_zero_nat = C) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3578])). 120.83/55.32 thf(4043,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <=> (B = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4512_zdvd__iff__zgcd)). 120.83/55.32 thf(18986,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (B = (hAPP_int_int @ (legacy_zgcd @ A) @ B))) & ((B = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4043])). 120.83/55.32 thf(1716,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_mult__left__mono)). 120.83/55.32 thf(10856,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716])). 120.83/55.32 thf(3063,axiom,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2134_add__diff__cancel)). 120.83/55.32 thf(15608,plain,((! [A:$i,B:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3063])). 120.83/55.32 thf(4061,axiom,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) | (B = zero_zero_int)) <=> (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2607_zdiv__eq__0__iff)). 120.83/55.32 thf(19118,plain,((! [A:$i,B:$i]: ((((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) | (B = zero_zero_int)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) & ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) | (B = zero_zero_int)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4061])). 120.83/55.32 thf(3089,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1964_add_Ocomm__neutral)). 120.83/55.32 thf(15693,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3089])). 120.83/55.32 thf(1149,axiom,((! [A:$i]: ((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) <=> (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1976_double__zero__sym)). 120.83/55.32 thf(8890,plain,((! [A:$i]: (((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) => (zero_zero_real = A)) & ((zero_zero_real = A) => (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149])). 120.83/55.32 thf(2732,axiom,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ number_number_of_int @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_number__of__is__id)). 120.83/55.32 thf(14444,plain,((! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ number_number_of_int @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2732])). 120.83/55.32 thf(3341,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_dvd__0__right)). 120.83/55.32 thf(16564,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3341])). 120.83/55.32 thf(3861,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ abs_abs_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3420_zdvd__self__abs1)). 120.83/55.32 thf(18341,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ abs_abs_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3861])). 120.83/55.32 thf(2066,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.32 thf(12056,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066])). 120.83/55.32 thf(4023,axiom,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3196_semiring__norm_I115_J)). 120.83/55.32 thf(18923,plain,(((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4023])). 120.83/55.32 thf(4604,axiom,(((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_numeral__1__eq__1)). 120.83/55.32 thf(21251,plain,(((hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4604])). 120.83/55.32 thf(1,conjecture,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 120.83/55.32 thf(2,negated_conjecture,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)) @ zero_zero_int)))),inference(neg_conjecture,[status(cth)],[1])). 120.83/55.32 thf(4950,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 120.83/55.32 thf(2763,axiom,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1212_zero__le__one)). 120.83/55.32 thf(14557,plain,((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ one_on1645066479umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2763])). 120.83/55.32 thf(4282,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_right__distrib__number__of)). 120.83/55.32 thf(19954,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4282])). 120.83/55.32 thf(3471,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.32 thf(16974,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3471])). 120.83/55.32 thf(4034,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) => (((~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) => ((posDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A) = (posDivAlg @ A @ B)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2784_posDivAlg_Opsimps)). 120.83/55.32 thf(18957,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) => (((~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) => ((posDivAlg @ A @ B) = (hAPP_P1975530577nt_int @ (adjust @ B) @ (posDivAlg @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ A) = (posDivAlg @ A @ B)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4034])). 120.83/55.32 thf(4491,axiom,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_semiring__norm_I112_J)). 120.83/55.32 thf(20753,plain,((zero_zero_int = (hAPP_int_int @ number_number_of_int @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4491])). 120.83/55.32 thf(3249,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1252_zero__less__power)). 120.83/55.32 thf(16266,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3249])). 120.83/55.32 thf(244,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ invers1449016382omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4139_complex__Re__inverse)). 120.83/55.32 thf(5748,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ invers1449016382omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 120.83/55.32 thf(4864,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <= (A != B))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_order__le__neq__implies__less)). 120.83/55.32 thf(22192,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | (A = B))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4864])). 120.83/55.32 thf(2435,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4329_gcd__semilattice__nat_Ole__iff__inf)). 120.83/55.32 thf(13399,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))) & ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2435])). 120.83/55.32 thf(2045,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1883_add__neg__nonpos)). 120.83/55.32 thf(11989,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045])). 120.83/55.32 thf(300,axiom,((zero_zero_real = (hAPP_real_real @ sin @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3649_sin__pi)). 120.83/55.32 thf(5944,plain,((zero_zero_real = (hAPP_real_real @ sin @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 120.83/55.32 thf(1626,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))) <=> (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ C))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ A @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3194_zdiff__int__split)). 120.83/55.32 thf(10572,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ C))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ A @ zero_zero_int))))) & ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ B)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ C))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ A @ zero_zero_int)))) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626])). 120.83/55.32 thf(2843,axiom,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A) = zero_zero_nat) <= (A != zero_zero_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A) = one_one_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1433_power__0__left)). 120.83/55.32 thf(14842,plain,((! [A:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A) = zero_zero_nat) | (A = zero_zero_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A) = one_one_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2843])). 120.83/55.32 thf(942,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2703_mod__less__divisor)). 120.83/55.32 thf(8163,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[942])). 120.83/55.32 thf(39,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3964_complex__diff)). 120.83/55.32 thf(5074,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 120.83/55.32 thf(1708,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_dvd__refl)). 120.83/55.32 thf(10835,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708])). 120.83/55.32 thf(4751,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2529_Divides_Otransfer__nat__int__function__closures_I2_J)). 120.83/55.32 thf(21818,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4751])). 120.83/55.32 thf(2275,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1865_add__nonneg__pos)). 120.83/55.32 thf(12807,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275])). 120.83/55.32 thf(932,axiom,((! [A:$i,B:$i]: ((archim791455193or_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4683_floor__Fract)). 120.83/55.32 thf(8128,plain,((! [A:$i,B:$i]: ((archim791455193or_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[932])). 120.83/55.32 thf(312,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ E))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3412_lemma__interval)). 120.83/55.32 thf(5980,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ E))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ D))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 120.83/55.32 thf(3199,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_power2__less__imp__less)). 120.83/55.32 thf(16079,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3199])). 120.83/55.32 thf(4760,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_zmult__zless__mono2)). 120.83/55.32 thf(21846,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4760])). 120.83/55.32 thf(1198,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ real_nat @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3655_real__of__nat__power)). 120.83/55.32 thf(9061,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ real_nat @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198])). 120.83/55.32 thf(175,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ size_size_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4059_nat__size)). 120.83/55.32 thf(5523,plain,((! [A:$i]: (A = (hAPP_nat_nat @ size_size_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 120.83/55.32 thf(4312,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1554_diff__bin__simps_I3_J)). 120.83/55.32 thf(20055,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ pls) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4312])). 120.83/55.32 thf(3347,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2157_add__increasing)). 120.83/55.32 thf(16579,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3347])). 120.83/55.32 thf(2925,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1648_add__leD1)). 120.83/55.32 thf(15122,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2925])). 120.83/55.32 thf(3288,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2106_mult__1__right)). 120.83/55.32 thf(16396,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3288])). 120.83/55.32 thf(1915,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1415_power__increasing__iff)). 120.83/55.32 thf(11594,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915])). 120.83/55.32 thf(233,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3651_real__of__nat__mult)). 120.83/55.32 thf(5721,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 120.83/55.32 thf(3939,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_rel__simps_I16_J)). 120.83/55.32 thf(18619,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3939])). 120.83/55.32 thf(746,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4785_le__Suc__number__of)). 120.83/55.32 thf(7462,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 120.83/55.32 thf(1999,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1801_realpow__minus__mult)). 120.83/55.32 thf(11855,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999])). 120.83/55.32 thf(1403,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real)) @ (hAPP_nat_real @ real_nat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3685_nat__less__real__le)). 120.83/55.32 thf(9766,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real)) @ (hAPP_nat_real @ real_nat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real)) @ (hAPP_nat_real @ real_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403])). 120.83/55.32 thf(1345,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_right__distrib__number__of)). 120.83/55.32 thf(9578,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345])). 120.83/55.32 thf(1610,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ A)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2581_div__power)). 120.83/55.32 thf(10521,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610])). 120.83/55.32 thf(3768,axiom,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_number__of__Bit1)). 120.83/55.32 thf(18009,plain,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3768])). 120.83/55.32 thf(2320,axiom,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_complex @ semiri2020571505omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2825_number__of__int)). 120.83/55.32 thf(12968,plain,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_complex @ semiri2020571505omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2320])). 120.83/55.32 thf(3682,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_int_int @ fact_fact_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4282_fact__ge__one__int)). 120.83/55.32 thf(17717,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_int_int @ fact_fact_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3682])). 120.83/55.32 thf(4507,axiom,((! [A:$i]: ((? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3797_even__square)). 120.83/55.32 thf(20824,plain,((! [A:$i]: (? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | ~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4507])). 120.83/55.32 thf(4014,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_mult__nonneg__nonpos)). 120.83/55.32 thf(18886,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4014])). 120.83/55.32 thf(7,axiom,((! [A:$i,B:$i,C:$i]: (((divmod_nat @ A @ B) = C) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4216_divmod__nat__eq)). 120.83/55.32 thf(4961,plain,((! [A:$i,B:$i,C:$i]: (((divmod_nat @ A @ B) = C) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 120.83/55.32 thf(2339,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_dvd__mult__left)). 120.83/55.32 thf(13042,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339])). 120.83/55.32 thf(884,axiom,((! [A:$i,B:$i]: ((B != zero_z126310315umeral) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2547_div__mult__self2__is__id)). 120.83/55.32 thf(7967,plain,((! [A:$i,B:$i]: ((~ (B = zero_z126310315umeral)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])). 120.83/55.32 thf(2191,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2198_add__le__less__mono)). 120.83/55.32 thf(12519,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191])). 120.83/55.32 thf(3159,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_dvd__refl)). 120.83/55.32 thf(15924,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3159])). 120.83/55.32 thf(1324,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1637_less__or__eq__imp__le)). 120.83/55.32 thf(9499,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324])). 120.83/55.32 thf(2862,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ A) = one_one_nat) <= (zero_zero_nat != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4366_coprime__minus__one__nat)). 120.83/55.32 thf(14902,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ A) = one_one_nat) | (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2862])). 120.83/55.32 thf(4791,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_zero__le__even__power_H)). 120.83/55.32 thf(21941,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4791])). 120.83/55.32 thf(4568,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((zero_zero_int = A) | (zero_zero_int = B)) <=> (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_mult__eq__0__iff)). 120.83/55.32 thf(21126,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((zero_zero_int = A) | (zero_zero_int = B)) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) & ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) => ((zero_zero_int = A) | (zero_zero_int = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4568])). 120.83/55.32 thf(4912,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4981_dvd__gcd__D1__int)). 120.83/55.32 thf(22344,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4912])). 120.83/55.32 thf(2693,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3909_real__root__power)). 120.83/55.32 thf(14314,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2693])). 120.83/55.32 thf(4407,axiom,((! [A:$i]: ((A != zero_zero_rat) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zero__less__power2)). 120.83/55.32 thf(20435,plain,((! [A:$i]: (((~ (A = zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (~ (A = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4407])). 120.83/55.32 thf(1561,axiom,((! [A:$i]: (A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_power__one__right)). 120.83/55.32 thf(10333,plain,((! [A:$i]: (A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561])). 120.83/55.32 thf(1519,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1857_add__pos__nonneg)). 120.83/55.32 thf(10159,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519])). 120.83/55.32 thf(4578,axiom,((! [A:$i,B:$i,C:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ A)) @ B) @ C)) <= (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (setS @ B @ C)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4813_SetS__setprod__prop)). 120.83/55.32 thf(21163,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ A)) @ B) @ C)) | ~ (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ (setS @ B @ C)))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4578])). 120.83/55.32 thf(1541,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1323_mult__left__le__imp__le)). 120.83/55.32 thf(10246,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C))) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541])). 120.83/55.32 thf(4538,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_power2__eq__square)). 120.83/55.32 thf(20948,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4538])). 120.83/55.32 thf(1125,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2410_zmod__simps_I1_J)). 120.83/55.32 thf(8813,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125])). 120.83/55.32 thf(2937,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1650_add__mult__distrib2)). 120.83/55.32 thf(15163,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2937])). 120.83/55.32 thf(497,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ sgn_sgn_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4105_Im__sgn)). 120.83/55.32 thf(6596,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ sgn_sgn_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 120.83/55.32 thf(837,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2111_mult__1__right)). 120.83/55.32 thf(7811,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])). 120.83/55.32 thf(780,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ one_on1645066479umeral) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2480_div__by__1)). 120.83/55.32 thf(7586,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ one_on1645066479umeral) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])). 120.83/55.32 thf(1388,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3177_lemma__realpow__diff)). 120.83/55.32 thf(9715,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ C)) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388])). 120.83/55.32 thf(3747,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (inv @ B) @ A))) @ one_one_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2140_inv__is__inv)). 120.83/55.32 thf(17943,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (inv @ B) @ A))) @ one_one_int) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3747])). 120.83/55.32 thf(1316,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ C @ A)) @ B)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))) <= (! [D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ E))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2243_mono__nat__linear__lb)). 120.83/55.32 thf(9473,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ C @ A)) @ B)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))) | ~ (! [D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ E))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316])). 120.83/55.32 thf(2957,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2190_double__add__less__zero__iff__single__add__less__zero)). 120.83/55.32 thf(15220,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2957])). 120.83/55.32 thf(2486,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4646_Frct__code__post_I5_J)). 120.83/55.32 thf(13573,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (frct @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486])). 120.83/55.32 thf(258,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2107_mult__1__right)). 120.83/55.32 thf(5790,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 120.83/55.32 thf(3719,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1531_inf__period_I3_J)). 120.83/55.32 thf(17833,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ C))) @ A))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3719])). 120.83/55.32 thf(22,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ A @ C) @ B) = (hAPP_real_real @ (hAPP_n546711566l_real @ (hAPP_f248847589l_real @ cOMBC_real_nat_real @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__RealDef__Oreal_000tc__Nat__Onat_000tc__RealDef__Orea)). 120.83/55.32 thf(5018,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ A @ C) @ B) = (hAPP_real_real @ (hAPP_n546711566l_real @ (hAPP_f248847589l_real @ cOMBC_real_nat_real @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 120.83/55.32 thf(3637,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) @ A)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1687_QuadRes__def)). 120.83/55.32 thf(17536,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ A) @ B)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3637])). 120.83/55.32 thf(1099,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ one_one_real) @ A) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4380_powr__one__eq__one)). 120.83/55.32 thf(8744,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ one_one_real) @ A) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099])). 120.83/55.32 thf(4477,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A) = (hAPP_int_int @ bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_Bit1__def)). 120.83/55.32 thf(20714,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A) = (hAPP_int_int @ bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4477])). 120.83/55.32 thf(2579,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1838_nat__less__add__iff1)). 120.83/55.32 thf(13893,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ B)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2579])). 120.83/55.32 thf(2368,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3113_power__le__imp__le__base)). 120.83/55.32 thf(13136,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368])). 120.83/55.32 thf(801,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2030_add__le__cancel__right)). 120.83/55.32 thf(7672,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 120.83/55.32 thf(223,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))) = (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3488_abs__minus__add__cancel)). 120.83/55.32 thf(5684,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))) = (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 120.83/55.32 thf(4447,axiom,((! [A:$i,B:$i,C:$i]: (((C = A) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) <= ((is_int @ A) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1909_add__right__imp__eq)). 120.83/55.32 thf(20577,plain,((! [A:$i,B:$i,C:$i]: ((C = A) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) | ~ ((is_int @ A) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4447])). 120.83/55.32 thf(304,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E)) <=> ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1537_eq__add__iff2)). 120.83/55.32 thf(5955,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E) = C)) & (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ A)) @ B)) @ E) = C) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 120.83/55.32 thf(4098,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) <=> ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_eq__0__number__of)). 120.83/55.32 thf(19265,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) & (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4098])). 120.83/55.32 thf(4334,axiom,((! [A:$i,B:$i]: (((hAPP_int_nat @ number_number_of_nat @ A) = B) <=> ((hAPP_int_nat @ number_number_of_nat @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_number__of__reorient)). 120.83/55.32 thf(20169,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4334])). 120.83/55.32 thf(4010,axiom,((! [A:$i]: ((((A != zero_zero_int) => ((((hAPP_int_int @ sgn_sgn_int @ A) = one_one_int) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) => ((hAPP_int_int @ sgn_sgn_int @ A) = (hAPP_int_int @ uminus_uminus_int @ one_one_int))))) & (((hAPP_int_int @ sgn_sgn_int @ A) = zero_zero_int) <= (A = zero_zero_int))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3602_zsgn__def)). 120.83/55.32 thf(18868,plain,((! [A:$i]: ((((~ (A = zero_zero_int)) => ((((hAPP_int_int @ sgn_sgn_int @ A) = one_one_int) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) => ((hAPP_int_int @ sgn_sgn_int @ A) = (hAPP_int_int @ uminus_uminus_int @ one_one_int))))) & (((hAPP_int_int @ sgn_sgn_int @ A) = zero_zero_int) | ~ (A = zero_zero_int))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4010])). 120.83/55.32 thf(3487,axiom,((! [A:$i]: ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_real @ sequentially)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5045_LIMSEQ__rabs__realpow__zero2)). 120.83/55.32 thf(17034,plain,((! [A:$i]: ((hBOOL @ (tendsto_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ zero_zero_real @ sequentially)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3487])). 120.83/55.32 thf(2747,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) <= (C != zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2536_div__mult__mult1)). 120.83/55.32 thf(14491,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) | (C = zero_z891286103de_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2747])). 120.83/55.32 thf(4032,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ A) @ B) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U)). 120.83/55.32 thf(18952,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ A) @ B) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4032])). 120.83/55.32 thf(2595,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3759_even__Suc)). 120.83/55.32 thf(13957,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ suc @ A)))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ suc @ A))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2595])). 120.83/55.32 thf(3982,axiom,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2973_of__nat__1)). 120.83/55.32 thf(18771,plain,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3982])). 120.83/55.32 thf(2683,axiom,((! [A:$i]: (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3790_lemma__not__even__div2)). 120.83/55.32 thf(14272,plain,((! [A:$i]: (((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2683])). 120.83/55.32 thf(3194,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.32 thf(16047,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3194])). 120.83/55.32 thf(3364,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => ((zero_zero_int != D) => ((((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ D)) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <= (zero_zero_int != C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4662_normalize__crossproduct)). 120.83/55.32 thf(16628,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ C) & (is_int @ D)) => ((~ (zero_zero_int = D)) => ((((normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ D)) = (normalize @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) | (zero_zero_int = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3364])). 120.83/55.32 thf(1646,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2365_mod__self)). 120.83/55.32 thf(10636,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646])). 120.83/55.32 thf(3268,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1575_add__number__of__diff1)). 120.83/55.32 thf(16330,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3268])). 120.83/55.32 thf(3845,axiom,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3169_numeral__3__eq__3)). 120.83/55.32 thf(18271,plain,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3845])). 120.83/55.32 thf(911,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4439_real__of__int__gt__zero__cancel__iff)). 120.83/55.32 thf(8060,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_int_real @ real_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[911])). 120.83/55.32 thf(1008,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mult__2)). 120.83/55.32 thf(8396,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])). 120.83/55.32 thf(3914,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3435_zero__le__zpower__abs)). 120.83/55.32 thf(18537,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3914])). 120.83/55.32 thf(3560,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5171_isCont__root__pos)). 120.83/55.32 thf(17255,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ (hAPP_n546711566l_real @ root @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3560])). 120.83/55.32 thf(1313,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1683_mult__le__cancel1)). 120.83/55.32 thf(9462,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313])). 120.83/55.32 thf(1988,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1361_mult__less__le__imp__less)). 120.83/55.32 thf(11823,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988])). 120.83/55.32 thf(1744,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B)) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4122_Re_Oadd)). 120.83/55.32 thf(10994,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B)) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744])). 120.83/55.32 thf(1869,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2393_mod__mult__mult2)). 120.83/55.32 thf(11443,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869])). 120.83/55.32 thf(1038,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_dvd__triv__left)). 120.83/55.32 thf(8498,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038])). 120.83/55.32 thf(3978,axiom,((! [A:$i,B:$i]: ((((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2743_Nat__Transfer_Otransfer__nat__int__functions_I1_J)). 120.83/55.32 thf(18756,plain,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3978])). 120.83/55.32 thf(4630,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ pls)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_rel__simps_I27_J)). 120.83/55.32 thf(21333,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit0 @ A)) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4630])). 120.83/55.32 thf(1605,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((B != A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_order__le__neq__implies__less)). 120.83/55.32 thf(10504,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((~ (B = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605])). 120.83/55.32 thf(1469,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))) = B))) <=> ((hAPP_nat_nat @ suc @ B) = (hAPP_int_nat @ number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4779_eq__number__of__Suc)). 120.83/55.32 thf(9991,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))) = B))) => ((hAPP_nat_nat @ suc @ B) = (hAPP_int_nat @ number_number_of_nat @ A))) & (((hAPP_nat_nat @ suc @ B) = (hAPP_int_nat @ number_number_of_nat @ A)) => (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))) = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469])). 120.83/55.32 thf(926,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ D) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2259_minf_I9_J)). 120.83/55.32 thf(8111,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[926])). 120.83/55.32 thf(1995,axiom,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ B) = A) <= (B != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2543_div__mult__self1__is__id)). 120.83/55.32 thf(11842,plain,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ B) = A) | (B = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995])). 120.83/55.32 thf(689,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 120.83/55.32 thf(7264,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 120.83/55.32 thf(754,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1961_add_Ocomm__neutral)). 120.83/55.32 thf(7494,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])). 120.83/55.32 thf(1465,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1747_diff__add__inverse2)). 120.83/55.32 thf(9980,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465])). 120.83/55.32 thf(237,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2114_mult__1)). 120.83/55.32 thf(5731,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 120.83/55.32 thf(1263,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((zero_zero_int != B) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2798_divmod__int__rel__div__mod)). 120.83/55.32 thf(9281,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((~ (zero_zero_int = B)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263])). 120.83/55.32 thf(3909,axiom,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (isCont156215680omplex @ cnj) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5165_cnj_OisCont)). 120.83/55.32 thf(18526,plain,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (isCont156215680omplex @ cnj) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3909])). 120.83/55.32 thf(2760,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.32 thf(14550,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2760])). 120.83/55.32 thf(2655,axiom,((zero_zero_real = (hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2926_of__nat__0)). 120.83/55.32 thf(14186,plain,((zero_zero_real = (hAPP_nat_real @ semiri132038758t_real @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2655])). 120.83/55.32 thf(4725,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1408_power__le__imp__le__exp)). 120.83/55.32 thf(21708,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4725])). 120.83/55.32 thf(4237,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2210_less__iff__diff__less__0)). 120.83/55.32 thf(19761,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4237])). 120.83/55.32 thf(2695,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3182_div__geq)). 120.83/55.32 thf(14319,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2695])). 120.83/55.32 thf(2550,axiom,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_semiring__norm_I110_J)). 120.83/55.32 thf(13801,plain,(((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2550])). 120.83/55.32 thf(2252,axiom,((! [A:$i]: ((A != one_one_nat) => (? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ prime @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4205_prime__factor)). 120.83/55.32 thf(12720,plain,((! [A:$i]: ((~ (A = one_one_nat)) => (? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ prime @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252])). 120.83/55.32 thf(2154,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls))) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mult__numeral__1)). 120.83/55.32 thf(12364,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls))) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154])). 120.83/55.32 thf(1569,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2397_zmod__simps_I4_J)). 120.83/55.32 thf(10360,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569])). 120.83/55.32 thf(4901,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) & (is_int @ C))) <=> (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ zero_zero_int))) & (hBOOL @ (hAPP_int_bool @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1680_unity__coeff__ex)). 120.83/55.32 thf(22312,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) & (is_int @ C))) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ zero_zero_int))) & (hBOOL @ (hAPP_int_bool @ A @ C))))) & ((? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ zero_zero_int))) & (hBOOL @ (hAPP_int_bool @ A @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) & (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4901])). 120.83/55.32 thf(327,axiom,((zero_zero_real = (hAPP_complex_real @ im @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4097_complex__Im__one)). 120.83/55.32 thf(6037,plain,((zero_zero_real = (hAPP_complex_real @ im @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 120.83/55.32 thf(2797,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2025_add__le__cancel__left)). 120.83/55.32 thf(14692,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2797])). 120.83/55.32 thf(1351,axiom,((! [A:$i]: (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1299_power__0)). 120.83/55.32 thf(9599,plain,((! [A:$i]: (one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351])). 120.83/55.32 thf(593,axiom,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4099_complex__Im__number__of)). 120.83/55.32 thf(6912,plain,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 120.83/55.32 thf(1521,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.32 thf(10164,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521])). 120.83/55.32 thf(3976,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ one_one_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1605_zcong__square)). 120.83/55.32 thf(18752,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ one_one_int) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3976])). 120.83/55.32 thf(4198,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_nat @ nat @ A))) @ one_one_nat) = (hAPP_list_int_nat @ size_size_list_int @ (quickc666637781d_zero @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4289_length__around__zero)). 120.83/55.32 thf(19628,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_nat @ nat @ A))) @ one_one_nat) = (hAPP_list_int_nat @ size_size_list_int @ (quickc666637781d_zero @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4198])). 120.83/55.32 thf(4756,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2154_add__increasing)). 120.83/55.32 thf(21831,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4756])). 120.83/55.32 thf(4374,axiom,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ pred @ (hAPP_int_int @ uminus_uminus_int @ A))) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4046_minus__Bit1)). 120.83/55.32 thf(20287,plain,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ pred @ (hAPP_int_int @ uminus_uminus_int @ A))) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4374])). 120.83/55.32 thf(3294,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mult__numeral__1)). 120.83/55.32 thf(16411,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3294])). 120.83/55.32 thf(2353,axiom,((! [A:$i,B:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2493_mod__mult__self1__is__0)). 120.83/55.32 thf(13089,plain,((! [A:$i,B:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353])). 120.83/55.32 thf(4841,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ A)))) @ (hAPP_i1948725293t_bool @ sRStar @ C))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ C)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2672_SRStar__mult__prop2)). 120.83/55.32 thf(22123,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ A)))) @ (hAPP_i1948725293t_bool @ sRStar @ C))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ C))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4841])). 120.83/55.32 thf(1015,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3014_power__Suc)). 120.83/55.32 thf(8428,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015])). 120.83/55.32 thf(4727,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3782_pos__int__even__equiv__nat__even)). 120.83/55.32 thf(21721,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_int_nat @ nat @ A)))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_int_nat @ nat @ A))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4727])). 120.83/55.32 thf(2504,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (monoseq_real @ (hAPP_r474017924t_real @ power_power_real @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4806_monoseq__realpow)). 120.83/55.32 thf(13645,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (monoseq_real @ (hAPP_r474017924t_real @ power_power_real @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2504])). 120.83/55.32 thf(1864,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ one_on1645066479umeral)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.32 thf(11429,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ one_on1645066479umeral)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864])). 120.83/55.32 thf(4457,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) <=> ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3227_even__def)). 120.83/55.32 thf(20613,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => ((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int)) & (((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_int) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4457])). 120.83/55.32 thf(289,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ sin @ A))) @ (hAPP_real_real @ cos @ A)) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3710_sin__double)). 120.83/55.32 thf(5912,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_real_real @ sin @ A))) @ (hAPP_real_real @ cos @ A)) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 120.83/55.32 thf(2022,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ (hAPP_nat_nat @ suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3109_power__le__imp__le__base)). 120.83/55.32 thf(11915,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022])). 120.83/55.32 thf(3811,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2760_Int2_Oaux__1)). 120.83/55.32 thf(18153,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3811])). 120.83/55.32 thf(4394,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((B = A) <=> ((hAPP_int_nat @ nat @ A) = (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2710_eq__nat__nat__iff)). 120.83/55.32 thf(20379,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((((B = A) => ((hAPP_int_nat @ nat @ A) = (hAPP_int_nat @ nat @ B))) & (((hAPP_int_nat @ nat @ A) = (hAPP_int_nat @ nat @ B)) => (B = A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4394])). 120.83/55.32 thf(1079,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2448_mod__mod__cancel)). 120.83/55.32 thf(8669,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079])). 120.83/55.32 thf(1488,axiom,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3021_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.32 thf(10055,plain,((! [A:$i,B:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488])). 120.83/55.32 thf(1501,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_not__sum__squares__lt__zero)). 120.83/55.32 thf(10095,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501])). 120.83/55.32 thf(246,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2303_mult__right_Odiff)). 120.83/55.32 thf(5753,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 120.83/55.32 thf(2282,axiom,((! [A:$i]: ((hAPP_P1175774780nt_int @ (produc1298267108nt_int @ div_div_int) @ (quotient_of @ A)) = (archim791455193or_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4833_rat__floor__code)). 120.83/55.32 thf(12826,plain,((! [A:$i]: ((hAPP_P1175774780nt_int @ (produc1298267108nt_int @ div_div_int) @ (quotient_of @ A)) = (archim791455193or_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282])). 120.83/55.32 thf(3255,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.32 thf(16281,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3255])). 120.83/55.32 thf(1037,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2177_add__neg__neg)). 120.83/55.32 thf(8496,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037])). 120.83/55.32 thf(1830,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2941_of__nat__less__iff)). 120.83/55.32 thf(11295,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830])). 120.83/55.32 thf(4092,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_zcong__sym)). 120.83/55.32 thf(19248,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4092])). 120.83/55.32 thf(741,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.32 thf(7443,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 120.83/55.32 thf(2808,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ pls)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_add__numeral__0)). 120.83/55.32 thf(14728,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ pls)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2808])). 120.83/55.32 thf(3863,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1876_add__strict__increasing2)). 120.83/55.32 thf(18346,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3863])). 120.83/55.32 thf(1670,axiom,((! [A:$i,B:$i]: (is_int @ (hAPP_f1594865479ol_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Int__Oint)). 120.83/55.32 thf(10717,plain,((! [A:$i,B:$i]: (is_int @ (hAPP_f1594865479ol_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670])). 120.83/55.32 thf(3053,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))) <= (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_split__mult__pos__le)). 120.83/55.32 thf(15556,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))) | ~ (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))) | ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3053])). 120.83/55.32 thf(3305,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.32 thf(16446,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3305])). 120.83/55.32 thf(4804,axiom,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3042_int__1)). 120.83/55.32 thf(21987,plain,((one_one_int = (hAPP_nat_int @ semiri1621563631at_int @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4804])). 120.83/55.32 thf(2601,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ cOMBI_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Int__Oint_U)). 120.83/55.32 thf(13978,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ cOMBI_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2601])). 120.83/55.32 thf(4602,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4500_zgcd__pos)). 120.83/55.32 thf(21247,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4602])). 120.83/55.32 thf(1718,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4303_gcd__semilattice__nat_Oinf_Oidem)). 120.83/55.32 thf(10861,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718])). 120.83/55.32 thf(891,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4487_zgcd__eq)). 120.83/55.32 thf(7988,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B)) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[891])). 120.83/55.32 thf(4665,axiom,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ A))) => (A = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3277_not__neg__nat)). 120.83/55.32 thf(21464,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ A))) => (A = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4665])). 120.83/55.32 thf(958,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2416_zmod__simps_I2_J)). 120.83/55.32 thf(8216,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[958])). 120.83/55.32 thf(4153,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ (hAPP_int_complex @ number528085621omplex @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_semiring__add__number__of)). 120.83/55.32 thf(19470,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ (hAPP_int_complex @ number528085621omplex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4153])). 120.83/55.32 thf(3718,axiom,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_pos2)). 120.83/55.32 thf(17832,plain,((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3718])). 120.83/55.32 thf(3310,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.32 thf(16461,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3310])). 120.83/55.32 thf(4291,axiom,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_semiring__one__add__one__is__two)). 120.83/55.32 thf(19983,plain,(((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4291])). 120.83/55.32 thf(4577,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) @ one_one_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1583_inv__not__p__minus__1__aux)). 120.83/55.32 thf(21158,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) @ one_one_int) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4577])). 120.83/55.32 thf(2219,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_mult__zero__left)). 120.83/55.32 thf(12612,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219])). 120.83/55.32 thf(770,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3001_zmult__int)). 120.83/55.32 thf(7543,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 120.83/55.32 thf(405,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2780_transfer__morphism__def)). 120.83/55.32 thf(6298,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 120.83/55.32 thf(470,axiom,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ A)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4153_DeMoivre)). 120.83/55.32 thf(6508,plain,((! [A:$i,B:$i]: ((cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ A)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 120.83/55.32 thf(2738,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3323_real__sqrt__ge__zero)). 120.83/55.32 thf(14459,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2738])). 120.83/55.32 thf(858,axiom,((! [A:$i,B:$i,C:$i]: ((C = B) <= ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1927_add__left__imp__eq)). 120.83/55.32 thf(7879,plain,((! [A:$i,B:$i,C:$i]: ((C = B) | ~ ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[858])). 120.83/55.32 thf(26,axiom,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ uminus473333897omplex @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4100_Im_Ominus)). 120.83/55.32 thf(5030,plain,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ uminus473333897omplex @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 120.83/55.32 thf(1207,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ B)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3207_div__Suc__eq__div__add3)). 120.83/55.32 thf(9082,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ B)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207])). 120.83/55.32 thf(4675,axiom,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5140_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J)). 120.83/55.32 thf(21496,plain,((hBOOL @ (hAPP_int_bool @ nat_is_nat @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4675])). 120.83/55.32 thf(3381,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_mult__mono_H)). 120.83/55.32 thf(16695,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3381])). 120.83/55.32 thf(3764,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ zero_zero_int) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2474_div__0)). 120.83/55.32 thf(17996,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ zero_zero_int) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3764])). 120.83/55.32 thf(4767,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_Euler_Oaux2)). 120.83/55.32 thf(21863,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4767])). 120.83/55.32 thf(2166,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_nat_nat @ semiri984289939at_nat @ B) = (hAPP_nat_nat @ semiri984289939at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2830_of__nat__eq__iff)). 120.83/55.32 thf(12396,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_nat_nat @ semiri984289939at_nat @ B) = (hAPP_nat_nat @ semiri984289939at_nat @ A))) & (((hAPP_nat_nat @ semiri984289939at_nat @ B) = (hAPP_nat_nat @ semiri984289939at_nat @ A)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166])). 120.83/55.32 thf(3238,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2908_zero__le__imp__of__nat)). 120.83/55.32 thf(16234,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3238])). 120.83/55.32 thf(3853,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f1791153283t_bool @ (hAPP_f1399575567t_bool @ cOMBB_118231410ol_int @ A) @ B) @ C) = (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_)). 120.83/55.32 thf(18318,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f1791153283t_bool @ (hAPP_f1399575567t_bool @ cOMBB_118231410ol_int @ A) @ B) @ C) = (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3853])). 120.83/55.32 thf(1821,axiom,((! [A:$i,B:$i]: ((((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) <=> ((B = zero_zero_rat) & (A = zero_zero_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2164_add__nonneg__eq__0__iff)). 120.83/55.32 thf(11257,plain,((! [A:$i,B:$i]: ((((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) => ((B = zero_zero_rat) & (A = zero_zero_rat))) & (((B = zero_zero_rat) & (A = zero_zero_rat)) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821])). 120.83/55.32 thf(1379,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2156_add__increasing)). 120.83/55.32 thf(9683,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379])). 120.83/55.32 thf(4265,axiom,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ (hAPP_int_int @ bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1581_diff__bin__simps_I5_J)). 120.83/55.32 thf(19893,plain,((! [A:$i]: ((hAPP_int_int @ bit1 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ min) @ (hAPP_int_int @ bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4265])). 120.83/55.32 thf(3508,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2584_div__power)). 120.83/55.32 thf(17092,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3508])). 120.83/55.32 thf(1776,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2004_add__mono)). 120.83/55.32 thf(11109,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776])). 120.83/55.32 thf(2541,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zEven)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3097_odd__minus__odd)). 120.83/55.32 thf(13774,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zOdd)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A)) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2541])). 120.83/55.32 thf(4878,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))) <= (C != zero_zero_int)) <= (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2624_div__mult__self2)). 120.83/55.32 thf(22231,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C))) | (C = zero_zero_int) | ~ (is_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4878])). 120.83/55.32 thf(513,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_lcm @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (nat_gcd @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4610_Nitpick_Onat__lcm__def)). 120.83/55.32 thf(6653,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_lcm @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (nat_gcd @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 120.83/55.32 thf(936,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1430_power__gt1__lemma)). 120.83/55.32 thf(8148,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ one_on1684967323de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[936])). 120.83/55.32 thf(1794,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3110_power__le__imp__le__base)). 120.83/55.32 thf(11180,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794])). 120.83/55.32 thf(2576,axiom,((! [A:$i]: ((((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & (((hAPP_int_nat @ number_number_of_nat @ A) != zero_zero_nat) => (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_power__0__left__number__of)). 120.83/55.32 thf(13880,plain,((! [A:$i]: ((((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) => (one_one_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((~ ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) => (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2576])). 120.83/55.32 thf(3849,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_le__special_I4_J)). 120.83/55.32 thf(18307,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3849])). 120.83/55.32 thf(779,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2578_div__add)). 120.83/55.32 thf(7583,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 120.83/55.32 thf(4327,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => ((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (((D != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B))) <= (is_int @ F)))))) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C) != A) <= (D != A))))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5097_aset_I4_J)). 120.83/55.32 thf(20137,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => ((! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) | ~ (is_int @ F)))))) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C) = A) | (D = A))))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4327])). 120.83/55.32 thf(966,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != (hAPP_int_nat @ number_number_of_nat @ B)) & (A = zero_z126310315umeral)) <=> ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_power__eq__0__iff__number__of)). 120.83/55.32 thf(8248,plain,((! [A:$i,B:$i]: (((~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ B)) & (A = zero_z126310315umeral)) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z126310315umeral)) & (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)) = zero_z126310315umeral) => (~ (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ B)) & (A = zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])). 120.83/55.32 thf(3941,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_power__mult__distrib)). 120.83/55.32 thf(18625,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3941])). 120.83/55.32 thf(1802,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_int_int @ (div_mod_int @ B) @ D) = (hAPP_int_int @ (div_mod_int @ A) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ B)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ D))) <= ((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2401_mod__mult__cong)). 120.83/55.32 thf(11198,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_int_int @ (div_mod_int @ B) @ D) = (hAPP_int_int @ (div_mod_int @ A) @ D)) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ E) @ B)) @ D) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ D))) | ~ ((hAPP_int_int @ (div_mod_int @ E) @ D) = (hAPP_int_int @ (div_mod_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802])). 120.83/55.32 thf(1211,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2252_minf_I10_J)). 120.83/55.32 thf(9093,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211])). 120.83/55.32 thf(1072,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = B) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1614_add__eq__self__zero)). 120.83/55.32 thf(8644,plain,((! [A:$i,B:$i]: ((zero_zero_nat = B) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072])). 120.83/55.32 thf(12,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3991_complex__of__real__mult__Complex)). 120.83/55.32 thf(4982,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 120.83/55.32 thf(4927,axiom,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1502__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096)). 120.83/55.32 thf(22395,plain,(((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ number_number_of_int @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4927])). 120.83/55.32 thf(3388,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int) = (archim856651990g_real @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4376_ceiling__eq2)). 120.83/55.32 thf(16710,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int) = (archim856651990g_real @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ A)) @ one_one_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3388])). 120.83/55.32 thf(2640,axiom,((! [A:$i,B:$i]: ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_P1975530577nt_int @ negateSnd @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4189_negateSnd__eq)). 120.83/55.32 thf(14143,plain,((! [A:$i,B:$i]: ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_P1975530577nt_int @ negateSnd @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2640])). 120.83/55.32 thf(4626,axiom,(((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ one_one_rat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_one__power2)). 120.83/55.32 thf(21324,plain,(((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ one_one_rat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4626])). 120.83/55.32 thf(1473,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1444_power__strict__increasing)). 120.83/55.32 thf(10012,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473])). 120.83/55.32 thf(1764,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3905_real__root__less__iff)). 120.83/55.32 thf(11049,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764])). 120.83/55.32 thf(4904,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2681_Euler__part3)). 120.83/55.32 thf(22327,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4904])). 120.83/55.32 thf(3776,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_nat__number__of__mult__left)). 120.83/55.32 thf(18032,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B)))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ B))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3776])). 120.83/55.32 thf(3008,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_mult__2__right)). 120.83/55.32 thf(15411,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3008])). 120.83/55.32 thf(652,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = C) | (D = B)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_crossproduct__eq)). 120.83/55.32 thf(7127,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((A = C) | (D = B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ D)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D))) => ((A = C) | (D = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])). 120.83/55.32 thf(3212,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4378_real__of__int__less__iff)). 120.83/55.32 thf(16126,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3212])). 120.83/55.32 thf(2667,axiom,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ minus_534354567de_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4562_minus__code__int__def)). 120.83/55.32 thf(14226,plain,((! [A:$i,B:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (quickcheck_int_of @ A)) @ (quickcheck_int_of @ B))) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ minus_534354567de_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2667])). 120.83/55.32 thf(3569,axiom,((! [A:$i,B:$i]: (((zero_zero_rat = B) & (zero_zero_rat = A)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_sum__squares__le__zero__iff)). 120.83/55.32 thf(17283,plain,((! [A:$i,B:$i]: ((((zero_zero_rat = B) & (zero_zero_rat = A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B))) @ zero_zero_rat)) => ((zero_zero_rat = B) & (zero_zero_rat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3569])). 120.83/55.32 thf(4851,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) => (B = zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1459_zcong__zless__0)). 120.83/55.32 thf(22156,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) => (B = zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4851])). 120.83/55.32 thf(2714,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1544_right__diff__distrib__number__of)). 120.83/55.32 thf(14389,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2714])). 120.83/55.32 thf(1458,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2046_add__strict__mono)). 120.83/55.32 thf(9963,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458])). 120.83/55.32 thf(4945,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2649_Euler_Oaux__2)). 120.83/55.32 thf(22454,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4945])). 120.83/55.32 thf(2652,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3156_realpow__Suc__le__self)). 120.83/55.32 thf(14179,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2652])). 120.83/55.32 thf(3688,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_mult__nonneg__nonneg)). 120.83/55.32 thf(17730,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3688])). 120.83/55.32 thf(2772,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3055_less__add__Suc2)). 120.83/55.32 thf(14589,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2772])). 120.83/55.32 thf(3146,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3061_le__imp__less__Suc)). 120.83/55.32 thf(15888,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3146])). 120.83/55.32 thf(3689,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_split__mult__neg__le)). 120.83/55.32 thf(17732,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3689])). 120.83/55.32 thf(154,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3823_exp__le__cancel__iff)). 120.83/55.32 thf(5450,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 120.83/55.32 thf(376,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ B)) @ one_one_real)) => (((hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ arctan @ B)) @ (hAPP_real_real @ arctan @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3408_arctan__add)). 120.83/55.32 thf(6206,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ B)) @ one_one_real)) => (((hAPP_real_real @ arctan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ arctan @ B)) @ (hAPP_real_real @ arctan @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 120.83/55.32 thf(4471,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) <=> ((B != zero_zero_nat) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3090_even__power)). 120.83/55.32 thf(20685,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) => (~ (B = zero_zero_nat) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))) & ((~ (B = zero_zero_nat) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4471])). 120.83/55.32 thf(3017,axiom,((! [A:$i,B:$i]: ((zero_zero_nat != B) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1609_gr__implies__not0)). 120.83/55.32 thf(15443,plain,((! [A:$i,B:$i]: (~ (zero_zero_nat = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3017])). 120.83/55.32 thf(4608,axiom,((one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ one_on1645066479umeral) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_one__power2)). 120.83/55.32 thf(21266,plain,((one_on1645066479umeral = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ one_on1645066479umeral) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4608])). 120.83/55.32 thf(625,axiom,((! [A:$i]: ((natfloor @ A) = (hAPP_int_nat @ nat @ (archim1246769320r_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4021_natfloor__def)). 120.83/55.32 thf(7009,plain,((! [A:$i]: ((natfloor @ A) = (hAPP_int_nat @ nat @ (archim1246769320r_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])). 120.83/55.32 thf(709,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1914_add__right__imp__eq)). 120.83/55.32 thf(7319,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 120.83/55.32 thf(2944,axiom,((! [A:$i]: (((! [B:$i]: (A != (hAPP_nat_int @ semiri1621563631at_int @ B))) => (~ (! [B:$i]: (A != (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ B))))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4547_int__cases)). 120.83/55.32 thf(15184,plain,((! [A:$i]: (((! [B:$i]: ~ (A = (hAPP_nat_int @ semiri1621563631at_int @ B))) => (~ (! [B:$i]: ~ (A = (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ B))))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2944])). 120.83/55.32 thf(3893,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_rel__simps_I2_J)). 120.83/55.32 thf(18456,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3893])). 120.83/55.32 thf(1976,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4171_prime__dvd__mult)). 120.83/55.32 thf(11788,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976])). 120.83/55.32 thf(3825,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_semiring__mult__2__right)). 120.83/55.32 thf(18202,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3825])). 120.83/55.32 thf(4055,axiom,((! [A:$i,B:$i]: (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <=> ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3458_power2__eq__iff__abs__eq)). 120.83/55.32 thf(19061,plain,((! [A:$i,B:$i]: ((((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ B))) & (((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ B)) => ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4055])). 120.83/55.32 thf(1636,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3588_cos__gt__zero)). 120.83/55.32 thf(10608,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636])). 120.83/55.32 thf(4422,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1944_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.32 thf(20489,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4422])). 120.83/55.32 thf(4221,axiom,((! [A:$i]: (((hAPP_int_int @ abs_abs_int @ A) = one_one_int) <= (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3463_power2__eq1__iff)). 120.83/55.32 thf(19712,plain,((! [A:$i]: (((hAPP_int_int @ abs_abs_int @ A) = one_one_int) | ~ (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4221])). 120.83/55.32 thf(2375,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A)) = (big_co1705425894at_nat @ cOMBI_nat @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5083_fact__div__fact)). 120.83/55.32 thf(13172,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ fact_fact_nat @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ A)) = (big_co1705425894at_nat @ cOMBI_nat @ (hAPP_n1699378549t_bool @ (ord_at238088361st_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375])). 120.83/55.32 thf(3229,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (? [B:$i]: ((hAPP_nat_nat @ suc @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3265_gr0__implies__Suc)). 120.83/55.32 thf(16206,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (? [B:$i]: ((hAPP_nat_nat @ suc @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3229])). 120.83/55.32 thf(4104,axiom,((! [A:$i]: ((! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))) <=> (! [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2708_all__nat)). 120.83/55.32 thf(19295,plain,((! [A:$i]: (((! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))) => (! [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B)))) & ((! [B:$i]: (hBOOL @ (hAPP_nat_bool @ A @ B))) => (! [B:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4104])). 120.83/55.32 thf(1084,axiom,((! [A:$i,B:$i]: ((B = A) <= ((quotient_of @ B) = (quotient_of @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4654_quotient__of__inject)). 120.83/55.32 thf(8679,plain,((! [A:$i,B:$i]: ((B = A) | ~ ((quotient_of @ B) = (quotient_of @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084])). 120.83/55.32 thf(1027,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3824_exp__less__cancel)). 120.83/55.32 thf(8464,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027])). 120.83/55.32 thf(4413,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4997_coprime__lmult__int)). 120.83/55.32 thf(20457,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4413])). 120.83/55.32 thf(57,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) <=> ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ C)) | (zero_zero_real = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1267_dvd__mult__cancel__right)). 120.83/55.32 thf(5147,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ C)) | (zero_zero_real = B))) & (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ C)) | (zero_zero_real = B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 120.83/55.32 thf(456,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3716_cos__npi2)). 120.83/55.32 thf(6457,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ pi) @ (hAPP_nat_real @ real_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 120.83/55.32 thf(2871,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ tan @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (zero_zero_real != (hAPP_real_real @ cos @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3878_DERIV__tan)). 120.83/55.32 thf(14938,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ tan @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | (zero_zero_real = (hAPP_real_real @ cos @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2871])). 120.83/55.32 thf(1216,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1728_dvd_Oless__asym)). 120.83/55.32 thf(9109,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216])). 120.83/55.32 thf(3357,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1475_power__strict__decreasing)). 120.83/55.32 thf(16607,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3357])). 120.83/55.32 thf(512,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ zero_zero_nat) @ A) = (divmod_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4210_divmod__nat__base)). 120.83/55.32 thf(6650,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ zero_zero_nat) @ A) = (divmod_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 120.83/55.32 thf(302,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3477_abs__ln__one__plus__x__minus__x__bound__nonpos)). 120.83/55.32 thf(5949,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 120.83/55.32 thf(3092,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2685_div__mult1__eq)). 120.83/55.32 thf(15704,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3092])). 120.83/55.32 thf(2230,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2861_less__antisym)). 120.83/55.32 thf(12647,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230])). 120.83/55.32 thf(369,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.32 thf(6188,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 120.83/55.32 thf(1094,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2125_mult__1__left)). 120.83/55.32 thf(8729,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ one_one_rat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094])). 120.83/55.32 thf(1774,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1699_dvd_Oeq__iff)). 120.83/55.32 thf(11094,plain,((! [A:$i,B:$i]: (((A = B) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774])). 120.83/55.32 thf(4540,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ A) = (hAPP_int_int @ (div_mod_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2429_mod__add__self1)). 120.83/55.32 thf(20974,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ A) = (hAPP_int_int @ (div_mod_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4540])). 120.83/55.32 thf(3128,axiom,((! [A:$i,B:$i]: (((one_one_real = A) <=> (one_one_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3911_real__root__eq__1__iff)). 120.83/55.32 thf(15828,plain,((! [A:$i,B:$i]: ((((one_one_real = A) => (one_one_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) & ((one_one_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) => (one_one_real = A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3128])). 120.83/55.32 thf(857,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (? [C:$i]: (B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3262_less__imp__Suc__add)). 120.83/55.32 thf(7876,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (? [C:$i]: (B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[857])). 120.83/55.32 thf(2485,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3019_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.32 thf(13570,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2485])). 120.83/55.32 thf(3858,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3520_uminus__dvd__conv_I1_J)). 120.83/55.32 thf(18330,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3858])). 120.83/55.32 thf(2964,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.32 thf(15241,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ C)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2964])). 120.83/55.32 thf(4281,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ one_one_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ number_number_of_int @ min)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_zcong__neg__1__impl__ne__1)). 120.83/55.32 thf(19952,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ one_one_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ number_number_of_int @ min)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4281])). 120.83/55.32 thf(3647,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3114_power__le__imp__le__base)). 120.83/55.32 thf(17570,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3647])). 120.83/55.32 thf(3431,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_zero__le__even__power_H)). 120.83/55.32 thf(16839,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3431])). 120.83/55.32 thf(287,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3414_abs__ln__one__plus__x__minus__x__bound)). 120.83/55.32 thf(5902,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 120.83/55.32 thf(417,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ C) @ A)))) <= (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1517_dvd__diff)). 120.83/55.32 thf(6337,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ C) @ A)))) | ~ (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 120.83/55.32 thf(3507,axiom,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (collect_int @ (hAPP_i1948725293t_bool @ (hAPP_f428220345t_bool @ cOMBC_int_int_bool @ dvd_dvd_int) @ A)))) <= (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4753_finite__divisors__int)). 120.83/55.32 thf(17089,plain,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (collect_int @ (hAPP_i1948725293t_bool @ (hAPP_f428220345t_bool @ cOMBC_int_int_bool @ dvd_dvd_int) @ A)))) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3507])). 120.83/55.32 thf(521,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4384_powr__powr__swap)). 120.83/55.32 thf(6679,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 120.83/55.32 thf(4759,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ nat @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3554_neg__even__power)). 120.83/55.32 thf(21843,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_nat @ nat @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4759])). 120.83/55.32 thf(1962,axiom,(((hAPP_int_nat @ nat @ one_one_int) = (hAPP_nat_nat @ suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3136_nat__1)). 120.83/55.32 thf(11749,plain,(((hAPP_int_nat @ nat @ one_one_int) = (hAPP_nat_nat @ suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962])). 120.83/55.32 thf(4534,axiom,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ min) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4048_add__Min)). 120.83/55.32 thf(20938,plain,((! [A:$i]: ((hAPP_int_int @ pred @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ min) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4534])). 120.83/55.32 thf(3511,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_comm__semiring__class_Odistrib)). 120.83/55.32 thf(17099,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3511])). 120.83/55.32 thf(6,axiom,((zero_zero_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3958_complex__zero__def)). 120.83/55.32 thf(4959,plain,((zero_zero_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 120.83/55.32 thf(713,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E)) <=> ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ A)) @ B)) @ E) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1538_eq__add__iff2)). 120.83/55.32 thf(7331,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ A)) @ B)) @ E) = C)) & (((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ D) @ A)) @ B)) @ E) = C) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ D) @ B)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])). 120.83/55.32 thf(1621,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5119_min__number__of__Suc)). 120.83/55.32 thf(10558,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621])). 120.83/55.32 thf(340,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => ((! [E:$i]: ((E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => ((? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ B @ E)) @ (hAPP_real_real @ B @ C))))) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5181_lemma__isCont__inj2)). 120.83/55.32 thf(6073,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => ((! [E:$i]: ((E = (hAPP_real_real @ A @ (hAPP_real_real @ B @ E))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ B @ E)) @ (hAPP_real_real @ B @ C)))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 120.83/55.32 thf(207,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3840_one__le__exp__iff)). 120.83/55.32 thf(5628,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 120.83/55.32 thf(239,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4451_real__of__int__floor__add__one__ge)). 120.83/55.32 thf(5736,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 120.83/55.32 thf(3572,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1478_power__strict__decreasing)). 120.83/55.32 thf(17308,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3572])). 120.83/55.32 thf(870,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3367_real__sum__of__halves)). 120.83/55.32 thf(7921,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[870])). 120.83/55.32 thf(3816,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1131_comm__mult__strict__left__mono)). 120.83/55.32 thf(18170,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3816])). 120.83/55.32 thf(2271,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) @ C)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_P1975530577nt_int @ negateSnd @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4190_divmod__int__rel__neg)). 120.83/55.32 thf(12790,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) @ C)) => (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_P1975530577nt_int @ negateSnd @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271])). 120.83/55.32 thf(3315,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1603_power__dvd__imp__le)). 120.83/55.32 thf(16475,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3315])). 120.83/55.32 thf(1724,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) <=> (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1939_add__left__cancel)). 120.83/55.32 thf(10885,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) => (B = C)) & ((B = C) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724])). 120.83/55.32 thf(760,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2099_mult_Ocomm__neutral)). 120.83/55.32 thf(7515,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 120.83/55.32 thf(869,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4294_Bnor__fin)). 120.83/55.32 thf(7919,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])). 120.83/55.32 thf(1058,axiom,((one_one_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4672_rat__number__collapse_I2_J)). 120.83/55.32 thf(8564,plain,((one_one_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058])). 120.83/55.32 thf(2676,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2872_Suc__le__mono)). 120.83/55.32 thf(14252,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2676])). 120.83/55.32 thf(4185,axiom,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ min)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_rel__simps_I7_J)). 120.83/55.32 thf(19569,plain,((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ min)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4185])). 120.83/55.32 thf(120,axiom,((! [A:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (quickcheck_int_of @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4555_int__of__inverse)). 120.83/55.32 thf(5347,plain,((! [A:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (quickcheck_int_of @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 120.83/55.32 thf(4474,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3283_power__nat__number__of__number__of)). 120.83/55.32 thf(20699,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4474])). 120.83/55.32 thf(1510,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_mult__numeral__1__right)). 120.83/55.32 thf(10128,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510])). 120.83/55.32 thf(1225,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_dvd__triv__right)). 120.83/55.32 thf(9151,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225])). 120.83/55.32 thf(4569,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.32 thf(21135,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4569])). 120.83/55.32 thf(412,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: (((hAPP_real_real @ A @ (hAPP_real_real @ B @ E)) = E) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => ((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ B @ C)) @ (hAPP_real_real @ B @ E))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5182_lemma__isCont__inj)). 120.83/55.32 thf(6318,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: (((hAPP_real_real @ A @ (hAPP_real_real @ B @ E)) = E) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => ((! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ B) @ E)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ E) @ C))) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ B @ C)) @ (hAPP_real_real @ B @ E))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 120.83/55.32 thf(3876,axiom,(((hAPP_int_int @ bit1 @ pls) = (hAPP_int_int @ uminus_uminus_int @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3538_minus__Min)). 120.83/55.32 thf(18394,plain,(((hAPP_int_int @ bit1 @ pls) = (hAPP_int_int @ uminus_uminus_int @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3876])). 120.83/55.32 thf(10,axiom,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ ii)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3982_Complex__mult__i)). 120.83/55.32 thf(4976,plain,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ ii)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 120.83/55.32 thf(3085,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1739_minus__nat_Odiff__0)). 120.83/55.32 thf(15677,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3085])). 120.83/55.32 thf(2817,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) <=> (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1594_nat__add__left__cancel)). 120.83/55.32 thf(14755,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) => (B = C)) & ((B = C) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2817])). 120.83/55.32 thf(2705,axiom,((! [A:$i,B:$i]: ((B != zero_zero_real) => ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_field__power__not__zero)). 120.83/55.32 thf(14359,plain,((! [A:$i,B:$i]: ((~ (B = zero_zero_real)) => (~ ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2705])). 120.83/55.32 thf(4831,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3240_even__sum__div__2)). 120.83/55.32 thf(22087,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4831])). 120.83/55.32 thf(3485,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A)) => (((image_int_nat @ nat @ B) = (image_int_nat @ nat @ A)) <=> (A = B))) <= (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4616_transfer__int__nat__set__relations_I3_J)). 120.83/55.32 thf(17027,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ A)) => ((((image_int_nat @ nat @ B) = (image_int_nat @ nat @ A)) => (A = B)) & ((A = B) => ((image_int_nat @ nat @ B) = (image_int_nat @ nat @ A))))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3485])). 120.83/55.32 thf(685,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_dvd__power__same)). 120.83/55.32 thf(7251,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 120.83/55.32 thf(554,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2778_transfer__morphismI)). 120.83/55.32 thf(6775,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_f448129468l_bool @ (nat_tr876908586nt_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 120.83/55.32 thf(3130,axiom,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.32 thf(15837,plain,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3130])). 120.83/55.32 thf(202,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4465_real__of__int__div3)). 120.83/55.32 thf(5613,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 120.83/55.32 thf(427,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ C))) <= (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ E)) & (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4550_DERIV__nonneg__imp__nonincreasing)). 120.83/55.32 thf(6369,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ C))) | ~ (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ E)) & (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 120.83/55.32 thf(3147,axiom,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_power__m1__even)). 120.83/55.32 thf(15890,plain,((! [A:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_int_rat @ number_number_of_rat @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3147])). 120.83/55.32 thf(2290,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2816_Suc__mono)). 120.83/55.32 thf(12868,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290])). 120.83/55.32 thf(2277,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1871_add__strict__increasing)). 120.83/55.32 thf(12811,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2277])). 120.83/55.32 thf(4887,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ upto_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ upto_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int)) @ E))))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4573_upto_Opinduct)). 120.83/55.32 thf(22262,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ upto_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((! [D:$i,E:$i]: (((is_int @ E) & (is_int @ D)) => ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ upto_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int)) @ E))))))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4887])). 120.83/55.32 thf(789,axiom,((! [A:$i,B:$i,C:$i]: ((C = A) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1910_add__right__imp__eq)). 120.83/55.32 thf(7621,plain,((! [A:$i,B:$i,C:$i]: ((C = A) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 120.83/55.32 thf(171,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2352_div__mod__equality2)). 120.83/55.32 thf(5504,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 120.83/55.32 thf(2376,axiom,((! [A:$i]: ((! [B:$i]: ? [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3751_reals__Archimedean3)). 120.83/55.32 thf(13175,plain,((! [A:$i]: (! [B:$i]: ? [C:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376])). 120.83/55.32 thf(1258,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))) <=> ((zero_zero_nat != A) | (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4344_gcd__pos__nat)). 120.83/55.32 thf(9257,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))) => (~ (zero_zero_nat = A) | ~ (B = zero_zero_nat))) & ((~ (zero_zero_nat = A) | ~ (B = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258])). 120.83/55.32 thf(3365,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat) <=> ((one_one_nat = B) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1660_nat__mult__eq__1__iff)). 120.83/55.32 thf(16631,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat) => ((one_one_nat = B) & (A = one_one_nat))) & (((one_one_nat = B) & (A = one_one_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3365])). 120.83/55.32 thf(2948,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2261_minf_I9_J)). 120.83/55.32 thf(15196,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2948])). 120.83/55.32 thf(1453,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [C:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) & ! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) & ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ B) = A)) => (D = C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1827_realpow__pos__nth__unique)). 120.83/55.32 thf(9947,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [C:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) & ! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) & ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ D) @ B) = A)) => (D = C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453])). 120.83/55.32 thf(3115,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.32 thf(15790,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3115])). 120.83/55.32 thf(15,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (of_real_complex @ C)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3992_Complex__add__complex__of__real)). 120.83/55.32 thf(4991,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) @ (of_real_complex @ C)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 120.83/55.32 thf(371,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4456_real__of__int__floor__gt__diff__one)). 120.83/55.32 thf(6193,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ one_one_real)) @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 120.83/55.32 thf(4289,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) <= (hBOOL @ (hAPP_int_bool @ B @ D))))) <= (! [D:$i]: (((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))) <= (hBOOL @ (hAPP_int_bool @ B @ D))) <= (is_int @ D)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1692_incr__mult__lemma)). 120.83/55.32 thf(19976,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D))))) | ~ (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ B @ D)) | ~ (is_int @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4289])). 120.83/55.32 thf(2851,axiom,((! [A:$i,B:$i]: (((one_one_nat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4188_prime__coprime)). 120.83/55.32 thf(14868,plain,((! [A:$i,B:$i]: ((one_one_nat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2851])). 120.83/55.32 thf(4446,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1310_zcong__not)). 120.83/55.32 thf(20575,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4446])). 120.83/55.32 thf(4232,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2595_zdiv__mono1__neg)). 120.83/55.32 thf(19742,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4232])). 120.83/55.32 thf(4263,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2812_of__nat__double)). 120.83/55.32 thf(19888,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ A))) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4263])). 120.83/55.32 thf(208,axiom,((! [A:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (archim1246769320r_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ real_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4033_floor__minus__real__of__nat)). 120.83/55.32 thf(5633,plain,((! [A:$i]: ((hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (archim1246769320r_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ real_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 120.83/55.32 thf(4395,axiom,(((hAPP_int_int @ uminus_uminus_int @ pls) = pls)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3512_minus__Pls)). 120.83/55.32 thf(20385,plain,(((hAPP_int_int @ uminus_uminus_int @ pls) = pls)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4395])). 120.83/55.32 thf(661,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ exp_real @ one_one_real))) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3882_log__base__10__eq2)). 120.83/55.32 thf(7163,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ exp_real @ one_one_real))) @ (hAPP_real_real @ ln @ A)) = (hAPP_real_real @ (log @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])). 120.83/55.32 thf(4452,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((C != zero_zero_int) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => ((big_co1548731110nt_int @ cOMBI_int @ (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ C) @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4812_Bnor__prod__power)). 120.83/55.32 thf(20599,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((~ (C = zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => ((big_co1548731110nt_int @ cOMBI_int @ (image_int_int @ (hAPP_int_fun_int_int @ (hAPP_f2135977429nt_int @ cOMBC_int_int_int @ times_times_int) @ C) @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4452])). 120.83/55.32 thf(2753,axiom,((! [A:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3342_real__sqrt__pow2__iff)). 120.83/55.32 thf(14507,plain,((! [A:$i]: (((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2753])). 120.83/55.32 thf(703,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2170_add__nonneg__nonneg)). 120.83/55.32 thf(7303,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 120.83/55.32 thf(1363,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.32 thf(9632,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363])). 120.83/55.32 thf(3402,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4178_prime__coprime__strong)). 120.83/55.32 thf(16749,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ B) @ A)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3402])). 120.83/55.32 thf(2877,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) <= (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ C))) => (hBOOL @ (hAPP_nat_bool @ A @ C))))) <= (hBOOL @ (hAPP_nat_bool @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3310_zero__induct)). 120.83/55.32 thf(14955,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) | ~ (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ C))) => (hBOOL @ (hAPP_nat_bool @ A @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2877])). 120.83/55.32 thf(1655,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ B)) <= (zero_zero_nat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4345_gcd__le1__nat)). 120.83/55.32 thf(10663,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) @ B)) | (zero_zero_nat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655])). 120.83/55.32 thf(3928,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => (((negDivAlg @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2376_negDivAlg__div__mod)). 120.83/55.32 thf(18574,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => (((negDivAlg @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ (hAPP_int_int @ (div_mod_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3928])). 120.83/55.32 thf(4214,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (C = B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1312_zcong__less__eq)). 120.83/55.32 thf(19688,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (C = B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4214])). 120.83/55.32 thf(1466,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ d22set @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2266_d22set__le)). 120.83/55.32 thf(9983,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ d22set @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466])). 120.83/55.32 thf(4929,axiom,((one_one_complex = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_semiring__numeral__1__eq__1)). 120.83/55.32 thf(22401,plain,((one_one_complex = (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4929])). 120.83/55.32 thf(4882,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ B) | (hBOOL @ (fdisj @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U)). 120.83/55.32 thf(22247,plain,((! [A:$i,B:$i]: (~ (hBOOL @ B) | (hBOOL @ (fdisj @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4882])). 120.83/55.32 thf(1553,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3126_one__less__mult)). 120.83/55.32 thf(10283,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553])). 120.83/55.32 thf(3461,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) <=> (A = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1284_power__inject__exp)). 120.83/55.32 thf(16934,plain,((! [A:$i,B:$i,C:$i]: (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) => (A = B)) & ((A = B) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3461])). 120.83/55.32 thf(786,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.32 thf(7612,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])). 120.83/55.32 thf(4012,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = one_one_int) => ((hAPP_int_int @ abs_abs_int @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3421_abs__zmult__eq__1)). 120.83/55.32 thf(18879,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) = one_one_int) => ((hAPP_int_int @ abs_abs_int @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4012])). 120.83/55.32 thf(4408,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_mult__less__cancel__left__neg)). 120.83/55.32 thf(20442,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4408])). 120.83/55.32 thf(1842,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_mult__2)). 120.83/55.32 thf(11349,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842])). 120.83/55.32 thf(1360,axiom,((one_one_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4671_one__rat)). 120.83/55.32 thf(9622,plain,((one_one_rat = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ one_one_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360])). 120.83/55.32 thf(1989,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__special_I2_J)). 120.83/55.32 thf(11825,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ (hAPP_int_rat @ number_number_of_rat @ A)) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989])). 120.83/55.32 thf(1187,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_dvd__mult2)). 120.83/55.32 thf(9019,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187])). 120.83/55.32 thf(1022,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.32 thf(8449,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ C) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022])). 120.83/55.32 thf(1711,axiom,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ (hAPP_int_complex @ number528085621omplex @ A))) @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_number__of__Bit0)). 120.83/55.32 thf(10841,plain,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ (hAPP_int_complex @ number528085621omplex @ A))) @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711])). 120.83/55.32 thf(1297,axiom,((! [A:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3668_real__of__nat__Suc)). 120.83/55.32 thf(9406,plain,((! [A:$i]: ((hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297])). 120.83/55.32 thf(2315,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D != zero_z126310315umeral) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ D) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A)) => (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ D) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)) <=> ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))))) <= (C != zero_z126310315umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2636_dvd__div__div__eq__mult)). 120.83/55.32 thf(12952,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (D = zero_z126310315umeral)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ D) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A)) => ((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ D) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C))) & (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ D) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)))))) | (C = zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315])). 120.83/55.32 thf(925,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4311_gcd__assoc__nat)). 120.83/55.32 thf(8108,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])). 120.83/55.32 thf(3785,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2614_pos__mod__conj)). 120.83/55.32 thf(18066,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3785])). 120.83/55.32 thf(3137,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.32 thf(15860,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3137])). 120.83/55.32 thf(2450,axiom,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ zero_zero_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.32 thf(13460,plain,((! [A:$i]: (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ zero_zero_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450])). 120.83/55.32 thf(2232,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3037_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.32 thf(12652,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232])). 120.83/55.32 thf(3003,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3473_ln__one__plus__pos__lower__bound)). 120.83/55.32 thf(15397,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3003])). 120.83/55.32 thf(595,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ (of_real_complex @ (hAPP_complex_real @ norm_norm_complex @ A))) = (hAPP_complex_complex @ sgn_sgn_complex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3989_sgn__eq)). 120.83/55.32 thf(6917,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ (of_real_complex @ (hAPP_complex_real @ norm_norm_complex @ A))) = (hAPP_complex_complex @ sgn_sgn_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])). 120.83/55.32 thf(2516,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3497_realpow__square__minus__le)). 120.83/55.32 thf(13674,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516])). 120.83/55.32 thf(4575,axiom,((! [A:$i,B:$i]: ((((image_int_int @ (rRset2norRR @ A @ B) @ A) = (hAPP_i1948725293t_bool @ norRRset @ B)) <= (hBOOL @ (hAPP_int_bool @ (is_RRset @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4597_RRset2norRR__eq__norR)). 120.83/55.32 thf(21152,plain,((! [A:$i,B:$i]: (((image_int_int @ (rRset2norRR @ A @ B) @ A) = (hAPP_i1948725293t_bool @ norRRset @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (is_RRset @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4575])). 120.83/55.32 thf(3408,axiom,((! [A:$i]: ((is_int @ A) => ((one_one_int = A) <=> (one_one_int = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1950_one__reorient)). 120.83/55.32 thf(16781,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3408])). 120.83/55.32 thf(2120,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1702_dvd_Oless__le__not__le)). 120.83/55.32 thf(12241,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120])). 120.83/55.32 thf(1928,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_power__commutes)). 120.83/55.32 thf(11636,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928])). 120.83/55.32 thf(4431,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_mult__le__0__iff)). 120.83/55.32 thf(20519,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ zero_zero_int)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) | ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4431])). 120.83/55.32 thf(1017,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1989_add__0__left)). 120.83/55.32 thf(8433,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ zero_zero_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017])). 120.83/55.32 thf(2328,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1203_pos__add__strict)). 120.83/55.32 thf(13008,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328])). 120.83/55.32 thf(3837,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3236_even__div__2__l)). 120.83/55.32 thf(18246,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3837])). 120.83/55.32 thf(4755,axiom,((pls != min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_rel__simps_I40_J)). 120.83/55.32 thf(21828,plain,((~ (pls = min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4755])). 120.83/55.32 thf(2887,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => (! [D:$i,E:$i]: ((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A)))) <=> (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1534_inf__period_I4_J)). 120.83/55.32 thf(14992,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => (! [D:$i,E:$i]: (((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A)))) => (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A))))) & ((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ A)))) => (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ D) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ E) @ C))) @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2887])). 120.83/55.32 thf(42,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ sin @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3998_cmod__complex__polar)). 120.83/55.32 thf(5083,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (of_real_complex @ A)) @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ sin @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 120.83/55.32 thf(388,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ B) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2334_mod__div__trivial)). 120.83/55.32 thf(6245,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ B) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 120.83/55.32 thf(4371,axiom,(((hAPP_int_int @ bit1 @ min) = min)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_Bit1__Min)). 120.83/55.32 thf(20279,plain,(((hAPP_int_int @ bit1 @ min) = min)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4371])). 120.83/55.32 thf(471,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A)))) <=> (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1532_inf__period_I4_J)). 120.83/55.32 thf(6511,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i]: (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A)))) => (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A))))) & ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ E) @ C))) @ A)))) => (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ A)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 120.83/55.32 thf(362,axiom,(((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3611_tan__45)). 120.83/55.32 thf(6161,plain,(((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 120.83/55.32 thf(2814,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = (hAPP_nat_nat @ (nat_gcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4612_gcd__eq__nitpick__gcd)). 120.83/55.32 thf(14747,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = (hAPP_nat_nat @ (nat_gcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2814])). 120.83/55.32 thf(3182,axiom,((! [A:$i,B:$i]: ((~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1718_dvd_Oless__not__sym)). 120.83/55.32 thf(16014,plain,((! [A:$i,B:$i]: (~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3182])). 120.83/55.32 thf(4822,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) <=> ((hBOOL @ B) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ B) <=> (hBOOL @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1616_imp__le__cong)). 120.83/55.32 thf(22050,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => ((hBOOL @ B) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)))) & (((hBOOL @ B) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => ((hBOOL @ A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => (((hBOOL @ B) => (hBOOL @ A)) & ((hBOOL @ A) => (hBOOL @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4822])). 120.83/55.32 thf(45,axiom,((one_one_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ one_one_real) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3960_complex__one__def)). 120.83/55.32 thf(5100,plain,((one_one_complex = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ one_one_real) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 120.83/55.32 thf(4063,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2495_mod__mult__self2__is__0)). 120.83/55.32 thf(19137,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4063])). 120.83/55.32 thf(3762,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2883_Parity_Oeven__product)). 120.83/55.32 thf(17987,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) => ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) | (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3762])). 120.83/55.32 thf(196,axiom,((! [A:$i]: ((code_S1047413653umeral @ A) != zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4081_code__numeral_Osimps_I3_J)). 120.83/55.32 thf(5596,plain,((! [A:$i]: ~ ((code_S1047413653umeral @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 120.83/55.32 thf(4548,axiom,((! [A:$i]: (((hAPP_nat_nat @ suc @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3204_Suc__nat__eq__nat__zadd1)). 120.83/55.32 thf(21028,plain,((! [A:$i]: (((hAPP_nat_nat @ suc @ (hAPP_int_nat @ nat @ A)) = (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4548])). 120.83/55.32 thf(2019,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3401_natceiling__le__eq__one)). 120.83/55.32 thf(11906,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ one_one_nat))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ one_one_nat)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019])). 120.83/55.32 thf(2350,axiom,((! [A:$i,B:$i,C:$i]: ((((! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => ((hBOOL @ (hAPP_nat_bool @ A @ D)) <= (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ D)))))) => (hBOOL @ (hAPP_nat_bool @ A @ B))) <= (hBOOL @ (hAPP_nat_bool @ A @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3254_inc__induct)). 120.83/55.32 thf(13076,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => ((hBOOL @ (hAPP_nat_bool @ A @ D)) | ~ (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ suc @ D)))))) => (hBOOL @ (hAPP_nat_bool @ A @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ A @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350])). 120.83/55.32 thf(476,axiom,((! [A:$i]: (((? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= ((hAPP_real_real @ sin @ A) = zero_zero_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3793_sin__zero__lemma)). 120.83/55.32 thf(6531,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ ((hAPP_real_real @ sin @ A) = zero_zero_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 120.83/55.32 thf(2951,axiom,((! [A:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2312_gcd__lcm__complete__lattice__nat_Onot__less__bot)). 120.83/55.32 thf(15203,plain,((! [A:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ one_one_nat)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ one_one_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2951])). 120.83/55.32 thf(4650,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rel__simps_I15_J)). 120.83/55.32 thf(21423,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4650])). 120.83/55.32 thf(2982,axiom,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B))) & (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= ((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3545_zmod__zminus1__eq__if)). 120.83/55.32 thf(15319,plain,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B))) & (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2982])). 120.83/55.32 thf(3684,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2017_add__right__mono)). 120.83/55.32 thf(17721,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3684])). 120.83/55.32 thf(3998,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ C)) & ((hAPP_int_int @ abs_abs_int @ B) = (hAPP_int_int @ abs_abs_int @ D))) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ C)) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ D)))) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))) <= (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5014_coprime__crossproduct__int)). 120.83/55.32 thf(18823,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ C)) & ((hAPP_int_int @ abs_abs_int @ B) = (hAPP_int_int @ abs_abs_int @ D))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ C)) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ D)))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ C)) @ (hAPP_int_int @ abs_abs_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ D))) => (((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ abs_abs_int @ C)) & ((hAPP_int_int @ abs_abs_int @ B) = (hAPP_int_int @ abs_abs_int @ D))))) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)) | ~ (one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3998])). 120.83/55.32 thf(1875,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1668_nat__0__less__mult__iff)). 120.83/55.32 thf(11465,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875])). 120.83/55.32 thf(4785,axiom,(((hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit1 @ pls)) = one_on1645066479umeral)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3229_one__code__numeral__code)). 120.83/55.32 thf(21927,plain,(((hAPP_i769753017umeral @ number1443263063umeral @ (hAPP_int_int @ bit1 @ pls)) = one_on1645066479umeral)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4785])). 120.83/55.32 thf(1660,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2037_add__less__imp__less__left)). 120.83/55.32 thf(10680,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660])). 120.83/55.32 thf(2283,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2385_mod__mult__eq)). 120.83/55.32 thf(12829,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283])). 120.83/55.32 thf(4500,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ finite1395289673t_bool @ (setS @ A @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3370_SetS__finite)). 120.83/55.32 thf(20792,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ finite1395289673t_bool @ (setS @ A @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4500])). 120.83/55.32 thf(3651,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_int__0__less__1)). 120.83/55.32 thf(17589,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3651])). 120.83/55.32 thf(619,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4003_DERIV__pos__imp__increasing)). 120.83/55.32 thf(6992,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => ((! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])). 120.83/55.32 thf(2749,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_power__mult)). 120.83/55.32 thf(14496,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2749])). 120.83/55.32 thf(1753,axiom,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2346_mod__div__equality)). 120.83/55.32 thf(11017,plain,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ B)) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753])). 120.83/55.32 thf(1177,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 120.83/55.32 thf(8982,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177])). 120.83/55.32 thf(273,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ A)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ one_one_real)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3854_ln__x__over__x__mono)). 120.83/55.32 thf(5841,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ A)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ one_one_real)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 120.83/55.32 thf(1016,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3336_real__sqrt__mult__self__sum__ge__zero)). 120.83/55.32 thf(8431,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])). 120.83/55.32 thf(2352,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ zero_zero_nat))) & (hBOOL @ (hAPP_nat_bool @ A @ C)))) <=> (? [C:$i]: (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1681_unity__coeff__ex)). 120.83/55.32 thf(13082,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ zero_zero_nat))) & (hBOOL @ (hAPP_nat_bool @ A @ C)))) => (? [C:$i]: (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))) & ((? [C:$i]: (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ zero_zero_nat))) & (hBOOL @ (hAPP_nat_bool @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352])). 120.83/55.32 thf(504,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (cis @ B)) @ (cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))) = (cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4154_cis__real__of__nat__Suc__mult)). 120.83/55.32 thf(6622,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (cis @ B)) @ (cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))) = (cis @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ A))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 120.83/55.32 thf(3749,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_dvd__power__same)). 120.83/55.32 thf(17947,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3749])). 120.83/55.32 thf(4445,axiom,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)) = (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5080_atLeastLessThanPlusOne__atLeastAtMost__int)). 120.83/55.32 thf(20572,plain,((! [A:$i,B:$i]: ((hAPP_i1948725293t_bool @ (ord_at641636577an_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)) = (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4445])). 120.83/55.32 thf(1669,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1510_number__of__diff)). 120.83/55.32 thf(10714,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669])). 120.83/55.32 thf(3828,axiom,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ zero_zero_int) @ A) = (hAPP_int_int @ abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4506_zgcd__0__left)). 120.83/55.32 thf(18211,plain,((! [A:$i]: ((hAPP_int_int @ (legacy_zgcd @ zero_zero_int) @ A) = (hAPP_int_int @ abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3828])). 120.83/55.32 thf(3304,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1965_add_Ocomm__neutral)). 120.83/55.32 thf(16443,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3304])). 120.83/55.32 thf(4102,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3511_negative__zless)). 120.83/55.32 thf(19285,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A)))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4102])). 120.83/55.32 thf(252,axiom,((! [A:$i]: ((of_real_complex @ A) = (hAPP_complex_complex @ cnj @ (of_real_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4080_complex__cnj__complex__of__real)). 120.83/55.32 thf(5771,plain,((! [A:$i]: ((of_real_complex @ A) = (hAPP_complex_complex @ cnj @ (of_real_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 120.83/55.32 thf(1532,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A)))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_le__number__of__eq__not__less)). 120.83/55.32 thf(10214,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A)))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B))) => (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ B)) @ (hAPP_int_rat @ number_number_of_rat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532])). 120.83/55.32 thf(4100,axiom,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A)))) & ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3298_nat__number__of__add__1)). 120.83/55.32 thf(19275,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A)))) & ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4100])). 120.83/55.33 thf(2544,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2947_of__nat__le__iff)). 120.83/55.33 thf(13784,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2544])). 120.83/55.33 thf(681,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2343_mod__div__equality2)). 120.83/55.33 thf(7239,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 120.83/55.33 thf(2929,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3788_lemma__even__div2)). 120.83/55.33 thf(15131,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2929])). 120.83/55.33 thf(1131,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim856651990g_real @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4421_less__ceiling__eq)). 120.83/55.33 thf(8830,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim856651990g_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ real_int @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (archim856651990g_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131])). 120.83/55.33 thf(2740,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3918_real__root__ge__zero)). 120.83/55.33 thf(14464,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2740])). 120.83/55.33 thf(4523,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.33 thf(20888,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4523])). 120.83/55.33 thf(2733,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 120.83/55.33 thf(14447,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ C) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2733])). 120.83/55.33 thf(3479,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3726_sin__gt__zero2)). 120.83/55.33 thf(16998,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ sin @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3479])). 120.83/55.33 thf(400,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2295_mult_Oadd__left)). 120.83/55.33 thf(6286,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 120.83/55.33 thf(2969,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1773_le__diff__conv2)). 120.83/55.33 thf(15255,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2969])). 120.83/55.33 thf(3419,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_mult__nonneg__nonpos2)). 120.83/55.33 thf(16807,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3419])). 120.83/55.33 thf(643,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_real_real @ exp_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3853_exp__ge__add__one__self__aux)). 120.83/55.33 thf(7089,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A)) @ (hAPP_real_real @ exp_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])). 120.83/55.33 thf(3980,axiom,((! [A:$i,B:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2329_zmod__zdiv__trivial)). 120.83/55.33 thf(18762,plain,((! [A:$i,B:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3980])). 120.83/55.33 thf(2003,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ arcsin @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3881_DERIV__arcsin)). 120.83/55.33 thf(11864,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ arcsin @ A) @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003])). 120.83/55.33 thf(4892,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2985_zero__zle__int)). 120.83/55.33 thf(22280,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4892])). 120.83/55.33 thf(2620,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_power__mult__distrib)). 120.83/55.33 thf(14058,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ C)) @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2620])). 120.83/55.33 thf(3951,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1999_add__le__imp__le__right)). 120.83/55.33 thf(18651,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3951])). 120.83/55.33 thf(1192,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3921_real__root__gt__zero)). 120.83/55.33 thf(9046,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192])). 120.83/55.33 thf(2002,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2149_add__increasing2)). 120.83/55.33 thf(11862,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002])). 120.83/55.33 thf(4777,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_mult__nat__number__of)). 120.83/55.33 thf(21895,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4777])). 120.83/55.33 thf(1540,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3313_real__sqrt__le__iff)). 120.83/55.33 thf(10241,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540])). 120.83/55.33 thf(166,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4436_powr__minus__divide)). 120.83/55.33 thf(5490,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 120.83/55.33 thf(2771,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1984_add__0)). 120.83/55.33 thf(14586,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ zero_zero_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2771])). 120.83/55.33 thf(4745,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)))) <=> (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2891_even__sum)). 120.83/55.33 thf(21786,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)))) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) => (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)) & (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) | (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) & ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4745])). 120.83/55.33 thf(1164,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2079_right__minus__eq)). 120.83/55.33 thf(8946,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B) = zero_zero_rat)) & (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B) = zero_zero_rat) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164])). 120.83/55.33 thf(4460,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit0 @ B) != (hAPP_int_int @ bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_rel__simps_I50_J)). 120.83/55.33 thf(20639,plain,((! [A:$i,B:$i]: ~ ((hAPP_int_int @ bit0 @ B) = (hAPP_int_int @ bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4460])). 120.83/55.33 thf(611,axiom,((! [A:$i,B:$i]: ((zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2513_dvd__imp__mod__0)). 120.83/55.33 thf(6965,plain,((! [A:$i,B:$i]: ((zero_z891286103de_int = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])). 120.83/55.33 thf(3475,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ A)) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3808_Fact_Ofact__Suc)). 120.83/55.33 thf(16988,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ fact_fact_nat @ A)) = (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3475])). 120.83/55.33 thf(3803,axiom,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3198_add__2__eq__Suc_H)). 120.83/55.33 thf(18134,plain,((! [A:$i]: ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3803])). 120.83/55.33 thf(2130,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat) <= (zero_zero_nat = B)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) <= (zero_zero_nat != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1805_power__eq__if)). 120.83/55.33 thf(12277,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat) | ~ (zero_zero_nat = B)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) | (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130])). 120.83/55.33 thf(1179,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 120.83/55.33 thf(8987,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179])). 120.83/55.33 thf(3274,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.33 thf(16350,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3274])). 120.83/55.33 thf(3687,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1463_zcong__zmult__prop3)). 120.83/55.33 thf(17728,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))) => ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zero_zero_int) @ C))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3687])). 120.83/55.33 thf(291,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2348_mod__div__equality)). 120.83/55.33 thf(5917,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 120.83/55.33 thf(4622,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3537_diff__int__def__symmetric)). 120.83/55.33 thf(21315,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4622])). 120.83/55.33 thf(1163,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1892_add__nonpos__neg)). 120.83/55.33 thf(8944,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163])). 120.83/55.33 thf(64,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ ln @ A) @ (hAPP_real_real @ inverse_inverse_real @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3866_DERIV__ln)). 120.83/55.33 thf(5179,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ ln @ A) @ (hAPP_real_real @ inverse_inverse_real @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 120.83/55.33 thf(2548,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1653_le__cube)). 120.83/55.33 thf(13797,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548])). 120.83/55.33 thf(3943,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_mult__strict__left__mono__neg)). 120.83/55.33 thf(18630,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3943])). 120.83/55.33 thf(2436,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2959_of__nat__add)). 120.83/55.33 thf(13406,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2436])). 120.83/55.33 thf(547,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2287_mult_Ozero__right)). 120.83/55.33 thf(6758,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 120.83/55.33 thf(1443,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1869_add__strict__increasing)). 120.83/55.33 thf(9912,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443])). 120.83/55.33 thf(1331,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) <=> ((B = A) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1700_dvd_Ole__less)). 120.83/55.33 thf(9527,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((B = A) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))))) & (((B = A) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331])). 120.83/55.33 thf(1697,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1328_mult__right__le__imp__le)). 120.83/55.33 thf(10806,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ C)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697])). 120.83/55.33 thf(3629,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_mult__nonpos__nonpos)). 120.83/55.33 thf(17501,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3629])). 120.83/55.33 thf(2917,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ B)) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3686_nat__le__real__less)). 120.83/55.33 thf(15099,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ B)) @ one_one_real)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ B)) @ one_one_real))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2917])). 120.83/55.33 thf(708,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ A @ B))) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ A @ B))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4297_bezw__aux)). 120.83/55.33 thf(7316,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ (bezw @ A @ B))) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_P1175774780nt_int @ product_snd_int_int @ (bezw @ A @ B))) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 120.83/55.33 thf(1374,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2380_mod__mult__right__eq)). 120.83/55.33 thf(9664,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374])). 120.83/55.33 thf(3521,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1795_divides__mul__r)). 120.83/55.33 thf(17127,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3521])). 120.83/55.33 thf(442,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ ln) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5158_isCont__ln)). 120.83/55.33 thf(6408,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ ln) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 120.83/55.33 thf(3659,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ D) @ C))) @ C)) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B) @ D))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2238_aux______2)). 120.83/55.33 thf(17617,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ zprime @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ D) @ C))) @ C)) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B) @ D))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ zero_zero_int) @ D)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3659])). 120.83/55.33 thf(4114,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_mult__numeral__1)). 120.83/55.33 thf(19336,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4114])). 120.83/55.33 thf(4558,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2989_zless__int)). 120.83/55.33 thf(21088,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4558])). 120.83/55.33 thf(3989,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5146_transfer__int__nat__gcd__closures_I1_J)). 120.83/55.33 thf(18797,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3989])). 120.83/55.33 thf(731,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((divmod_int @ B @ A) = (posDivAlg @ B @ A))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) => (((B != zero_zero_int) => ((divmod_int @ B @ A) = (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A))))) & (((divmod_int @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int)) <= (zero_zero_int = B)))))) & ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) => ((divmod_int @ B @ A) = (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A))))) & (((negDivAlg @ B @ A) = (divmod_int @ B @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4162_divmod__int__def)). 120.83/55.33 thf(7395,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((divmod_int @ B @ A) = (posDivAlg @ B @ A))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) => (((~ (B = zero_zero_int)) => ((divmod_int @ B @ A) = (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A))))) & (((divmod_int @ B @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int)) | ~ (zero_zero_int = B)))))) & ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) => ((divmod_int @ B @ A) = (hAPP_P1975530577nt_int @ negateSnd @ (posDivAlg @ (hAPP_int_int @ uminus_uminus_int @ B) @ (hAPP_int_int @ uminus_uminus_int @ A))))) & (((negDivAlg @ B @ A) = (divmod_int @ B @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 120.83/55.33 thf(4526,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_int_bool @ zprime @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1508_zprime__factor__exists)). 120.83/55.33 thf(20906,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (? [B:$i]: ((is_int @ B) & (hBOOL @ (hAPP_int_bool @ zprime @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4526])). 120.83/55.33 thf(3243,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_sum__power2__ge__zero)). 120.83/55.33 thf(16245,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3243])). 120.83/55.33 thf(3994,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ zero_zero_int) = (hAPP_int_int @ abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5002_gcd__0__int)). 120.83/55.33 thf(18811,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ zero_zero_int) = (hAPP_int_int @ abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3994])). 120.83/55.33 thf(3046,axiom,((! [A:$i]: ((is_int @ A) => ((? [B:$i,C:$i]: ((is_int @ B) & (A = (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) & (is_int @ C))) <=> (hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1855_is__sum2sq__def)). 120.83/55.33 thf(15525,plain,((! [A:$i]: ((is_int @ A) => (((? [B:$i,C:$i]: ((is_int @ B) & (A = (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) & (is_int @ C))) => (hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ A))) & ((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ A)) => (? [B:$i,C:$i]: ((is_int @ B) & (A = (hAPP_P1175774780nt_int @ twoSqu1907779896sum2sq @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) & (is_int @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3046])). 120.83/55.33 thf(4349,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_power2__eq__square__number__of)). 120.83/55.33 thf(20214,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4349])). 120.83/55.33 thf(4149,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1569_less__add__iff1)). 120.83/55.33 thf(19456,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4149])). 120.83/55.33 thf(1308,axiom,((! [A:$i,B:$i,C:$i]: ((C = A) <=> ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1929_add__right__cancel)). 120.83/55.33 thf(9438,plain,((! [A:$i,B:$i,C:$i]: (((C = A) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B))) & (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308])). 120.83/55.33 thf(1290,axiom,((zero_zero_real != (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3467_pi__half__neq__zero)). 120.83/55.33 thf(9389,plain,((~ (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290])). 120.83/55.33 thf(254,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ C) @ D) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) => ((B = A) <=> (D = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1959_diff__eq__diff__eq)). 120.83/55.33 thf(5777,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ C) @ D) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) => (((B = A) => (D = C)) & ((D = C) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 120.83/55.33 thf(3819,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_bin__less__0__simps_I3_J)). 120.83/55.33 thf(18179,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3819])). 120.83/55.33 thf(3422,axiom,((! [A:$i,B:$i]: ((hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ sgn_sgn_int @ A)) @ (hAPP_int_int @ sgn_sgn_int @ B))) = (hAPP_rat_rat @ sgn_sgn_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4715_sgn__rat)). 120.83/55.33 thf(16814,plain,((! [A:$i,B:$i]: ((hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ sgn_sgn_int @ A)) @ (hAPP_int_int @ sgn_sgn_int @ B))) = (hAPP_rat_rat @ sgn_sgn_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3422])). 120.83/55.33 thf(2295,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ D) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4017_coprime__divisors)). 120.83/55.33 thf(12883,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ D) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295])). 120.83/55.33 thf(579,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3665_sin__add)). 120.83/55.33 thf(6861,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ sin @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])). 120.83/55.33 thf(4261,axiom,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2499_mod__by__1)). 120.83/55.33 thf(19876,plain,((! [A:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4261])). 120.83/55.33 thf(1301,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1247_less__1__mult)). 120.83/55.33 thf(9417,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301])). 120.83/55.33 thf(3163,axiom,((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3758_even__zero__nat)). 120.83/55.33 thf(15957,plain,((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3163])). 120.83/55.33 thf(3783,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4991_gcd__neg2__int)). 120.83/55.33 thf(18061,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3783])). 120.83/55.33 thf(307,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2482_div__dvd__div)). 120.83/55.33 thf(5966,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ C) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 120.83/55.33 thf(4776,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.33 thf(21892,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4776])). 120.83/55.33 thf(2613,axiom,((! [A:$i]: ((hAPP_real_real @ (log @ A) @ one_one_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3863_log__one)). 120.83/55.33 thf(14037,plain,((! [A:$i]: ((hAPP_real_real @ (log @ A) @ one_one_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2613])). 120.83/55.33 thf(355,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3318_real__sqrt__mult)). 120.83/55.33 thf(6137,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sqrt @ A)) @ (hAPP_real_real @ sqrt @ B)) = (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 120.83/55.33 thf(3072,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_mult__right__mono)). 120.83/55.33 thf(15644,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3072])). 120.83/55.33 thf(2677,axiom,((! [A:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4677_Fract__of__nat__eq)). 120.83/55.33 thf(14257,plain,((! [A:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ A) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2677])). 120.83/55.33 thf(190,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (rcis @ A @ B)) @ C) = (rcis @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4251_DeMoivre2)). 120.83/55.33 thf(5573,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (rcis @ A @ B)) @ C) = (rcis @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ C)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 120.83/55.33 thf(781,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => ((((A = zero_z891286103de_int) & (zero_z891286103de_int = B)) <=> (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2163_add__nonneg__eq__0__iff)). 120.83/55.33 thf(7589,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (((((A = zero_z891286103de_int) & (zero_z891286103de_int = B)) => (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) & ((zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) => ((A = zero_z891286103de_int) & (zero_z891286103de_int = B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])). 120.83/55.33 thf(4519,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) <=> (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1937_add__left__cancel)). 120.83/55.33 thf(20874,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)) => (B = C)) & ((B = C) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4519])). 120.83/55.33 thf(17,axiom,(((hAPP_complex_complex @ uminus473333897omplex @ one_one_complex) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3985_i__mult__eq2)). 120.83/55.33 thf(4997,plain,(((hAPP_complex_complex @ uminus473333897omplex @ one_one_complex) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 120.83/55.33 thf(3104,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2052_add__strict__left__mono)). 120.83/55.33 thf(15749,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3104])). 120.83/55.33 thf(1518,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int))) | ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_split__mult__neg__le)). 120.83/55.33 thf(10156,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int))) | ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ zero_z891286103de_int)) & (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)))) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518])). 120.83/55.33 thf(3662,axiom,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2741_nat__mult__distrib)). 120.83/55.33 thf(17640,plain,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3662])). 120.83/55.33 thf(4426,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3523_zdiv__zminus__zminus)). 120.83/55.33 thf(20502,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4426])). 120.83/55.33 thf(3632,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P880235623l_bool @ B @ A)) <=> (hBOOL @ (hAPP_f1469637905l_bool @ (hAPP_P1681069257l_bool @ member308914164t_bool @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_mem__def)). 120.83/55.33 thf(17508,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_P880235623l_bool @ B @ A)) => (hBOOL @ (hAPP_f1469637905l_bool @ (hAPP_P1681069257l_bool @ member308914164t_bool @ A) @ B))) & ((hBOOL @ (hAPP_f1469637905l_bool @ (hAPP_P1681069257l_bool @ member308914164t_bool @ A) @ B)) => (hBOOL @ (hAPP_P880235623l_bool @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3632])). 120.83/55.33 thf(3368,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((zero_zero_nat = B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1811_divides__ge)). 120.83/55.33 thf(16650,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((zero_zero_nat = B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3368])). 120.83/55.33 thf(297,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ B)) <=> ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3485_abs__le__interval__iff)). 120.83/55.33 thf(5934,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A)))) & (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ B)) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 120.83/55.33 thf(143,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3833_exp__ge__zero)). 120.83/55.33 thf(5421,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 120.83/55.33 thf(1129,axiom,(((hAPP_int_complex @ number528085621omplex @ min) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3984_i__squared)). 120.83/55.33 thf(8825,plain,(((hAPP_int_complex @ number528085621omplex @ min) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129])). 120.83/55.33 thf(4916,axiom,((! [A:$i]: (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3278_neg__imp__number__of__eq__0)). 120.83/55.33 thf(22356,plain,((! [A:$i]: (((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4916])). 120.83/55.33 thf(3631,axiom,(((hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit1 @ pls)) = one_on1684967323de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4249_one__code__int__code)). 120.83/55.33 thf(17506,plain,(((hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit1 @ pls)) = one_on1684967323de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3631])). 120.83/55.33 thf(3414,axiom,((! [A:$i,B:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1796_realpow__minus__mult)). 120.83/55.33 thf(16795,plain,((! [A:$i,B:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3414])). 120.83/55.33 thf(2092,axiom,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ A) = one_one_complex)) & ((zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ A)) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1436_power__0__left)). 120.83/55.33 thf(12130,plain,((! [A:$i]: (((A = zero_zero_nat) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ A) = one_one_complex)) & ((zero_zero_complex = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ A)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092])). 120.83/55.33 thf(3518,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) <= (A != zero_zero_nat)) <= (zero_zero_nat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_no__zero__divisors)). 120.83/55.33 thf(17120,plain,((! [A:$i,B:$i]: (~ (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) | (A = zero_zero_nat) | (zero_zero_nat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3518])). 120.83/55.33 thf(3570,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) <=> (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1934_add__right__cancel)). 120.83/55.33 thf(17294,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) => (A = C)) & ((A = C) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3570])). 120.83/55.33 thf(2630,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2561_dvd__div__mult)). 120.83/55.33 thf(14098,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ C) @ B)) @ A) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2630])). 120.83/55.33 thf(616,axiom,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_int_complex @ ring_11397209091omplex @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4578_complex__Im__of__int)). 120.83/55.33 thf(6980,plain,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_int_complex @ ring_11397209091omplex @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])). 120.83/55.33 thf(1006,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3938_real__root__strict__increasing)). 120.83/55.33 thf(8392,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006])). 120.83/55.33 thf(4112,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_comm__semiring__class_Odistrib)). 120.83/55.33 thf(19331,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4112])). 120.83/55.33 thf(624,axiom,((zero_zero_real = (hAPP_real_real @ tan @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3597_tan__zero)). 120.83/55.33 thf(7007,plain,((zero_zero_real = (hAPP_real_real @ tan @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 120.83/55.33 thf(4907,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2571_div__mult__swap)). 120.83/55.33 thf(22334,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4907])). 120.83/55.33 thf(2499,axiom,((! [A:$i,B:$i]: ((B != A) => ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_linorder__neqE__linordered__idom)). 120.83/55.33 thf(13632,plain,((! [A:$i,B:$i]: ((~ (B = A)) => ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2499])). 120.83/55.33 thf(974,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) <=> (B = A)) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2862_not__less__less__Suc__eq)). 120.83/55.33 thf(8285,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (B = A)) & ((B = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[974])). 120.83/55.33 thf(581,axiom,((! [A:$i,B:$i]: (((hAPP_complex_real @ re @ A) = (hAPP_complex_real @ re @ B)) => ((A = B) <= ((hAPP_complex_real @ im @ A) = (hAPP_complex_real @ im @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4117_complex__eqI)). 120.83/55.33 thf(6867,plain,((! [A:$i,B:$i]: (((hAPP_complex_real @ re @ A) = (hAPP_complex_real @ re @ B)) => ((A = B) | ~ ((hAPP_complex_real @ im @ A) = (hAPP_complex_real @ im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 120.83/55.33 thf(1898,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1800_realpow__minus__mult)). 120.83/55.33 thf(11541,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat))) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898])). 120.83/55.33 thf(4135,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_bool @ (hAPP_f1154658180t_bool @ (hAPP_f1361476881t_bool @ cOMBB_int_bool_nat @ A) @ B) @ C) = (hAPP_int_bool @ A @ (hAPP_nat_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U)). 120.83/55.33 thf(19407,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_bool @ (hAPP_f1154658180t_bool @ (hAPP_f1361476881t_bool @ cOMBB_int_bool_nat @ A) @ B) @ C) = (hAPP_int_bool @ A @ (hAPP_nat_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4135])). 120.83/55.33 thf(3988,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i345030060t_bool @ (hAPP_f725770969t_bool @ (hAPP_f983569339t_bool @ cOMBB_550562460ol_int @ A) @ B) @ C) = (hAPP_f1791153283t_bool @ A @ (hAPP_int_fun_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___018)). 120.83/55.33 thf(18794,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i345030060t_bool @ (hAPP_f725770969t_bool @ (hAPP_f983569339t_bool @ cOMBB_550562460ol_int @ A) @ B) @ C) = (hAPP_f1791153283t_bool @ A @ (hAPP_int_fun_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3988])). 120.83/55.33 thf(3622,axiom,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2737_transfer__nat__int__numerals_I4_J)). 120.83/55.33 thf(17479,plain,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3622])). 120.83/55.33 thf(938,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ pls)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_add__numeral__0__right)). 120.83/55.33 thf(8153,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ pls)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[938])). 120.83/55.33 thf(4647,axiom,((! [A:$i,B:$i]: (((((hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ B)) @ (posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ B)))) = (posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) & (((posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2770_posDivAlg__eqn__number__of)). 120.83/55.33 thf(21411,plain,((! [A:$i,B:$i]: (((((hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ B)) @ (posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ B)))) = (posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) & (((posDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4647])). 120.83/55.33 thf(1357,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2721_div__mult__self__is__m)). 120.83/55.33 thf(9615,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357])). 120.83/55.33 thf(1223,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3371_le__Suc__ex__iff)). 120.83/55.33 thf(9141,plain,((! [A:$i,B:$i]: (((? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (? [C:$i]: (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223])). 120.83/55.33 thf(2437,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2269_pinf_I9_J)). 120.83/55.33 thf(13409,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437])). 120.83/55.33 thf(3083,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_power2__less__0)). 120.83/55.33 thf(15672,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3083])). 120.83/55.33 thf(4225,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1519_dvd__diff)). 120.83/55.33 thf(19725,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4225])). 120.83/55.33 thf(2972,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1880_add__strict__increasing2)). 120.83/55.33 thf(15268,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2972])). 120.83/55.33 thf(114,axiom,(((hAPP_complex_real @ re @ one_one_complex) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4123_complex__Re__one)). 120.83/55.33 thf(5332,plain,(((hAPP_complex_real @ re @ one_one_complex) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 120.83/55.33 thf(132,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4668_Ratreal__number__of__quotient2)). 120.83/55.33 thf(5389,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ (hAPP_int_rat @ number_number_of_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 120.83/55.33 thf(2829,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) <=> (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2271_pinf_I9_J)). 120.83/55.33 thf(14802,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2829])). 120.83/55.33 thf(4393,axiom,((! [A:$i]: ((! [B:$i]: (((hBOOL @ (hAPP_int_bool @ A @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (is_int @ B))) <=> (! [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2988_transfer__int__nat__quantifiers_I1_J)). 120.83/55.33 thf(20372,plain,((! [A:$i]: (((! [B:$i]: ((hBOOL @ (hAPP_int_bool @ A @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (is_int @ B))) => (! [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B))))) & ((! [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) => (! [B:$i]: ((hBOOL @ (hAPP_int_bool @ A @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (is_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4393])). 120.83/55.33 thf(1078,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4313_gcd__semilattice__nat_Oless__infI2)). 120.83/55.33 thf(8666,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078])). 120.83/55.33 thf(3835,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C)) @ A))) <= (! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) != D) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B))))))))) <= (is_int @ D))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5089_aset_I6_J)). 120.83/55.33 thf(18234,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ C)) @ A))) | ~ (! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E) = D) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))))))) | ~ (is_int @ D)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3835])). 120.83/55.33 thf(742,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2937_less__imp__of__nat__less)). 120.83/55.33 thf(7446,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A)) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])). 120.83/55.33 thf(1565,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_less__number__of)). 120.83/55.33 thf(10347,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565])). 120.83/55.33 thf(4808,axiom,((! [A:$i]: ((hAPP_int_int @ succ @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3293_succ__Bit0)). 120.83/55.33 thf(21996,plain,((! [A:$i]: ((hAPP_int_int @ succ @ (hAPP_int_int @ bit0 @ A)) = (hAPP_int_int @ bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4808])). 120.83/55.33 thf(934,axiom,((! [A:$i,B:$i]: (((one_one_nat = A) & (B = one_one_nat)) <=> (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1658_nat__1__eq__mult__iff)). 120.83/55.33 thf(8134,plain,((! [A:$i,B:$i]: ((((one_one_nat = A) & (B = one_one_nat)) => (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) & ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => ((one_one_nat = A) & (B = one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])). 120.83/55.33 thf(1029,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1634_le__eq__less__or__eq)). 120.83/55.33 thf(8469,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (A = B))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (A = B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])). 120.83/55.33 thf(66,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ A) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2367_mod__self)). 120.83/55.33 thf(5184,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ A) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 120.83/55.33 thf(4807,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_mult__strict__right__mono)). 120.83/55.33 thf(21994,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4807])). 120.83/55.33 thf(566,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3578_cos__monotone__minus__pi__0)). 120.83/55.33 thf(6814,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ pi)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 120.83/55.33 thf(2204,axiom,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2104_mult_Ocomm__neutral)). 120.83/55.33 thf(12569,plain,((! [A:$i]: (A = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204])). 120.83/55.33 thf(4091,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_rel__simps_I14_J)). 120.83/55.33 thf(19243,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4091])). 120.83/55.33 thf(4326,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2230_MultInv__zcong__prop1)). 120.83/55.33 thf(20135,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (multInv @ D) @ C))) @ D)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4326])). 120.83/55.33 thf(532,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2281_mult_Oprod__diff__prod)). 120.83/55.33 thf(6711,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ C)) @ D))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])). 120.83/55.33 thf(537,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2328_mod__mod__trivial)). 120.83/55.33 thf(6726,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])). 120.83/55.33 thf(2481,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2122_mult__1__left)). 120.83/55.33 thf(13549,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2481])). 120.83/55.33 thf(4151,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1316_zcong__zero__equiv__div)). 120.83/55.33 thf(19463,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4151])). 120.83/55.33 thf(800,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_dvd__triv__right)). 120.83/55.33 thf(7670,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])). 120.83/55.33 thf(3424,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3492_real__add__less__0__iff)). 120.83/55.33 thf(16820,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ uminus_uminus_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3424])). 120.83/55.33 thf(3122,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2205_add__less__le__mono)). 120.83/55.33 thf(15809,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3122])). 120.83/55.33 thf(2316,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2180_add__neg__neg)). 120.83/55.33 thf(12957,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)) @ zero_zero_real))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2316])). 120.83/55.33 thf(4288,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ C) @ A)) @ (hAPP_int_int @ (multInv @ C) @ B)) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2228_MultInv__prop1)). 120.83/55.33 thf(19974,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ C) @ A)) @ (hAPP_int_int @ (multInv @ C) @ B)) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4288])). 120.83/55.33 thf(996,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ one_on1684967323de_int))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3154_realpow__Suc__le__self)). 120.83/55.33 thf(8356,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_nat_nat @ suc @ A))) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ B) @ one_on1684967323de_int)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])). 120.83/55.33 thf(2087,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1619_mult__0)). 120.83/55.33 thf(12112,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087])). 120.83/55.33 thf(2124,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2863_Suc__less__eq)). 120.83/55.33 thf(12258,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124])). 120.83/55.33 thf(3166,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3215_of__nat__less__two__power)). 120.83/55.33 thf(15964,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3166])). 120.83/55.33 thf(2037,axiom,(((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_semiring__one__add__one__is__two)). 120.83/55.33 thf(11963,plain,(((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat) = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037])). 120.83/55.33 thf(590,axiom,((! [A:$i,B:$i,C:$i]: (((((((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ C))) @ (hAPP_real_real @ (log @ B) @ A)) = (hAPP_real_real @ (log @ C) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (one_one_real != B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (C != one_one_real)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3876_log__eq__div__ln__mult__log)). 120.83/55.33 thf(6903,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ C))) @ (hAPP_real_real @ (log @ B) @ A)) = (hAPP_real_real @ (log @ C) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | (one_one_real = B) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) | (C = one_one_real) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 120.83/55.33 thf(3246,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_dvd__power__le)). 120.83/55.33 thf(16257,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3246])). 120.83/55.33 thf(3790,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_number__of__add)). 120.83/55.33 thf(18078,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3790])). 120.83/55.33 thf(3509,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ fact @ A)) @ (hAPP_nat_nat @ fact @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4559_fact__mono)). 120.83/55.33 thf(17095,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ fact @ A)) @ (hAPP_nat_nat @ fact @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3509])). 120.83/55.33 thf(3575,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3330_real__sqrt__ge__one)). 120.83/55.33 thf(17316,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3575])). 120.83/55.33 thf(3638,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2563_dvd__div__mult)). 120.83/55.33 thf(17543,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3638])). 120.83/55.33 thf(2535,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ A)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3365_real__average__minus__first)). 120.83/55.33 thf(13752,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ A)) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2535])). 120.83/55.33 thf(1390,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1588_less__not__refl2)). 120.83/55.33 thf(9724,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390])). 120.83/55.33 thf(1823,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))) <=> ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3053_mult__eq__1__iff)). 120.83/55.33 thf(11267,plain,((! [A:$i,B:$i]: (((((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))) => ((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) & (((hAPP_nat_nat @ suc @ zero_zero_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) => (((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823])). 120.83/55.33 thf(4174,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_less__number__of__int__code)). 120.83/55.33 thf(19536,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4174])). 120.83/55.33 thf(4310,axiom,(((hAPP_int_int @ bit0 @ min) = (hAPP_int_int @ pred @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4044_pred__Min)). 120.83/55.33 thf(20050,plain,(((hAPP_int_int @ bit0 @ min) = (hAPP_int_int @ pred @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4310])). 120.83/55.33 thf(4292,axiom,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_semiring__one__add__one__is__two)). 120.83/55.33 thf(19985,plain,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4292])). 120.83/55.33 thf(4071,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ C)) <= ((hAPP_nat_int @ semiri1621563631at_int @ C) = B)) & ((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)))) <=> (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3165_split__nat)). 120.83/55.33 thf(19160,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ C)) | ~ ((hAPP_nat_int @ semiri1621563631at_int @ C) = B)) & ((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)))) => (hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ A @ (hAPP_int_nat @ nat @ B))) => (! [C:$i]: ((hBOOL @ (hAPP_nat_bool @ A @ C)) | ~ ((hAPP_nat_int @ semiri1621563631at_int @ C) = B)) & ((hBOOL @ (hAPP_nat_bool @ A @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4071])). 120.83/55.33 thf(3087,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3062_Suc__le__eq)). 120.83/55.33 thf(15685,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3087])). 120.83/55.33 thf(3930,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (big_co1548731110nt_int @ A @ B))) <= (! [C:$i]: ((is_int @ C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ A @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4816_transfer__nat__int__sum__prod__closure_I2_J)). 120.83/55.33 thf(18579,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (big_co1548731110nt_int @ A @ B))) | ~ (! [C:$i]: ((is_int @ C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ A @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3930])). 120.83/55.33 thf(1929,axiom,((! [A:$i]: ((of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_complex_real @ re @ A))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ cnj @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4137_complex__add__cnj)). 120.83/55.33 thf(11639,plain,((! [A:$i]: ((of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_complex_real @ re @ A))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ (hAPP_complex_complex @ cnj @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929])). 120.83/55.33 thf(234,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4424_ceiling__le__real)). 120.83/55.33 thf(5724,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ real_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (archim856651990g_real @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 120.83/55.33 thf(2643,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4098_Im_Oadd)). 120.83/55.33 thf(14150,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2643])). 120.83/55.33 thf(4566,axiom,((one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ one_one_real) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_one__power2)). 120.83/55.33 thf(21120,plain,((one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ one_one_real) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4566])). 120.83/55.33 thf(2407,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_number__of__add)). 120.83/55.33 thf(13303,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2407])). 120.83/55.33 thf(419,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ sin @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3682_cos__diff2)). 120.83/55.33 thf(6341,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ sin @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 120.83/55.33 thf(500,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1731_real__le__trans)). 120.83/55.33 thf(6607,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 120.83/55.33 thf(4356,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ B) @ A) = zero_zero_int) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2514_dvd__imp__mod__0)). 120.83/55.33 thf(20234,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ B) @ A) = zero_zero_int) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4356])). 120.83/55.33 thf(3571,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1724_dvd_Oord__less__eq__trans)). 120.83/55.33 thf(17301,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) | ~ (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3571])). 120.83/55.33 thf(883,axiom,((! [A:$i,B:$i,C:$i]: ((C = B) <= ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1925_add__left__imp__eq)). 120.83/55.33 thf(7964,plain,((! [A:$i,B:$i,C:$i]: ((C = B) | ~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])). 120.83/55.33 thf(2267,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3450_dvd__int__iff)). 120.83/55.33 thf(12775,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267])). 120.83/55.33 thf(1146,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5121_min__diff)). 120.83/55.33 thf(8882,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ C)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146])). 120.83/55.33 thf(716,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat)))))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4193_prime__dvd__square)). 120.83/55.33 thf(7344,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 120.83/55.33 thf(2611,axiom,((! [A:$i]: ((one_one_real = A) <=> ((hAPP_real_real @ sqrt @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3320_real__sqrt__eq__1__iff)). 120.83/55.33 thf(14026,plain,((! [A:$i]: (((one_one_real = A) => ((hAPP_real_real @ sqrt @ A) = one_one_real)) & (((hAPP_real_real @ sqrt @ A) = one_one_real) => (one_one_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2611])). 120.83/55.33 thf(325,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (log @ A) @ C)) = (hAPP_real_real @ (log @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4473_log__powr)). 120.83/55.33 thf(6030,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (log @ A) @ C)) = (hAPP_real_real @ (log @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 120.83/55.33 thf(4106,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2192_zero__less__double__add__iff__zero__less__single__add)). 120.83/55.33 thf(19307,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4106])). 120.83/55.33 thf(898,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_power2__sum)). 120.83/55.33 thf(8011,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[898])). 120.83/55.33 thf(589,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ D)) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C))))) => ((! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => ((hAPP_real_real @ A @ D) = (hAPP_real_real @ A @ B)))) <= (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ zero_zero_real)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5179_DERIV__isconst1)). 120.83/55.33 thf(6893,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ A) @ D)) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C))))) => (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ C)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ D))) => ((hAPP_real_real @ A @ D) = (hAPP_real_real @ A @ B))) | ~ (! [D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ D) @ zero_zero_real)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 120.83/55.33 thf(4903,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))) @ one_one_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2319_neg__zmod__mult__2)). 120.83/55.33 thf(22324,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ B))) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4903])). 120.83/55.33 thf(4230,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A))) @ one_one_int)) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3465_incr__lemma)). 120.83/55.33 thf(19738,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ A))) @ one_one_int)) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4230])). 120.83/55.33 thf(261,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2357_div__mod__equality)). 120.83/55.33 thf(5800,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ B)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 120.83/55.33 thf(3608,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (comple219730294t_bool @ (setS @ A @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3352_Union__SetS__finite)). 120.83/55.33 thf(17427,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (comple219730294t_bool @ (setS @ A @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3608])). 120.83/55.33 thf(3833,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.33 thf(18224,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3833])). 120.83/55.33 thf(3181,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ B @ A)) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mem__def)). 120.83/55.33 thf(16009,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ B @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3181])). 120.83/55.33 thf(4601,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2484_div__dvd__div)). 120.83/55.33 thf(21244,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ C) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4601])). 120.83/55.33 thf(2910,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) => (? [E:$i,F:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ E) @ B) = C) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ F) @ B) = D)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4480_coprime__pow)). 120.83/55.33 thf(15067,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ D)) => (? [E:$i,F:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ E) @ B) = C) & ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ F) @ B) = D)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2910])). 120.83/55.33 thf(2258,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1488_one__less__power)). 120.83/55.33 thf(12743,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258])). 120.83/55.33 thf(2623,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4304_gcd__idem__nat)). 120.83/55.33 thf(14069,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2623])). 120.83/55.33 thf(1063,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) <= (B != zero_zero_int)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))) <= ((is_int @ B) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2795_divmod__int__rel__div)). 120.83/55.33 thf(8584,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) | (B = zero_zero_int) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D))) | ~ ((is_int @ B) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063])). 120.83/55.33 thf(3014,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (of_real_complex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3986_complex__inverse__complex__split)). 120.83/55.33 thf(15436,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (of_real_complex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ ii) @ (of_real_complex @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3014])). 120.83/55.33 thf(676,axiom,((! [A:$i,B:$i]: (((A = (hAPP_nat_nat @ suc @ B)) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2874_le__SucE)). 120.83/55.33 thf(7219,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ suc @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])). 120.83/55.33 thf(3429,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3818_aux4)). 120.83/55.33 thf(16835,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3429])). 120.83/55.33 thf(3650,axiom,((! [A:$i]: ? [B:$i]: ((A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B))) & ! [C:$i]: ((B = C) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C))) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ C)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C)) = one_one_int) & ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ C)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C)) = A))) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B)) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5024_quotient__of__unique)). 120.83/55.33 thf(17580,plain,((! [A:$i]: ? [B:$i]: ((A = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B))) & ! [C:$i]: ((B = C) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C))) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ C)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C)) = one_one_int) & ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_P1175774780nt_int @ product_fst_int_int @ C)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ C)) = A))) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_P1175774780nt_int @ product_fst_int_int @ B)) @ (hAPP_P1175774780nt_int @ product_snd_int_int @ B)) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3650])). 120.83/55.33 thf(1955,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2712_mod__if)). 120.83/55.33 thf(11717,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955])). 120.83/55.33 thf(2068,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1223_zero__less__one)). 120.83/55.33 thf(12061,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068])). 120.83/55.33 thf(1566,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ D) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2560_div__mult__div__if__dvd)). 120.83/55.33 thf(10352,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ D) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566])). 120.83/55.33 thf(2156,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2294_mult__right_Oadd)). 120.83/55.33 thf(12370,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156])). 120.83/55.33 thf(2294,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ fequal_real @ A) @ B)) | (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__RealDef__Oreal_T)). 120.83/55.33 thf(12880,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ fequal_real @ A) @ B)) | (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294])). 120.83/55.33 thf(626,axiom,((zero_zero_nat = (natfloor @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3384_natfloor__zero)). 120.83/55.33 thf(7012,plain,((zero_zero_nat = (natfloor @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])). 120.83/55.33 thf(2365,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1250_less__1__mult)). 120.83/55.33 thf(13129,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365])). 120.83/55.33 thf(2946,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1258_less__add__one)). 120.83/55.33 thf(15191,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2946])). 120.83/55.33 thf(4435,axiom,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4918_finite__atLeastZeroLessThan__int)). 120.83/55.33 thf(20540,plain,((! [A:$i]: (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4435])). 120.83/55.33 thf(847,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3054_less__iff__Suc__add)). 120.83/55.33 thf(7840,plain,((! [A:$i,B:$i]: (((? [C:$i]: (B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (? [C:$i]: (B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])). 120.83/55.33 thf(2844,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hAPP_nat_nat @ suc @ C) = B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3290_Suc__le__D)). 120.83/55.33 thf(14849,plain,((! [A:$i,B:$i]: (? [C:$i]: ((hAPP_nat_nat @ suc @ C) = B) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2844])). 120.83/55.33 thf(559,axiom,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_dvd__0__right)). 120.83/55.33 thf(6790,plain,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 120.83/55.33 thf(3886,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ min))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_rel__simps_I24_J)). 120.83/55.33 thf(18430,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ min))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3886])). 120.83/55.33 thf(3232,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4786_le__number__of__Suc)). 120.83/55.33 thf(16213,plain,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3232])). 120.83/55.33 thf(3285,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (nat_case_bool @ fFalse @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A)) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4877_less__eq__nat_Osimps_I2_J)). 120.83/55.33 thf(16388,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (nat_case_bool @ fFalse @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (nat_case_bool @ fFalse @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3285])). 120.83/55.33 thf(4217,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2728_nat__mono__iff)). 120.83/55.33 thf(19697,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4217])). 120.83/55.33 thf(1156,axiom,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) <=> (? [C:$i]: ((is_int @ C) & (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2530_zmod__eq__0__iff)). 120.83/55.33 thf(8912,plain,((! [A:$i,B:$i]: ((((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => (? [C:$i]: ((is_int @ C) & (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))) & ((? [C:$i]: ((is_int @ C) & (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)))) => (zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156])). 120.83/55.33 thf(4815,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1372_mult__strict__mono)). 120.83/55.33 thf(22025,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4815])). 120.83/55.33 thf(1560,axiom,((! [A:$i]: ((? [B:$i]: ((hAPP_nat_nat @ suc @ B) = A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3049_gr0__conv__Suc)). 120.83/55.33 thf(10325,plain,((! [A:$i]: (((? [B:$i]: ((hAPP_nat_nat @ suc @ B) = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (? [B:$i]: ((hAPP_nat_nat @ suc @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560])). 120.83/55.33 thf(3674,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1902_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.33 thf(17672,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3674])). 120.83/55.33 thf(4439,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ one_one_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_self__quotient__aux2)). 120.83/55.33 thf(20555,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = C) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4439])). 120.83/55.33 thf(4171,axiom,((! [A:$i]: ((zero_zero_complex = A) <=> ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zero__eq__power2)). 120.83/55.33 thf(19522,plain,((! [A:$i]: (((zero_zero_complex = A) => ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_complex)) & (((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_complex) => (zero_zero_complex = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4171])). 120.83/55.33 thf(317,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4457_real__of__int__ceiling__le__add__one)). 120.83/55.33 thf(6003,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (archim856651990g_real @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 120.83/55.33 thf(3981,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((B = A) <=> ((hAPP_int_int @ bit0 @ B) = (hAPP_int_int @ bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_rel__simps_I48_J)). 120.83/55.33 thf(18765,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((B = A) => ((hAPP_int_int @ bit0 @ B) = (hAPP_int_int @ bit0 @ A))) & (((hAPP_int_int @ bit0 @ B) = (hAPP_int_int @ bit0 @ A)) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3981])). 120.83/55.33 thf(322,axiom,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ tan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3600_tan__periodic__pi)). 120.83/55.33 thf(6023,plain,((! [A:$i]: ((hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ pi)) = (hAPP_real_real @ tan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 120.83/55.33 thf(4629,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ A))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2567_dvd__div__mult__self)). 120.83/55.33 thf(21330,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => (B = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ A))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4629])). 120.83/55.33 thf(3215,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) <=> (! [C:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ prime @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4179_coprime__prime__eq)). 120.83/55.33 thf(16134,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (! [C:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ prime @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B))))) & ((! [C:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ prime @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3215])). 120.83/55.33 thf(2959,axiom,((! [A:$i,B:$i]: (((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3706_natceiling__add)). 120.83/55.33 thf(15228,plain,((! [A:$i,B:$i]: (((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2959])). 120.83/55.33 thf(3031,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_zero__less__power__nat__eq__number__of)). 120.83/55.33 thf(15476,plain,((! [A:$i,B:$i]: ((((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ B)))) => ((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ B)) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3031])). 120.83/55.33 thf(2737,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2152_add__increasing2)). 120.83/55.33 thf(14457,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2737])). 120.83/55.33 thf(79,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ arctan @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3375_arctan__monotone_H)). 120.83/55.33 thf(5228,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arctan @ A)) @ (hAPP_real_real @ arctan @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 120.83/55.33 thf(3967,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ C) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4496_zgcd__power__distrib)). 120.83/55.33 thf(18711,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (legacy_zgcd @ A) @ B)) @ C) = (hAPP_int_int @ (legacy_zgcd @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3967])). 120.83/55.33 thf(641,axiom,((! [A:$i,B:$i]: ((A != B) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1704_dvd_Oneq__le__trans)). 120.83/55.33 thf(7082,plain,((! [A:$i,B:$i]: ((~ (A = B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])). 120.83/55.33 thf(1637,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1205_pos__add__strict)). 120.83/55.33 thf(10610,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637])). 120.83/55.33 thf(1312,axiom,((! [A:$i]: ((zero_z891286103de_int = A) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ zero_z891286103de_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_dvd__0__left)). 120.83/55.33 thf(9459,plain,((! [A:$i]: ((zero_z891286103de_int = A) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ zero_z891286103de_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312])). 120.83/55.33 thf(3439,axiom,((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1230_not__one__less__zero)). 120.83/55.33 thf(16867,plain,((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3439])). 120.83/55.33 thf(3709,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_add__numeral__0)). 120.83/55.33 thf(17804,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ pls)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3709])). 120.83/55.33 thf(1747,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1207_pos__add__strict)). 120.83/55.33 thf(11001,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747])). 120.83/55.33 thf(1069,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1428_power__gt1__lemma)). 120.83/55.33 thf(8634,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069])). 120.83/55.33 thf(4249,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2886_Parity_Oodd__times__odd)). 120.83/55.33 thf(19830,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))) => ((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4249])). 120.83/55.33 thf(4379,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => ((A != (hAPP_int_int @ (inv @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2130_inv__distinct)). 120.83/55.33 thf(20314,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A)) => (~ (A = (hAPP_int_int @ (inv @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4379])). 120.83/55.33 thf(3870,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5143_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J)). 120.83/55.33 thf(18381,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_nat_int @ semiri1621563631at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3870])). 120.83/55.33 thf(4557,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: ((is_int @ D) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ A))) <= (! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E) != D) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5094_bset_I5_J)). 120.83/55.33 thf(21081,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (! [D:$i]: ((is_int @ D) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ A)) | ~ (! [E:$i]: ((is_int @ E) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))) => (! [F:$i]: ((is_int @ F) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E) = D) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4557])). 120.83/55.33 thf(1150,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2411_zmod__simps_I1_J)). 120.83/55.33 thf(8897,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)) @ B) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150])). 120.83/55.33 thf(4096,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ C) @ B)) @ (hAPP_int_int @ (multInv @ C) @ A)) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2233_MultInv__prop5)). 120.83/55.33 thf(19260,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (multInv @ C) @ B)) @ (hAPP_int_int @ (multInv @ C) @ A)) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ A) @ C)))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4096])). 120.83/55.33 thf(3848,axiom,(((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ one_one_complex) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_one__power2)). 120.83/55.33 thf(18305,plain,(((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ one_one_complex) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3848])). 120.83/55.33 thf(2351,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_dvd__power__same)). 120.83/55.33 thf(13080,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351])). 120.83/55.33 thf(4272,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2559_div__mult__div__if__dvd)). 120.83/55.33 thf(19916,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ D) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4272])). 120.83/55.33 thf(134,axiom,((! [A:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (quickcheck_int_of @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4556_of__int__int__of)). 120.83/55.33 thf(5394,plain,((! [A:$i]: ((hAPP_i1732201573de_int @ quickcheck_of_int @ (quickcheck_int_of @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 120.83/55.33 thf(247,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1904_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.33 thf(5756,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 120.83/55.33 thf(1908,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2713_mod__mult__self3)). 120.83/55.33 thf(11567,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908])). 120.83/55.33 thf(3611,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((one_one_int = (hAPP_int_int @ (legacy_zgcd @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4515_zcong__zgcd__zmult__zmod)). 120.83/55.33 thf(17434,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ D) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3611])). 120.83/55.33 thf(1416,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ (hAPP_nat_complex @ semiri2020571505omplex @ B)) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2956_of__nat__add)). 120.83/55.33 thf(9824,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) @ (hAPP_nat_complex @ semiri2020571505omplex @ B)) = (hAPP_nat_complex @ semiri2020571505omplex @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416])). 120.83/55.33 thf(3924,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3529_zadd__zminus__inverse2)). 120.83/55.33 thf(18564,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3924])). 120.83/55.33 thf(1113,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (natceiling @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3390_zero__le__natceiling)). 120.83/55.33 thf(8781,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ (natceiling @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113])). 120.83/55.33 thf(4093,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_i1948725293t_bool @ sRStar @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2767_StandardRes__SRStar__prop2)). 120.83/55.33 thf(19253,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) => ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sRStar @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (standardRes @ B) @ (hAPP_int_int @ (multInv @ B) @ A))) @ (hAPP_i1948725293t_bool @ sRStar @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4093])). 120.83/55.33 thf(649,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) => ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4165_primes__eq)). 120.83/55.33 thf(7114,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ B)) => ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])). 120.83/55.33 thf(1721,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B)))) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3859_reals__Archimedean)). 120.83/55.33 thf(10870,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (? [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B)))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721])). 120.83/55.33 thf(3360,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1626_nat__add__left__cancel__less)). 120.83/55.33 thf(16614,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3360])). 120.83/55.33 thf(4709,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2990_Nat__Transfer_Otransfer__int__nat__relations_I2_J)). 120.83/55.33 thf(21648,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4709])). 120.83/55.33 thf(916,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2919_of__nat__less__0__iff)). 120.83/55.33 thf(8083,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])). 120.83/55.33 thf(4772,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1366_mult__strict__mono_H)). 120.83/55.33 thf(21875,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4772])). 120.83/55.33 thf(4065,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_dvd__mult2)). 120.83/55.33 thf(19143,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4065])). 120.83/55.33 thf(3830,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4510_zgcd__zmult__distrib2)). 120.83/55.33 thf(18217,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_int_int @ (legacy_zgcd @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ (hAPP_int_int @ (legacy_zgcd @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3830])). 120.83/55.33 thf(2530,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5021_gcd__int__def)). 120.83/55.33 thf(13733,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2530])). 120.83/55.33 thf(4718,axiom,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.33 thf(21685,plain,((! [A:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4718])). 120.83/55.33 thf(3751,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_zdvd__not__zless)). 120.83/55.33 thf(17951,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3751])). 120.83/55.33 thf(3706,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2657_zmult2__lemma__aux1)). 120.83/55.33 thf(17797,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ D))) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3706])). 120.83/55.33 thf(1797,axiom,((! [A:$i,B:$i]: (((hAPP_int_real @ number267125858f_real @ A) = B) <=> ((hAPP_int_real @ number267125858f_real @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_number__of__reorient)). 120.83/55.33 thf(11187,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797])). 120.83/55.33 thf(4117,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_int)) <=> ((zero_zero_int = A) & (zero_zero_int = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_sum__power2__le__zero__iff)). 120.83/55.33 thf(19346,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_int)) => ((zero_zero_int = A) & (zero_zero_int = B))) & (((zero_zero_int = A) & (zero_zero_int = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4117])). 120.83/55.33 thf(2396,axiom,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2492_mod__mult__self1__is__0)). 120.83/55.33 thf(13252,plain,((! [A:$i,B:$i]: (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2396])). 120.83/55.33 thf(2651,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_mult__right__mono__neg)). 120.83/55.33 thf(14177,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2651])). 120.83/55.33 thf(1773,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_number__of__mult)). 120.83/55.33 thf(11091,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773])). 120.83/55.33 thf(3401,axiom,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3012_power__Suc)). 120.83/55.33 thf(16746,plain,((! [A:$i,B:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3401])). 120.83/55.33 thf(1576,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_power__mult)). 120.83/55.33 thf(10386,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576])). 120.83/55.33 thf(2800,axiom,((! [A:$i,B:$i]: ((hAPP_P1175774780nt_int @ product_fst_int_int @ (divmod_int @ A @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4224_div__int__def)). 120.83/55.33 thf(14705,plain,((! [A:$i,B:$i]: ((hAPP_P1175774780nt_int @ product_fst_int_int @ (divmod_int @ A @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2800])). 120.83/55.33 thf(1392,axiom,((! [A:$i]: ((? [B:$i]: ! [C:$i]: ((hAPP_nat_nat @ A @ B) = (hAPP_nat_nat @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)))) <= (! [B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ A @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4571_weak__decr__stable)). 120.83/55.33 thf(9736,plain,((! [A:$i]: (? [B:$i]: ! [C:$i]: ((hAPP_nat_nat @ A @ B) = (hAPP_nat_nat @ A @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))) | ~ (! [B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ A @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392])). 120.83/55.33 thf(2723,axiom,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.33 thf(14415,plain,((! [A:$i]: (zero_zero_complex = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2723])). 120.83/55.33 thf(2821,axiom,((! [A:$i,B:$i]: ((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) <=> (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2083_eq__iff__diff__eq__0)). 120.83/55.33 thf(14770,plain,((! [A:$i,B:$i]: (((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)) => (A = B)) & ((A = B) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2821])). 120.83/55.33 thf(4378,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_zmult__1__right)). 120.83/55.33 thf(20311,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4378])). 120.83/55.33 thf(4046,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ F) @ E)) => ((hBOOL @ (hAPP_int_bool @ C @ F)) <=> (hBOOL @ (hAPP_int_bool @ B @ F)))))) => (((! [E:$i,F:$i]: (((hBOOL @ (hAPP_int_bool @ B @ E)) <=> (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D))))) <= ((is_int @ E) & (is_int @ F)))) => ((? [E:$i]: ((is_int @ E) & ? [F:$i]: ((is_int @ F) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D)))) | ? [E:$i]: ((hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E))) <=> (? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E))))) <= (! [E:$i]: ((is_int @ E) => ((! [F:$i]: ((! [G:$i]: ((E != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ A)))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))) => ((hBOOL @ (hAPP_int_bool @ C @ E)) => (hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D))))))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5154_cpmi)). 120.83/55.33 thf(18996,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ! [F:$i]: ((is_int @ F) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ F) @ E)) => (((hBOOL @ (hAPP_int_bool @ C @ F)) => (hBOOL @ (hAPP_int_bool @ B @ F))) & ((hBOOL @ (hAPP_int_bool @ B @ F)) => (hBOOL @ (hAPP_int_bool @ C @ F))))))) => (((! [E:$i,F:$i]: ((((hBOOL @ (hAPP_int_bool @ B @ E)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D))))) & ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D)))) => (hBOOL @ (hAPP_int_bool @ B @ E)))) | ~ ((is_int @ E) & (is_int @ F)))) => (((? [E:$i]: ((is_int @ E) & ? [F:$i]: ((is_int @ F) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D)))) | ? [E:$i]: ((hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E))) => (? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E)))) & ((? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E))) => (? [E:$i]: ((is_int @ E) & ? [F:$i]: ((is_int @ F) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D)))) | ? [E:$i]: ((hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E)))))) | ~ (! [E:$i]: ((is_int @ E) => ((! [F:$i]: (! [G:$i]: (~ (E = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ A))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))) => ((hBOOL @ (hAPP_int_bool @ C @ E)) => (hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D))))))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4046])). 120.83/55.33 thf(4504,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ (hAPP_int_int @ uminus_uminus_int @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ B))))) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ B))) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ (hAPP_int_int @ uminus_uminus_int @ B)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5008_gcd__cases__int)). 120.83/55.33 thf(20802,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ (hAPP_int_int @ uminus_uminus_int @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)))) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ B))))) => ((hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ B))) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ (hAPP_int_int @ uminus_uminus_int @ B)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4504])). 120.83/55.33 thf(1494,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1490_one__less__power)). 120.83/55.33 thf(10077,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494])). 120.83/55.33 thf(3705,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ B @ A)) <= (! [C:$i,D:$i]: (((hBOOL @ (hAPP_rat_bool @ B @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))) <= ((is_int @ C) & (is_int @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4729_Rat__induct__pos)). 120.83/55.33 thf(17792,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ B @ A)) | ~ (! [C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ B @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) | ~ ((is_int @ C) & (is_int @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3705])). 120.83/55.33 thf(1486,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3395_abs__add__one__not__less__self)). 120.83/55.33 thf(10050,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ abs_abs_real @ A)) @ one_one_real)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486])). 120.83/55.33 thf(197,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ (natceiling @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3391_natceiling__mono)). 120.83/55.33 thf(5600,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ (natceiling @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 120.83/55.33 thf(867,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) <= ((hAPP_int_int @ (div_mod_int @ A) @ B) != zero_zero_int)) & ((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))) <= (B != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3553_zdiv__zminus1__eq__if)). 120.83/55.33 thf(7912,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B)) | ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int)) & ((zero_zero_int = (hAPP_int_int @ (div_mod_int @ A) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ uminus_uminus_int @ A)) @ B) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))))) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])). 120.83/55.33 thf(2323,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_mult__less__cancel__left__disj)). 120.83/55.33 thf(12976,plain,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323])). 120.83/55.33 thf(1229,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1389_mult__right__le__one__le)). 120.83/55.33 thf(9160,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229])). 120.83/55.33 thf(1580,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_dvd__triv__left)). 120.83/55.33 thf(10400,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580])). 120.83/55.33 thf(1446,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1190_mult__pos__pos)). 120.83/55.33 thf(9919,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446])). 120.83/55.33 thf(4150,axiom,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)) = (hAPP_nat_nat @ suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3170_numeral__1__eq__Suc__0)). 120.83/55.33 thf(19461,plain,(((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ pls)) = (hAPP_nat_nat @ suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4150])). 120.83/55.33 thf(1101,axiom,(((hAPP_int_complex @ number528085621omplex @ pls) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_number__of__Pls)). 120.83/55.33 thf(8749,plain,(((hAPP_int_complex @ number528085621omplex @ pls) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101])). 120.83/55.33 thf(4090,axiom,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2470_div__by__0)). 120.83/55.33 thf(19240,plain,((! [A:$i]: (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4090])). 120.83/55.33 thf(270,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ B))) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ B))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3372_lemma__MVT)). 120.83/55.33 thf(5828,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ B))) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ C)) @ (hAPP_real_real @ A @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ B))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 120.83/55.33 thf(1140,axiom,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1214_zero__le__one)). 120.83/55.33 thf(8865,plain,((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140])). 120.83/55.33 thf(2765,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3115_power__gt1)). 120.83/55.33 thf(14560,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2765])). 120.83/55.33 thf(3605,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2280_dvd__pos__nat)). 120.83/55.33 thf(17417,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3605])). 120.83/55.33 thf(803,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4010_coprime__rmul2)). 120.83/55.33 thf(7680,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])). 120.83/55.33 thf(2577,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ cnj @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4078_complex__cnj__power)). 120.83/55.33 thf(13887,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_complex_complex @ cnj @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2577])). 120.83/55.33 thf(472,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C))) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2441_dvd__mod__iff)). 120.83/55.33 thf(6516,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ C)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ B) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 120.83/55.33 thf(4591,axiom,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3448_abs__power3__distrib)). 120.83/55.33 thf(21208,plain,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4591])). 120.83/55.33 thf(1883,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1407_power__decreasing)). 120.83/55.33 thf(11497,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883])). 120.83/55.33 thf(4673,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (legacy_zgcd @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4492_zgcd__greatest)). 120.83/55.33 thf(21487,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (legacy_zgcd @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4673])). 120.83/55.33 thf(4801,axiom,((! [A:$i]: (((~ (! [B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ B) != A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3259_nonneg__eq__int)). 120.83/55.33 thf(21977,plain,((! [A:$i]: (~ (! [B:$i]: ~ ((hAPP_nat_int @ semiri1621563631at_int @ B) = A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4801])). 120.83/55.33 thf(1389,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((zero_zero_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) <=> (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3904_real__root__eq__0__iff)). 120.83/55.33 thf(9718,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((zero_zero_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) => (A = zero_zero_real)) & ((A = zero_zero_real) => (zero_zero_real = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389])). 120.83/55.33 thf(1806,axiom,((! [A:$i,B:$i]: ((is_int @ A) => ((? [C:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) & (is_int @ C))) <= ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2773_zmod__eq__0D)). 120.83/55.33 thf(11210,plain,((! [A:$i,B:$i]: ((is_int @ A) => (? [C:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) & (is_int @ C)) | ~ ((hAPP_int_int @ (div_mod_int @ A) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806])). 120.83/55.33 thf(2880,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ B)) <=> (hBOOL @ (hAPP_f448129468l_bool @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_mem__def)). 120.83/55.33 thf(14970,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ B)) => (hBOOL @ (hAPP_f448129468l_bool @ B @ A))) & ((hBOOL @ (hAPP_f448129468l_bool @ B @ A)) => (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2880])). 120.83/55.33 thf(687,axiom,((! [A:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = zero_zero_real) <=> (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_double__eq__0__iff)). 120.83/55.33 thf(7256,plain,((! [A:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = zero_zero_real) => (zero_zero_real = A)) & ((zero_zero_real = A) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])). 120.83/55.33 thf(1034,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) = B) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3928_real__root__pos)). 120.83/55.33 thf(8488,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_n546711566l_real @ root @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_nat_nat @ suc @ A))) = B) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034])). 120.83/55.33 thf(2254,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3183_div__if)). 120.83/55.33 thf(12730,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ B))) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254])). 120.83/55.33 thf(3417,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4168_prime__g__zero)). 120.83/55.33 thf(16803,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3417])). 120.83/55.33 thf(408,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4415_real__of__int__div4)). 120.83/55.33 thf(6305,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 120.83/55.33 thf(4701,axiom,((! [A:$i,B:$i]: ((is_int @ B) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) = B) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2575_dvd__mult__div__cancel)). 120.83/55.33 thf(21618,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) = B) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4701])). 120.83/55.33 thf(1315,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ E)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A) = one_one_real) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) @ E))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_convex__bound__lt)). 120.83/55.33 thf(9470,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ E)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A) = one_one_real) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) @ E))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315])). 120.83/55.33 thf(4308,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i872162435t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ A) @ B) @ C) = (hAPP_f1512942609t_bool @ A @ (hAPP_i1948725293t_bool @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__025)). 120.83/55.33 thf(20045,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i872162435t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ A) @ B) @ C) = (hAPP_f1512942609t_bool @ A @ (hAPP_i1948725293t_bool @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4308])). 120.83/55.33 thf(4454,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (wset @ A) @ B))) @ one_one_int) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4814_wset__zcong__prod__1)). 120.83/55.33 thf(20604,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (big_co1548731110nt_int @ cOMBI_int @ (hAPP_i1948725293t_bool @ (wset @ A) @ B))) @ one_one_int) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4454])). 120.83/55.33 thf(2639,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4966_transfer__int__nat__gcd_I1_J)). 120.83/55.33 thf(14140,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2639])). 120.83/55.33 thf(2147,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2423_mod__add__left__eq)). 120.83/55.33 thf(12338,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147])). 120.83/55.33 thf(139,axiom,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4087_cnj_Ononneg__bounded)). 120.83/55.33 thf(5408,plain,((? [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) & ! [B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ cnj @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_complex_real @ norm_norm_complex @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 120.83/55.33 thf(438,axiom,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ sgn_sgn_complex @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4129_Re__sgn)). 120.83/55.33 thf(6397,plain,((! [A:$i]: ((hAPP_complex_real @ re @ (hAPP_complex_complex @ sgn_sgn_complex @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ norm_norm_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 120.83/55.33 thf(4332,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_rel__simps_I6_J)). 120.83/55.33 thf(20163,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ min) @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4332])). 120.83/55.33 thf(2991,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2867_add__Suc)). 120.83/55.33 thf(15351,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2991])). 120.83/55.33 thf(4798,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_int_nat @ number_number_of_nat @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))) @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4796_diff__nat__number__of)). 120.83/55.33 thf(21964,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_int_nat @ number_number_of_nat @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ pls))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))) @ zero_zero_nat) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4798])). 120.83/55.33 thf(3713,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2599_div__nonpos__pos__le0)). 120.83/55.33 thf(17814,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3713])). 120.83/55.33 thf(8,axiom,((! [A:$i,B:$i]: ~ (! [C:$i,D:$i]: ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4221_divmod__nat__rel__ex)). 120.83/55.33 thf(4964,plain,((! [A:$i,B:$i]: ~ (! [C:$i,D:$i]: ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ A @ B) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 120.83/55.33 thf(179,axiom,((! [A:$i,B:$i]: (((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (natceiling @ B)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3694_natceiling__subtract)). 120.83/55.33 thf(5532,plain,((! [A:$i,B:$i]: (((natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ (hAPP_nat_real @ real_nat @ A))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (natceiling @ B)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 120.83/55.33 thf(3384,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3460_pi__ge__two)). 120.83/55.33 thf(16702,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3384])). 120.83/55.33 thf(1341,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1243_zero__le__power)). 120.83/55.33 thf(9569,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341])). 120.83/55.33 thf(3112,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 120.83/55.33 thf(15777,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3112])). 120.83/55.33 thf(1457,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2250_minf_I10_J)). 120.83/55.33 thf(9962,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457])). 120.83/55.33 thf(2105,axiom,((! [A:$i]: ((zero_zero_nat = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2310_gcd__lcm__complete__lattice__nat_Otop__unique)). 120.83/55.33 thf(12176,plain,((! [A:$i]: (((zero_zero_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ zero_zero_nat) @ A)) => (zero_zero_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105])). 120.83/55.33 thf(2495,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((is_int @ A) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C))) => (? [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) & (A = (hAPP_nat_int @ B @ E)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ E) @ C))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ D)) @ A)))) <= (! [E:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ E) @ one_one_nat))) @ (hAPP_nat_int @ B @ E)))) @ one_one_int)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3505_nat__intermed__int__val)). 120.83/55.33 thf(13610,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((is_int @ A) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C))) => (? [E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) & (A = (hAPP_nat_int @ B @ E)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ E) @ C))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ D)) @ A)))) | ~ (! [E:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ E) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ E) @ one_one_nat))) @ (hAPP_nat_int @ B @ E)))) @ one_one_int)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2495])). 120.83/55.33 thf(3081,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1505_le0)). 120.83/55.33 thf(15667,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3081])). 120.83/55.33 thf(4527,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) & ! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ D) @ B))) => (D = C)) <= (is_int @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1695_zcong__zless__unique)). 120.83/55.33 thf(20910,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) & ! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ D) @ B))) => (D = C)) | ~ (is_int @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4527])). 120.83/55.33 thf(4159,axiom,((one_one_rat = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_semiring__numeral__1__eq__1)). 120.83/55.33 thf(19489,plain,((one_one_rat = (hAPP_int_rat @ number_number_of_rat @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4159])). 120.83/55.33 thf(812,axiom,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)) <= (zero_zero_nat != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2546_div__mult__self2__is__id)). 120.83/55.33 thf(7715,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)) | (zero_zero_nat = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])). 120.83/55.33 thf(3732,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_zcong__scalar)). 120.83/55.33 thf(17885,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3732])). 120.83/55.33 thf(2565,axiom,((! [A:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = zero_zero_rat) <=> (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1977_double__zero__sym)). 120.83/55.33 thf(13846,plain,((! [A:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = zero_zero_rat) => (A = zero_zero_rat)) & ((A = zero_zero_rat) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2565])). 120.83/55.33 thf(4616,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2337_zdiv__zadd1__eq)). 120.83/55.33 thf(21298,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (div_mod_int @ A) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4616])). 120.83/55.33 thf(2837,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ (setS @ A @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3358_SetS__elems__finite)). 120.83/55.33 thf(14823,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ (setS @ A @ B))) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2837])). 120.83/55.33 thf(4932,axiom,((! [A:$i,B:$i]: ((((hAPP_int_nat @ nat @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ zprime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4290_Bnor__prime)). 120.83/55.33 thf(22408,plain,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (bnorRset @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4932])). 120.83/55.33 thf(2724,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2187_add__pos__pos)). 120.83/55.33 thf(14418,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2724])). 120.83/55.33 thf(330,axiom,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_int_real @ real_int @ A)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ abs_abs_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4400_real__of__int__abs)). 120.83/55.33 thf(6045,plain,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_int_real @ real_int @ A)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ abs_abs_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 120.83/55.33 thf(4763,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A) = (hAPP_int_int @ number_number_of_int @ min)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2662_div__pos__neg__trivial)). 120.83/55.33 thf(21853,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A) = (hAPP_int_int @ number_number_of_int @ min)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zero_zero_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4763])). 120.83/55.33 thf(3901,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4999_gcd__mult__cancel__int)). 120.83/55.33 thf(18500,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3901])). 120.83/55.33 thf(3291,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.33 thf(16403,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3291])). 120.83/55.33 thf(2524,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_power3__eq__cube)). 120.83/55.33 thf(13716,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2524])). 120.83/55.33 thf(1902,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1769_add__diff__assoc2)). 120.83/55.33 thf(11552,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902])). 120.83/55.33 thf(3667,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit1 @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_rel__simps_I26_J)). 120.83/55.33 thf(17653,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit1 @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ min) @ (hAPP_int_int @ bit1 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3667])). 120.83/55.33 thf(2932,axiom,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ one_one_nat))) @ (hAPP_nat_int @ B @ D)))) @ one_one_int)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)))) => (((? [D:$i]: (((hAPP_nat_int @ B @ D) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ zero_zero_nat)) @ A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3478_int__val__lemma)). 120.83/55.33 thf(15139,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ one_one_nat))) @ (hAPP_nat_int @ B @ D)))) @ one_one_int)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C)))) => (? [D:$i]: (((hAPP_nat_int @ B @ D) = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_nat_int @ B @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ B @ zero_zero_nat)) @ A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2932])). 120.83/55.33 thf(3808,axiom,((hBOOL @ fTrue)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U)). 120.83/55.33 thf(18147,plain,((hBOOL @ fTrue)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3808])). 120.83/55.33 thf(1513,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 120.83/55.33 thf(10137,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513])). 120.83/55.33 thf(2687,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_mult__zero__right)). 120.83/55.33 thf(14289,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2687])). 120.83/55.33 thf(3227,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) <=> (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1198_mult__less__cancel__right__disj)). 120.83/55.33 thf(16193,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C))))) & ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ A)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ C)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3227])). 120.83/55.33 thf(3143,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2580_div__add)). 120.83/55.33 thf(15875,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ C) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3143])). 120.83/55.33 thf(4702,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (A = B))) <= ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_power2__eq__imp__eq)). 120.83/55.33 thf(21621,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B)) => (A = B))) | ~ ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4702])). 120.83/55.33 thf(1811,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2998_zle__int)). 120.83/55.33 thf(11227,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811])). 120.83/55.33 thf(1009,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ C))) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2684_mod__mult2__eq)). 120.83/55.33 thf(8399,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ C))) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])). 120.83/55.33 thf(861,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ D) @ B))))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2253_pinf_I10_J)). 120.83/55.33 thf(7887,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[861])). 120.83/55.33 thf(2108,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1646_add__le__mono)). 120.83/55.33 thf(12194,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108])). 120.83/55.33 thf(2510,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4709_rat__number__collapse_I3_J)). 120.83/55.33 thf(13659,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2510])). 120.83/55.33 thf(3283,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((A = C) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1710_dvd_Oord__le__eq__trans)). 120.83/55.33 thf(16382,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) => ((A = C) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3283])). 120.83/55.33 thf(4559,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_mult__2__right)). 120.83/55.33 thf(21093,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4559])). 120.83/55.33 thf(1303,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1669_mult__less__cancel1)). 120.83/55.33 thf(9421,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303])). 120.83/55.33 thf(1490,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_power2__eq__square__number__of)). 120.83/55.33 thf(10065,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490])). 120.83/55.33 thf(923,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) & (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2246_less__imp__add__positive)). 120.83/55.33 thf(8102,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) & (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[923])). 120.83/55.33 thf(3517,axiom,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ fTrue) @ A) @ B)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Int__Oint_T)). 120.83/55.33 thf(17116,plain,((! [A:$i,B:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ fTrue) @ A) @ B)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3517])). 120.83/55.33 thf(493,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4103_abs__Im__le__cmod)). 120.83/55.33 thf(6586,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_complex_real @ im @ A))) @ (hAPP_complex_real @ norm_norm_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 120.83/55.33 thf(2890,axiom,((zero_zero_rat != one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_one__neq__zero)). 120.83/55.33 thf(15000,plain,((~ (zero_zero_rat = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2890])). 120.83/55.33 thf(477,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4401_real__of__int__floor__le)). 120.83/55.33 thf(6536,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ (archim1246769320r_real @ A))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 120.83/55.33 thf(2059,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2950_of__nat__le__iff)). 120.83/55.33 thf(12031,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059])). 120.83/55.33 thf(1337,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3509_arcsin__ubound)). 120.83/55.33 thf(9559,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337])). 120.83/55.33 thf(4524,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))) <= ((is_int @ D) & (is_int @ E)))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2586_split__pos__lemma)). 120.83/55.33 thf(20891,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ B) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => (((! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))) | ~ ((is_int @ D) & (is_int @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ C)) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) => (! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ E)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ C)) & ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) @ E) = B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E))) | ~ ((is_int @ D) & (is_int @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4524])). 120.83/55.33 thf(628,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (div_mod_nat @ D) @ A))) @ E)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))) <= (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ D) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4213_divmod__nat__rel__mult2__eq)). 120.83/55.33 thf(7017,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ A)) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ D) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ (hAPP_nat_nat @ (div_mod_nat @ D) @ A))) @ E)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) | ~ (hBOOL @ (hAPP_P1555980039t_bool @ (divmod_nat_rel @ B @ C) @ (hAPP_n1289843868at_nat @ (hAPP_n1865633855at_nat @ product_Pair_nat_nat @ D) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])). 120.83/55.33 thf(2032,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != B) => ((hAPP_nat_nat @ (nat_gcd @ A) @ B) = (hAPP_nat_nat @ (nat_gcd @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) & (((hAPP_nat_nat @ (nat_gcd @ A) @ B) = A) <= (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4617_nat__gcd_Osimps)). 120.83/55.33 thf(11946,plain,((! [A:$i,B:$i]: (((~ (zero_zero_nat = B)) => ((hAPP_nat_nat @ (nat_gcd @ A) @ B) = (hAPP_nat_nat @ (nat_gcd @ B) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) & (((hAPP_nat_nat @ (nat_gcd @ A) @ B) = A) | ~ (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032])). 120.83/55.33 thf(38,axiom,((ii = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3980_i__def)). 120.83/55.33 thf(5072,plain,((ii = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ zero_zero_real) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 120.83/55.33 thf(3702,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ A))) @ C))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C)))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2216_MultInvPair__distinct)). 120.83/55.33 thf(17782,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_int_int @ (multInv @ C) @ A))) @ C)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ C) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ C)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ C)))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3702])). 120.83/55.33 thf(364,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3585_cos__30)). 120.83/55.33 thf(6166,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 120.83/55.33 thf(2080,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_combine__common__factor)). 120.83/55.33 thf(12093,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ C) @ B)) @ D)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080])). 120.83/55.33 thf(4730,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) <= (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_dvdI)). 120.83/55.33 thf(21734,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4730])). 120.83/55.33 thf(3407,axiom,((! [A:$i,B:$i,C:$i]: ((C != zero_z126310315umeral) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2626_div__mult__self2)). 120.83/55.33 thf(16778,plain,((! [A:$i,B:$i,C:$i]: ((~ (C = zero_z126310315umeral)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ B))) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3407])). 120.83/55.33 thf(876,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_nat_int @ semiri1621563631at_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4180_prime__impl__zprime__int)). 120.83/55.33 thf(7939,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ A)) => (hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_nat_int @ semiri1621563631at_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])). 120.83/55.33 thf(3912,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_zadd__strict__right__mono)). 120.83/55.33 thf(18532,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3912])). 120.83/55.33 thf(2556,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1417_power__increasing__iff)). 120.83/55.33 thf(13816,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ A)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2556])). 120.83/55.33 thf(2926,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ D)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_power__le__dvd)). 120.83/55.33 thf(15124,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A)) @ D)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2926])). 120.83/55.33 thf(762,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.33 thf(7520,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])). 120.83/55.33 thf(3170,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3591_cos__gt__zero__pi)). 120.83/55.33 thf(15977,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ cos @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3170])). 120.83/55.33 thf(52,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D = B) & (A = C)) <=> ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3956_complex_Oinject)). 120.83/55.33 thf(5119,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((D = B) & (A = C)) => ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D))) & (((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ C) @ D)) => ((D = B) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 120.83/55.33 thf(75,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3486_real__diff__def)). 120.83/55.33 thf(5211,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 120.83/55.33 thf(2574,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3380_cos__x__y__le__one)). 120.83/55.33 thf(13873,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2574])). 120.83/55.33 thf(4209,axiom,((! [A:$i,B:$i]: (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ one_one_int) @ B))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4534_zcong__lineq__ex)). 120.83/55.33 thf(19669,plain,((! [A:$i,B:$i]: (((one_one_int = (hAPP_int_int @ (legacy_zgcd @ A) @ B)) => (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ one_one_int) @ B))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4209])). 120.83/55.33 thf(2444,axiom,((! [A:$i,B:$i]: (((zero_zero_real != A) | (zero_zero_real != B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_sum__squares__gt__zero__iff)). 120.83/55.33 thf(13428,plain,((! [A:$i,B:$i]: (((~ (zero_zero_real = A) | ~ (zero_zero_real = B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B)))) => (~ (zero_zero_real = A) | ~ (zero_zero_real = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2444])). 120.83/55.33 thf(4006,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (resSet @ B) @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4053_ResSet__finite)). 120.83/55.33 thf(18850,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (resSet @ B) @ A)) => (hBOOL @ (hAPP_f448129468l_bool @ finite_finite_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4006])). 120.83/55.33 thf(4774,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_le__special_I1_J)). 120.83/55.33 thf(21882,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4774])). 120.83/55.33 thf(489,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J)). 120.83/55.33 thf(6569,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 120.83/55.33 thf(173,axiom,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A) != zero_zero_real) <= (zero_zero_real != A)) <= (zero_zero_real != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_no__zero__divisors)). 120.83/55.33 thf(5517,plain,((! [A:$i,B:$i]: (~ ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A) = zero_zero_real) | (zero_zero_real = A) | (zero_zero_real = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 120.83/55.33 thf(2799,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_le__special_I3_J)). 120.83/55.33 thf(14700,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2799])). 120.83/55.33 thf(2249,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_power__le__dvd)). 120.83/55.33 thf(12711,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ B) @ A)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249])). 120.83/55.33 thf(970,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_nat__zero__less__power__iff)). 120.83/55.33 thf(8267,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) | (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])). 120.83/55.33 thf(3895,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3017_power__Suc)). 120.83/55.33 thf(18464,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3895])). 120.83/55.33 thf(1969,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5122_min__0R)). 120.83/55.33 thf(11772,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ A) @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969])). 120.83/55.33 thf(4238,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_less__eq__int__code_I15_J)). 120.83/55.33 thf(19766,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4238])). 120.83/55.33 thf(4880,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__int__code_I14_J)). 120.83/55.33 thf(22239,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit0 @ A)) @ (hAPP_int_int @ bit1 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4880])). 120.83/55.33 thf(1436,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_right__distrib__number__of)). 120.83/55.33 thf(9887,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436])). 120.83/55.33 thf(3261,axiom,((! [A:$i,B:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2979_of__nat__power)). 120.83/55.33 thf(16303,plain,((! [A:$i,B:$i]: ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3261])). 120.83/55.33 thf(1522,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ D) & (is_int @ C)) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) <=> ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D))) <= (zero_zero_int != C)) <= (D != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4687_eq__rat_I1_J)). 120.83/55.33 thf(10167,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((is_int @ D) & (is_int @ C)) => (((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) => ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D))) & (((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ B) @ C) = (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ D)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)))) | (zero_zero_int = C) | (D = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522])). 120.83/55.33 thf(4459,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => (((A != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) <= (A != D)) <= (! [E:$i]: ((is_int @ E) => ((! [F:$i]: ((is_int @ F) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E) != D) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B))))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))))))))))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5098_bset_I4_J)). 120.83/55.33 thf(20622,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((is_int @ D) => (~ (A = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C)) | (A = D) | ~ (! [E:$i]: ((is_int @ E) => (! [F:$i]: ((is_int @ F) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E) = D) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))))))))))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4459])). 120.83/55.33 thf(583,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (natfloor @ B)) @ A) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3692_natfloor__subtract)). 120.83/55.33 thf(6871,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (natfloor @ B)) @ A) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])). 120.83/55.33 thf(71,axiom,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_dvd__refl)). 120.83/55.33 thf(5196,plain,((! [A:$i]: (hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 120.83/55.33 thf(2186,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ D)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ C)) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3837_real__mult__inverse__cancel)). 120.83/55.33 thf(12491,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ D)) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ inverse_inverse_real @ C)) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186])). 120.83/55.33 thf(1408,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1703_divides__antisym)). 120.83/55.33 thf(9787,plain,((! [A:$i,B:$i]: (((A = B) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408])). 120.83/55.33 thf(2467,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1881_add__neg__nonpos)). 120.83/55.33 thf(13513,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2467])). 120.83/55.33 thf(1230,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2440_mod__diff__right__eq)). 120.83/55.33 thf(9162,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (div_mod_int @ B) @ C))) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230])). 120.83/55.33 thf(3468,axiom,((zero_zero_rat = (hAPP_int_rat @ number_number_of_rat @ pls))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_semiring__numeral__0__eq__0)). 120.83/55.33 thf(16963,plain,((zero_zero_rat = (hAPP_int_rat @ number_number_of_rat @ pls))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3468])). 120.83/55.33 thf(4490,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1317_zprime__zdvd__zmult__better)). 120.83/55.33 thf(20751,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4490])). 120.83/55.33 thf(3344,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3606_arccos__lbound)). 120.83/55.33 thf(16571,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3344])). 120.83/55.33 thf(2434,axiom,((! [A:$i,B:$i]: (((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B) = zero_zero_complex) <=> ((B = zero_zero_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_mult__eq__0__iff)). 120.83/55.33 thf(13389,plain,((! [A:$i,B:$i]: ((((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B) = zero_zero_complex) => ((B = zero_zero_complex) | (A = zero_zero_complex))) & (((B = zero_zero_complex) | (A = zero_zero_complex)) => ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434])). 120.83/55.33 thf(458,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ B)) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3689_natceiling__le__eq)). 120.83/55.33 thf(6462,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ B)) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_nat_real @ real_nat @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ (hAPP_nat_real @ real_nat @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ B)) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 120.83/55.33 thf(70,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ A)) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3560_ln__bound)). 120.83/55.33 thf(5194,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ A)) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 120.83/55.33 thf(1917,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2008_add__mono)). 120.83/55.33 thf(11604,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ C) @ D)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ D) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917])). 120.83/55.33 thf(227,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 120.83/55.33 thf(5704,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 120.83/55.33 thf(4268,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4992_gcd__proj1__if__dvd__int)). 120.83/55.33 thf(19901,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ B)) => ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4268])). 120.83/55.33 thf(3111,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1794_divides__mul__l)). 120.83/55.33 thf(15775,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3111])). 120.83/55.33 thf(2136,axiom,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1751_diff__diff__cancel)). 120.83/55.33 thf(12298,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136])). 120.83/55.33 thf(3842,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1579_zle__diff1__eq)). 120.83/55.33 thf(18263,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3842])). 120.83/55.33 thf(116,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_int_real @ number267125858f_real @ C))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1549_left__diff__distrib__number__of)). 120.83/55.33 thf(5336,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_int_real @ number267125858f_real @ C))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ (hAPP_int_real @ number267125858f_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 120.83/55.33 thf(2514,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_case_nat @ zero_zero_nat @ cOMBI_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4880_diff__Suc)). 120.83/55.33 thf(13669,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_case_nat @ zero_zero_nat @ cOMBI_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514])). 120.83/55.33 thf(2769,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ C) => ((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E)) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1536_eq__add__iff2)). 120.83/55.33 thf(14575,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ C) => (((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) => (C = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ A)) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2769])). 120.83/55.33 thf(2082,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1781_divides__add__revr)). 120.83/55.33 thf(12098,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082])). 120.83/55.33 thf(1285,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((((hAPP_int_int @ (legacy_zgcd @ C) @ D) = I) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))) <= (? [J:$i,K:$i]: ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ I) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ J) @ K)) = (xzgcda @ A @ B @ C @ D @ E @ F @ G @ H)))) <= (is_int @ I)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4532_xzgcd__correct__aux2)). 120.83/55.33 thf(9378,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((hAPP_int_int @ (legacy_zgcd @ C) @ D) = I) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) | ~ (? [J:$i,K:$i]: ((hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ I) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ J) @ K)) = (xzgcda @ A @ B @ C @ D @ E @ F @ G @ H))) | ~ (is_int @ I)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285])). 120.83/55.33 thf(4044,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zadd__commute)). 120.83/55.33 thf(18991,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4044])). 120.83/55.33 thf(4201,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((B = (hAPP_int_int @ (div_mod_int @ B) @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) <= (is_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2610_mod__neg__neg__trivial)). 120.83/55.33 thf(19637,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ zero_zero_int)) => ((B = (hAPP_int_int @ (div_mod_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))) | ~ (is_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4201])). 120.83/55.33 thf(1715,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3731_cos__squared__eq)). 120.83/55.33 thf(10853,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715])). 120.83/55.33 thf(2831,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (natfloor @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3400_le__natfloor__eq__one)). 120.83/55.33 thf(14806,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (natfloor @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (natfloor @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2831])). 120.83/55.33 thf(645,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = zero_zero_real) <=> ((hAPP_real_real @ uminus_uminus_real @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3484_real__add__eq__0__iff)). 120.83/55.33 thf(7093,plain,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = zero_zero_real) => ((hAPP_real_real @ uminus_uminus_real @ A) = B)) & (((hAPP_real_real @ uminus_uminus_real @ A) = B) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])). 120.83/55.33 thf(4258,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1271_power__increasing)). 120.83/55.33 thf(19869,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4258])). 120.83/55.33 thf(2119,axiom,((! [A:$i,B:$i]: (((zero_zero_nat != B) & (A = zero_z891286103de_int)) <=> ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1294_power__eq__0__iff)). 120.83/55.33 thf(12230,plain,((! [A:$i,B:$i]: (((~ (zero_zero_nat = B) & (A = zero_z891286103de_int)) => ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = zero_z891286103de_int)) & (((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B) = zero_z891286103de_int) => (~ (zero_zero_nat = B) & (A = zero_z891286103de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119])). 120.83/55.33 thf(2155,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3618_arccos__lt__bounded)). 120.83/55.33 thf(12367,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ one_one_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ arccos @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ arccos @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155])). 120.83/55.33 thf(4298,axiom,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3299_nat__1__add__number__of)). 120.83/55.33 thf(20013,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_int_nat @ number_number_of_nat @ A)) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4298])). 120.83/55.33 thf(3251,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2115_mult__1)). 120.83/55.33 thf(16271,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ one_on1645066479umeral) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3251])). 120.83/55.33 thf(1790,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 120.83/55.33 thf(11167,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790])). 120.83/55.33 thf(4207,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ A))) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ A))) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2808_of__nat__double)). 120.83/55.33 thf(19664,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ A))) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ A))) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4207])). 120.83/55.33 thf(67,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_dvd__mult__right)). 120.83/55.33 thf(5187,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 120.83/55.33 thf(3156,axiom,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ one_one_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_one__dvd)). 120.83/55.33 thf(15917,plain,((! [A:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ one_one_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3156])). 120.83/55.33 thf(991,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__special_I4_J)). 120.83/55.33 thf(8341,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ one_one_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])). 120.83/55.33 thf(2668,axiom,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2674_mod__div__decomp)). 120.83/55.33 thf(14229,plain,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B)) @ B)) @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2668])). 120.83/55.33 thf(2164,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2687_mult__div__cancel)). 120.83/55.33 thf(12391,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164])). 120.83/55.33 thf(2394,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat))) <= (hBOOL @ (hAPP_nat_bool @ B @ A))) <= (! [D:$i]: (((hBOOL @ (hAPP_nat_bool @ B @ D)) => (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ D)) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3249_mod__induct__0)). 120.83/55.33 thf(13242,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat))) | ~ (hBOOL @ (hAPP_nat_bool @ B @ A)) | ~ (! [D:$i]: (((hBOOL @ (hAPP_nat_bool @ B @ D)) => (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ D)) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ D) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2394])). 120.83/55.33 thf(1710,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ (hAPP_nat_nat @ suc @ B))) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (A = C)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3105_power__inject__base)). 120.83/55.33 thf(10838,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ (hAPP_nat_nat @ suc @ B))) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (A = C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710])). 120.83/55.33 thf(1413,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4726_rat__floor__lemma)). 120.83/55.33 thf(9812,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B))) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ (hAPP_int_rat @ ring_1_of_int_rat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B)) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413])). 120.83/55.33 thf(928,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_comm__semiring__class_Odistrib)). 120.83/55.33 thf(8115,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])). 120.83/55.33 thf(879,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1757_diff__mult__distrib)). 120.83/55.33 thf(7946,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])). 120.83/55.33 thf(3058,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2966_of__nat__mult)). 120.83/55.33 thf(15572,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3058])). 120.83/55.33 thf(4580,axiom,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) <= (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_linorder__neqE__linordered__idom)). 120.83/55.33 thf(21167,plain,((! [A:$i,B:$i]: (((is_int @ A) & (is_int @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A))) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4580])). 120.83/55.33 thf(1254,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) <=> (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3756_even__add)). 120.83/55.33 thf(9239,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))) => (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) & ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254])). 120.83/55.33 thf(2188,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3351_lemma__sqrt__hcomplex__capprox)). 120.83/55.33 thf(12498,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ C) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188])). 120.83/55.33 thf(4512,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_power2__sum)). 120.83/55.33 thf(20842,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4512])). 120.83/55.33 thf(796,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1570_less__add__iff1)). 120.83/55.33 thf(7649,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])). 120.83/55.33 thf(124,axiom,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ cnj @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4093_complex__Im__cnj)). 120.83/55.33 thf(5357,plain,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A)) = (hAPP_complex_real @ im @ (hAPP_complex_complex @ cnj @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 120.83/55.33 thf(2099,axiom,((! [A:$i,B:$i]: (((quickcheck_int_of @ B) = (quickcheck_int_of @ A)) <=> (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4254_code__int_Oint__of__inject)). 120.83/55.33 thf(12153,plain,((! [A:$i,B:$i]: ((((quickcheck_int_of @ B) = (quickcheck_int_of @ A)) => (B = A)) & ((B = A) => ((quickcheck_int_of @ B) = (quickcheck_int_of @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099])). 120.83/55.33 thf(2134,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 120.83/55.33 thf(12293,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134])). 120.83/55.33 thf(1625,axiom,((! [A:$i,B:$i]: (((zero_zero_nat = B) | (A = B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1689_divides__cases)). 120.83/55.33 thf(10569,plain,((! [A:$i,B:$i]: ((zero_zero_nat = B) | (A = B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625])). 120.83/55.33 thf(3723,axiom,((! [A:$i]: ((is_int @ A) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3228_two__times__even__div__two)). 120.83/55.33 thf(17846,plain,((! [A:$i]: ((is_int @ A) => ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3723])). 120.83/55.33 thf(4588,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1360_mult__less__le__imp__less)). 120.83/55.33 thf(21199,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4588])). 120.83/55.33 thf(2876,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2920_of__nat__less__0__iff)). 120.83/55.33 thf(14952,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2876])). 120.83/55.33 thf(4715,axiom,((! [A:$i]: ((zero_zero_nat = (hAPP_int_nat @ nat @ A)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2725_nat__le__0)). 120.83/55.33 thf(21670,plain,((! [A:$i]: ((zero_zero_nat = (hAPP_int_nat @ nat @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4715])). 120.83/55.33 thf(1910,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2498_mod__mult__self2__is__0)). 120.83/55.33 thf(11580,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910])). 120.83/55.33 thf(2361,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4430_powr__mono2)). 120.83/55.33 thf(13118,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361])). 120.83/55.33 thf(1075,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2326_mod__mod__trivial)). 120.83/55.33 thf(8660,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075])). 120.83/55.33 thf(3139,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ uminus_uminus_int @ A) @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ D) @ zero_zero_int)) @ (hAPP_int_int @ uminus_uminus_int @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ one_one_int))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ D) @ zero_zero_int)) @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D))))) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3556_zminus1__lemma)). 120.83/55.33 thf(15865,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ (hAPP_int_int @ uminus_uminus_int @ A) @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ D) @ zero_zero_int)) @ (hAPP_int_int @ uminus_uminus_int @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ uminus_uminus_int @ C)) @ one_one_int))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ (hAPP_b1463609396nt_int @ if_int @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ D) @ zero_zero_int)) @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D))))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3139])). 120.83/55.33 thf(3286,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2929_of__nat__less__imp__less)). 120.83/55.33 thf(16393,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3286])). 120.83/55.33 thf(3103,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => (((zero_zero_int = C) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) <= (C != zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2549_div__mult__mult1__if)). 120.83/55.33 thf(15743,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => (((zero_zero_int = C) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B))) | (C = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3103])). 120.83/55.33 thf(4949,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2071_add__less__cancel__right)). 120.83/55.33 thf(22477,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4949])). 120.83/55.33 thf(413,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B)) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4126_Re_Odiff)). 120.83/55.33 thf(6326,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B)) = (hAPP_complex_real @ re @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 120.83/55.33 thf(956,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2999_Nat__Transfer_Otransfer__int__nat__relations_I3_J)). 120.83/55.33 thf(8209,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[956])). 120.83/55.33 thf(236,axiom,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (of_real_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4094_Im__complex__of__real)). 120.83/55.33 thf(5728,plain,((! [A:$i]: (zero_zero_real = (hAPP_complex_real @ im @ (of_real_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 120.83/55.33 thf(3564,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3044_Nat__Transfer_Otransfer__int__nat__relations_I4_J)). 120.83/55.33 thf(17265,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3564])). 120.83/55.33 thf(892,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4310_gcd__semilattice__nat_Oinf__left__commute)). 120.83/55.33 thf(7991,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[892])). 120.83/55.33 thf(2988,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ one_on1684967323de_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2481_div__by__1)). 120.83/55.33 thf(15337,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ one_on1684967323de_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2988])). 120.83/55.33 thf(3258,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2864_less__Suc__eq)). 120.83/55.33 thf(16289,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3258])). 120.83/55.33 thf(720,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3728_sin__cos__squared__add)). 120.83/55.33 thf(7355,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])). 120.83/55.33 thf(2234,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 120.83/55.33 thf(12658,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234])). 120.83/55.33 thf(4443,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_not__sum__squares__lt__zero)). 120.83/55.33 thf(20567,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4443])). 120.83/55.33 thf(2220,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3008_power__Suc2)). 120.83/55.33 thf(12615,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220])). 120.83/55.33 thf(1758,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4411_powr__less__cancel)). 120.83/55.33 thf(11035,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758])). 120.83/55.33 thf(2036,axiom,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex)) @ (hAPP_int_complex @ number528085621omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_double__number__of__Bit0)). 120.83/55.33 thf(11960,plain,((! [A:$i]: ((hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ bit0 @ A)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex)) @ (hAPP_int_complex @ number528085621omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036])). 120.83/55.33 thf(2750,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4008_coprime__sos)). 120.83/55.33 thf(14499,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2750])). 120.83/55.33 thf(309,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ D))) @ B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3396_sin__bound__lemma)). 120.83/55.33 thf(5971,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ A)) @ D))) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ abs_abs_real @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 120.83/55.33 thf(526,axiom,((! [A:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ zero_zero_complex) @ A)) => (zero_zero_complex = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_dvd__0__left)). 120.83/55.33 thf(6693,plain,((! [A:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ zero_zero_complex) @ A)) => (zero_zero_complex = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 120.83/55.33 thf(1250,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4357_coprime__rmult__nat)). 120.83/55.33 thf(9229,plain,((! [A:$i,B:$i,C:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C)) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250])). 120.83/55.33 thf(1030,axiom,((! [A:$i,B:$i]: (((hAPP_int_rat @ number_number_of_rat @ A) = B) <=> ((hAPP_int_rat @ number_number_of_rat @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__reorient)). 120.83/55.33 thf(8478,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])). 120.83/55.33 thf(3309,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4673_rat__number__collapse_I1_J)). 120.83/55.33 thf(16458,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ zero_zero_int) @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3309])). 120.83/55.33 thf(569,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3608_arccos__ubound)). 120.83/55.33 thf(6822,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arccos @ A)) @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])). 120.83/55.33 thf(3831,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1858_add__pos__nonneg)). 120.83/55.33 thf(18220,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3831])). 120.83/55.33 thf(2421,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.33 thf(13349,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2421])). 120.83/55.33 thf(3892,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4984_gcd__red__int)). 120.83/55.33 thf(18453,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3892])). 120.83/55.33 thf(3441,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ E) @ B)) @ D)) <= ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ D))) <= ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ E) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2407_mod__add__cong)). 120.83/55.33 thf(16871,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ A)) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ E) @ B)) @ D)) | ~ ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ D)) | ~ ((hAPP_C498520661umeral @ (div_mo1740067990umeral @ C) @ D) = (hAPP_C498520661umeral @ (div_mo1740067990umeral @ E) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3441])). 120.83/55.33 thf(3484,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2386_mod__mult__eq)). 120.83/55.33 thf(17024,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3484])). 120.83/55.33 thf(4787,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1560_le__add__iff1)). 120.83/55.33 thf(21932,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4787])). 120.83/55.33 thf(2578,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_aux @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2772_nat__aux__def)). 120.83/55.33 thf(13890,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (nat_aux @ A) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_int_nat @ nat @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2578])). 120.83/55.33 thf(20,axiom,((! [A:$i]: (A = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4120_complex__surj)). 120.83/55.33 thf(5004,plain,((! [A:$i]: (A = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ im @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 120.83/55.33 thf(2384,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__number__of)). 120.83/55.33 thf(13207,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_int_real @ number267125858f_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384])). 120.83/55.33 thf(1103,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3089_exp__mono__le)). 120.83/55.33 thf(8754,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B))))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103])). 120.83/55.33 thf(657,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A)) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_power3__eq__cube)). 120.83/55.33 thf(7153,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A)) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])). 120.83/55.33 thf(1943,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1744_Nat_Odiff__cancel)). 120.83/55.33 thf(11680,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943])). 120.83/55.33 thf(3653,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3536_diff__int__def)). 120.83/55.33 thf(17592,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3653])). 120.83/55.33 thf(2367,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2116_mult__1)). 120.83/55.33 thf(13133,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367])). 120.83/55.33 thf(1012,axiom,(((quotient_of @ one_one_rat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4659_rat__one__code)). 120.83/55.33 thf(8412,plain,(((quotient_of @ one_one_rat) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ one_one_int) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012])). 120.83/55.33 thf(4662,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_power2__eq__square)). 120.83/55.33 thf(21458,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ A) = (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4662])). 120.83/55.33 thf(2912,axiom,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3234_Suc__Suc__mult__two__diff__two)). 120.83/55.33 thf(15076,plain,((! [A:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2912])). 120.83/55.33 thf(3221,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2048_add__strict__mono)). 120.83/55.33 thf(16165,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ D) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3221])). 120.83/55.33 thf(1634,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ E) @ B)) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ D)) <= ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ D))) <= ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ E) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2408_mod__add__cong)). 120.83/55.33 thf(10601,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ E) @ B)) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ A)) @ D)) | ~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ D)) | ~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ C) @ D) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ E) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634])). 120.83/55.33 thf(3326,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => ((B = A) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1706_dvd_Oantisym__conv)). 120.83/55.33 thf(16507,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) => (((B = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3326])). 120.83/55.33 thf(4448,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ A @ (hAPP_nat_int @ B @ C)) = (hAPP_nat_int @ (hAPP_f1139079189at_int @ (hAPP_f1431025877at_int @ cOMBB_int_int_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__Int__Oint_000tc__Nat__Onat_U)). 120.83/55.33 thf(20580,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ A @ (hAPP_nat_int @ B @ C)) = (hAPP_nat_int @ (hAPP_f1139079189at_int @ (hAPP_f1431025877at_int @ cOMBB_int_int_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4448])). 120.83/55.33 thf(2398,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1253_zero__less__power)). 120.83/55.33 thf(13257,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398])). 120.83/55.33 thf(1483,axiom,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4681_rat__number__of__def)). 120.83/55.33 thf(10041,plain,((! [A:$i]: ((hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ one_one_int) = (hAPP_int_rat @ number_number_of_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483])). 120.83/55.33 thf(4694,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))) <= (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2889_Parity_Oeven__plus__odd)). 120.83/55.33 thf(21566,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A))) => (~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))))) | ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4694])). 120.83/55.33 thf(598,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4417_le__floor)). 120.83/55.33 thf(6925,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 120.83/55.33 thf(3604,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3378_natceiling__add__number__of)). 120.83/55.33 thf(17414,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natceiling @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (natceiling @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3604])). 120.83/55.33 thf(682,axiom,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1457_four__x__squared)). 120.83/55.33 thf(7242,plain,((! [A:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])). 120.83/55.33 thf(4423,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_less__special_I4_J)). 120.83/55.33 thf(20492,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ number_number_of_rat @ A)) @ one_one_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4423])). 120.83/55.33 thf(2796,axiom,((! [A:$i]: ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)))) <=> (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1509_not__real__square__gt__zero)). 120.83/55.33 thf(14685,plain,((! [A:$i]: (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)))) => (zero_zero_real = A)) & ((zero_zero_real = A) => (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2796])). 120.83/55.33 thf(4351,axiom,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zero__power2)). 120.83/55.33 thf(20219,plain,(((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4351])). 120.83/55.33 thf(1595,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 120.83/55.33 thf(10453,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595])). 120.83/55.33 thf(181,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B))) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) = B)) <= (C != D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3891_DERIV__const__ratio__const2)). 120.83/55.33 thf(5537,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: (hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ B))) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) = B)) | (C = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 120.83/55.33 thf(4050,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.33 thf(19047,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ one_one_int)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4050])). 120.83/55.33 thf(4049,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_sum__squares__ge__zero)). 120.83/55.33 thf(19045,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4049])). 120.83/55.33 thf(2089,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3923_real__root__le__1__iff)). 120.83/55.33 thf(12117,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ one_one_real)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089])). 120.83/55.33 thf(147,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2121_mult__1__left)). 120.83/55.33 thf(5430,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ one_one_real) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 120.83/55.33 thf(752,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1280_one__le__power)). 120.83/55.33 thf(7489,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 120.83/55.33 thf(2811,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((zero_z891286103de_int != D) => ((((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ A)) <=> ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ D))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ D) @ B))) <= (zero_z891286103de_int != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2637_dvd__div__div__eq__mult)). 120.83/55.33 thf(14738,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (zero_z891286103de_int = D)) => (((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ A)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ D))) & (((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ D)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ D) @ A)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ C) @ A)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ D) @ B)) | (zero_z891286103de_int = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2811])). 120.83/55.33 thf(811,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4293_Bnor__mem__zle)). 120.83/55.33 thf(7712,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ (bnorRset @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])). 120.83/55.33 thf(4565,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ one_one_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))) = (hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4232_mod__pos__neg__1__number__of)). 120.83/55.33 thf(21117,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int)) => ((hAPP_P1175774780nt_int @ product_snd_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ one_one_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))) = (hAPP_int_int @ (div_mod_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4565])). 120.83/55.33 thf(4140,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ one_one_int)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2478_div__by__1)). 120.83/55.33 thf(19420,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ one_one_int)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4140])). 120.83/55.33 thf(2698,axiom,((! [A:$i,B:$i]: ((zero_z891286103de_int != B) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ one_on1684967323de_int) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2631_div__add__self1)). 120.83/55.33 thf(14332,plain,((! [A:$i,B:$i]: ((~ (zero_z891286103de_int = B)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) @ one_on1684967323de_int) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2698])). 120.83/55.33 thf(4182,axiom,((~ (! [A:$i]: ((is_int @ A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ A) != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_)). 120.83/55.33 thf(19558,plain,((~ (! [A:$i]: ((is_int @ A) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4182])). 120.83/55.33 thf(1093,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) <= (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1716_dvd_Ole__less__trans)). 120.83/55.33 thf(8726,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) | ~ (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093])). 120.83/55.33 thf(3753,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_nat__mult__2__right)). 120.83/55.33 thf(17956,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3753])). 120.83/55.33 thf(1953,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3819_exp__less__mono)). 120.83/55.33 thf(11712,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ exp_real @ A)) @ (hAPP_real_real @ exp_real @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953])). 120.83/55.33 thf(2823,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2960_of__nat__mult)). 120.83/55.33 thf(14779,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ B)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2823])). 120.83/55.33 thf(4115,axiom,((! [A:$i]: ((is_int @ A) => ((((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)) = A) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3121_int__nat__eq)). 120.83/55.33 thf(19339,plain,((! [A:$i]: ((is_int @ A) => ((((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A)) = A) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((zero_zero_int = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_int_nat @ nat @ A))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4115])). 120.83/55.33 thf(4059,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ! [F:$i]: ((((hBOOL @ (hAPP_int_bool @ C @ F)) <=> (hBOOL @ (hAPP_int_bool @ B @ F))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ F))) <= (is_int @ F))) => ((((? [E:$i]: (? [F:$i]: ((hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (is_int @ F)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E)) | ? [E:$i]: ((is_int @ E) & (hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))) <=> (? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E)))) <= (! [E:$i,F:$i]: (((is_int @ E) & (is_int @ F)) => ((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D)))) <=> (hBOOL @ (hAPP_int_bool @ B @ E)))))) <= (! [E:$i]: ((((hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D))) <= (hBOOL @ (hAPP_int_bool @ C @ E))) <= (! [F:$i]: ((! [G:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ A)) => (E != (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D)))))) <= (is_int @ E))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5156_cppi)). 120.83/55.33 thf(19073,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ! [F:$i]: ((((hBOOL @ (hAPP_int_bool @ C @ F)) => (hBOOL @ (hAPP_int_bool @ B @ F))) & ((hBOOL @ (hAPP_int_bool @ B @ F)) => (hBOOL @ (hAPP_int_bool @ C @ F)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ F)) | ~ (is_int @ F))) => ((((? [E:$i]: (? [F:$i]: ((hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (is_int @ F)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E)) | ? [E:$i]: ((is_int @ E) & (hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))) => (? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E)))) & ((? [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ E)) & (is_int @ E))) => (? [E:$i]: (? [F:$i]: ((hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ F) @ E))) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ A)) & (is_int @ F)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) & (is_int @ E)) | ? [E:$i]: ((is_int @ E) & (hBOOL @ (hAPP_int_bool @ B @ E)) & (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))))) | ~ (! [E:$i,F:$i]: (((is_int @ E) & (is_int @ F)) => (((hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D)))) => (hBOOL @ (hAPP_int_bool @ B @ E))) & ((hBOOL @ (hAPP_int_bool @ B @ E)) => (hBOOL @ (hAPP_int_bool @ B @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ F) @ D)))))))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_int_bool @ C @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ C @ E)) | ~ (! [F:$i]: (! [G:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ A)) => (~ (E = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ G) @ F)))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))))) | ~ (is_int @ E))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4059])). 120.83/55.33 thf(1645,axiom,((! [A:$i,B:$i]: (((one_one_rat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1495_dvd__power)). 120.83/55.33 thf(10631,plain,((! [A:$i,B:$i]: (((one_one_rat = A) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645])). 120.83/55.33 thf(3931,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => (zero_zero_nat = A)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_nat_int @ semiri1621563631at_int @ A) = B))) <=> ((hAPP_int_nat @ nat @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3166_nat__eq__iff2)). 120.83/55.33 thf(18583,plain,((! [A:$i,B:$i]: ((is_int @ B) => (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => (zero_zero_nat = A)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_nat_int @ semiri1621563631at_int @ A) = B))) => ((hAPP_int_nat @ nat @ B) = A)) & (((hAPP_int_nat @ nat @ B) = A) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) => (zero_zero_nat = A)) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_nat_int @ semiri1621563631at_int @ A) = B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3931])). 120.83/55.33 thf(2131,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3916_real__root__ge__0__iff)). 120.83/55.33 thf(12285,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A))))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131])). 120.83/55.33 thf(591,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B) = (hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ ln @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4437_powr__def)). 120.83/55.33 thf(6906,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B) = (hAPP_real_real @ exp_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_real_real @ ln @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 120.83/55.33 thf(2662,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_semiring__one__add__one__is__two)). 120.83/55.33 thf(14208,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ one_one_real) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2662])). 120.83/55.33 thf(3992,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ fact_fact_int @ B)) @ (hAPP_int_int @ fact_fact_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4274_fact__less__mono__int)). 120.83/55.33 thf(18804,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ fact_fact_int @ B)) @ (hAPP_int_int @ fact_fact_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3992])). 120.83/55.33 thf(1194,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2382_mod__mult__left__eq)). 120.83/55.33 thf(9051,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194])). 120.83/55.33 thf(4099,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4989_gcd__abs1__int)). 120.83/55.33 thf(19272,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4099])). 120.83/55.33 thf(684,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.83/55.33 thf(7248,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ one_one_complex) @ one_one_complex)) @ A) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 120.83/55.33 thf(2779,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ sqrt @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3877_DERIV__real__sqrt)). 120.83/55.33 thf(14615,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ sqrt @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ sqrt @ A))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2779])). 120.83/55.33 thf(2569,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_mult__neg__pos)). 120.83/55.33 thf(13862,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2569])). 120.83/55.33 thf(4390,axiom,((! [A:$i]: (((hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ one_one_int)) = one_one_int) <= (hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1504_Legendre__1mod4)). 120.83/55.33 thf(20361,plain,((! [A:$i]: (((hAPP_int_int @ (legendre @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ one_one_int)) = one_one_int) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A)) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4390])). 120.83/55.33 thf(1725,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_mult__less__cancel__left__pos)). 120.83/55.33 thf(10892,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725])). 120.83/55.33 thf(674,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) <= (C != zero_z891286103de_int)) & ((zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) <= (C = zero_z891286103de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2552_div__mult__mult1__if)). 120.83/55.33 thf(7210,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ B)) | (C = zero_z891286103de_int)) & ((zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) | ~ (C = zero_z891286103de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 120.83/55.33 thf(1391,axiom,((! [A:$i,B:$i]: (((B = zero_zero_nat) => (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) & (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1831_realpow__num__eq__if)). 120.83/55.33 thf(9728,plain,((! [A:$i,B:$i]: (((B = zero_zero_nat) => (one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))) & (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ one_one_nat)))) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391])). 120.83/55.33 thf(4948,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2092_diff__eq__diff__less__eq)). 120.83/55.33 thf(22472,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ C) @ D)))) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4948])). 120.83/55.33 thf(3644,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__special_I3_J)). 120.83/55.33 thf(17561,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int) = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ bit1 @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3644])). 120.83/55.33 thf(2274,axiom,((! [A:$i,B:$i]: (((A != B) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4657_less__rat__def)). 120.83/55.33 thf(12798,plain,((! [A:$i,B:$i]: (((~ (A = B) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ B)) => (~ (A = B) & (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274])). 120.83/55.33 thf(381,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2453_dvd__mod__imp__dvd)). 120.83/55.33 thf(6226,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 120.83/55.33 thf(491,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ tan @ A)) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3619_tan__inverse)). 120.83/55.33 thf(6580,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ one_one_real) @ (hAPP_real_real @ tan @ A)) = (hAPP_real_real @ tan @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 120.83/55.33 thf(1202,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4160_termination__basic__simps_I3_J)). 120.83/55.33 thf(9070,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202])). 120.83/55.33 thf(86,axiom,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ B)) @ A)) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4144_sin__n__Im__cis__pow__n)). 120.83/55.33 thf(5247,plain,((! [A:$i,B:$i]: ((hAPP_complex_real @ im @ (hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ (cis @ B)) @ A)) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 120.83/55.33 thf(3257,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2290_mult__right_Ozero)). 120.83/55.33 thf(16286,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3257])). 120.83/55.33 thf(1948,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2146_add__nonpos__nonpos)). 120.83/55.33 thf(11695,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A)) @ zero_zero_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948])). 120.83/55.33 thf(1422,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3334_real__sqrt__gt__1__iff)). 120.83/55.33 thf(9844,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422])). 120.83/55.33 thf(1552,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (nat_gcd @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4623_Nitpick_Oint__gcd__def)). 120.83/55.33 thf(10280,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (nat_gcd @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552])). 120.83/55.33 thf(3463,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_le__special_I1_J)). 120.83/55.33 thf(16943,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_int_real @ number267125858f_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3463])). 120.83/55.33 thf(3088,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2420_mod__add__eq)). 120.83/55.33 thf(15690,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3088])). 120.83/55.33 thf(3272,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_sum__squares__ge__zero)). 120.83/55.33 thf(16341,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3272])). 120.83/55.33 thf(3442,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2428_mod__add__right__eq)). 120.83/55.33 thf(16874,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3442])). 120.83/55.33 thf(1493,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_real)) => (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_even__power__le__0__imp__0)). 120.83/55.33 thf(10073,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_real)) => (zero_zero_real = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493])). 120.83/55.33 thf(2405,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ one_one_nat)))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) != zero_zero_nat)) & ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3800_fact__add__num__eq__if__nat)). 120.83/55.33 thf(13294,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ one_one_nat)))) | ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = zero_zero_nat)) & ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => ((hAPP_nat_nat @ fact_fact_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2405])). 120.83/55.33 thf(294,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4704_real__divide__code)). 120.83/55.33 thf(5926,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (ratreal @ A)) @ (ratreal @ B)) = (ratreal @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ inverse_divide_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 120.83/55.33 thf(426,axiom,((! [A:$i,B:$i]: ((zero_zero_real != (hAPP_real_real @ cos @ B)) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A)))) <= (zero_zero_real != (hAPP_real_real @ cos @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3713_add__tan__eq)). 120.83/55.33 thf(6366,plain,((! [A:$i,B:$i]: ((~ (zero_zero_real = (hAPP_real_real @ cos @ B))) => (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ tan @ B)) @ (hAPP_real_real @ tan @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ B)) @ (hAPP_real_real @ cos @ A)))) | (zero_zero_real = (hAPP_real_real @ cos @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 120.83/55.33 thf(556,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ A)) = (hAPP_real_real @ tan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3673_tan__def)). 120.83/55.33 thf(6782,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ cos @ A)) = (hAPP_real_real @ tan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])). 120.83/55.33 thf(2752,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.33 thf(14504,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2752])). 120.83/55.33 thf(1543,axiom,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ fTrue) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T)). 120.83/55.33 thf(10250,plain,((! [A:$i,B:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ fTrue) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543])). 120.83/55.33 thf(2128,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2015_add__left__mono)). 120.83/55.33 thf(12272,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128])). 120.83/55.33 thf(4466,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4967_gcd__add__mult__int)). 120.83/55.33 thf(20659,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4466])). 120.83/55.33 thf(30,axiom,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ norm_norm_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3382_real__norm__def)). 120.83/55.33 thf(5041,plain,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ norm_norm_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 120.83/55.33 thf(1383,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) <=> (C = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2880_exp__mono__eq)). 120.83/55.33 thf(9697,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))) => (C = A)) & ((C = A) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383])). 120.83/55.33 thf(4553,axiom,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => ((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) <=> ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & ! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) <= (is_int @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5009_gcd__unique__int)). 120.83/55.33 thf(21053,plain,((! [A:$i,B:$i,C:$i]: ((is_int @ C) => (((C = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & ! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) | ~ (is_int @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A)))) & (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & ! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ A)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ C))) | ~ (is_int @ D)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))) => (C = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4553])). 120.83/55.33 thf(4802,axiom,((! [A:$i,B:$i,C:$i]: (((((A = C) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_nat_nat @ suc @ B)))) <= ((is_int @ A) & (is_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3108_power__inject__base)). 120.83/55.33 thf(21981,plain,((! [A:$i,B:$i,C:$i]: ((A = C) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ (hAPP_nat_nat @ suc @ B))) | ~ ((is_int @ A) & (is_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4802])). 120.83/55.33 thf(2301,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ E)) => ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) @ E)) <= (one_one_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1465_convex__bound__le)). 120.83/55.33 thf(12904,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ D) @ E)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ D)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))) @ E)) | ~ (one_one_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301])). 120.83/55.33 thf(1582,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1887_add__nonpos__neg)). 120.83/55.33 thf(10408,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ zero_z126310315umeral)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ zero_z126310315umeral)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582])). 120.83/55.33 thf(4376,axiom,((! [A:$i,B:$i]: (((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) => ((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) = (norm_frac @ A @ B)) <= (~ ((A = zero_zero_int) | (zero_zero_int = B)))) & (((zero_zero_int = B) | (zero_zero_int = A)) => ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (norm_frac @ A @ B))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((norm_frac @ A @ B) = (norm_frac @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B)))) <= ((is_int @ A) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4804_norm__frac_Opsimps)). 120.83/55.33 thf(20297,plain,((! [A:$i,B:$i]: ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) => ((((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) = (norm_frac @ A @ B)) | (A = zero_zero_int) | (zero_zero_int = B)) & (((zero_zero_int = B) | (zero_zero_int = A)) => ((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int) = (norm_frac @ A @ B))))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int)) => ((norm_frac @ A @ B) = (norm_frac @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B))))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ A) @ B))) | ~ ((is_int @ A) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4376])). 120.83/55.33 thf(1051,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1279_one__le__power)). 120.83/55.33 thf(8542,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051])). 120.83/55.33 thf(2031,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2422_mod__add__left__eq)). 120.83/55.33 thf(11943,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ C)) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031])). 120.83/55.33 thf(4739,axiom,((! [A:$i]: (((hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_i1948725293t_bool @ d22set @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (hBOOL @ (hAPP_int_bool @ zprime @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2244_d22set__eq__wset)). 120.83/55.33 thf(21763,plain,((! [A:$i]: (((hAPP_i1948725293t_bool @ (wset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ A) = (hAPP_i1948725293t_bool @ d22set @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (hBOOL @ (hAPP_int_bool @ zprime @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4739])). 120.83/55.33 thf(2889,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ D) @ B))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2248_minf_I10_J)). 120.83/55.33 thf(14999,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2889])). 120.83/55.33 thf(4848,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2065_add__less__cancel__left)). 120.83/55.33 thf(22147,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4848])). 120.83/55.33 thf(3697,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) <=> (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_double__eq__0__iff)). 120.83/55.33 thf(17757,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) => (A = zero_zero_int)) & ((A = zero_zero_int) => (zero_zero_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3697])). 120.83/55.33 thf(2940,axiom,((! [A:$i,B:$i]: ((B != zero_z891286103de_int) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2548_div__mult__self2__is__id)). 120.83/55.33 thf(15172,plain,((! [A:$i,B:$i]: ((~ (B = zero_z891286103de_int)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2940])). 120.83/55.33 thf(3755,axiom,((~ (hBOOL @ fFalse))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U)). 120.83/55.33 thf(17961,plain,((~ (hBOOL @ fFalse))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3755])). 120.83/55.33 thf(4743,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_semiring__mult__2)). 120.83/55.33 thf(21778,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4743])). 120.83/55.33 thf(3300,axiom,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ one_on1684967323de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1213_zero__le__one)). 120.83/55.33 thf(16426,plain,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ one_on1684967323de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3300])). 120.83/55.33 thf(3946,axiom,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_semiring__add__number__of)). 120.83/55.33 thf(18638,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ (hAPP_int_real @ number267125858f_real @ A)) = (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ pls) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3946])). 120.83/55.33 thf(2758,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_rat)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ one_one_rat))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3159_power__Suc__less__one)). 120.83/55.33 thf(14546,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_nat_nat @ suc @ A))) @ one_one_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ one_one_rat)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2758])). 120.83/55.33 thf(849,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) <= (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4353_gcd__mult__cancel__nat)). 120.83/55.33 thf(7851,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ C)) | ~ (one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])). 120.83/55.33 thf(506,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) @ (hAPP_real_real @ B @ E))))) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ (hAPP_real_real @ B @ E))) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3945_MVT2)). 120.83/55.33 thf(6627,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ E)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ A @ D)) @ (hAPP_real_real @ A @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ D) @ C)) @ (hAPP_real_real @ B @ E)))) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ E) @ (hAPP_real_real @ B @ E))) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ E) @ D)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ C) @ E))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 120.83/55.33 thf(3745,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2742_Nat__Transfer_Otransfer__nat__int__functions_I2_J)). 120.83/55.33 thf(17937,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ B)) @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3745])). 120.83/55.33 thf(4705,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ d22set @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2268_d22set__mem)). 120.83/55.33 thf(21630,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ d22set @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4705])). 120.83/55.33 thf(4496,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ B @ A)) <= (! [C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ B @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))) <= ((is_int @ D) & (is_int @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5027_Rat__induct)). 120.83/55.33 thf(20769,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ B @ A)) | ~ (! [C:$i,D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ D)) => ((one_one_int = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ C) @ D)) => (hBOOL @ (hAPP_rat_bool @ B @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ C) @ D))))) | ~ ((is_int @ D) & (is_int @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4496])). 120.83/55.33 thf(1957,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)) <= (! [D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) <= ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ uminus_uminus_int @ D)) @ (hAPP_int_int @ uminus_uminus_int @ E))))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E)))) <= ((is_int @ E) & (is_int @ D))))) <= (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4572_norm__frac_Opinduct)). 120.83/55.33 thf(11727,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)) | ~ (! [D:$i,E:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) | ~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ E) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ (hAPP_int_int @ uminus_uminus_int @ D)) @ (hAPP_int_int @ uminus_uminus_int @ E)))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) | ~ ((is_int @ E) & (is_int @ D)))) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ norm_frac_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957])). 120.83/55.33 thf(3942,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2527_pos__mod__bound)). 120.83/55.33 thf(18628,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (div_mod_int @ A) @ B)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3942])). 120.83/55.33 thf(4462,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.33 thf(20648,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4462])). 120.83/55.33 thf(2557,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_mult__left__mono)). 120.83/55.33 thf(13819,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557])). 120.83/55.33 thf(4405,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((A = C) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1479_power__eq__imp__eq__base)). 120.83/55.33 thf(20429,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((A = C) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ B) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4405])). 120.83/55.33 thf(2357,axiom,((! [A:$i]: ((is_int @ A) => ((min = A) <=> (min = (hAPP_int_int @ bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_rel__simps_I43_J)). 120.83/55.33 thf(13101,plain,((! [A:$i]: ((is_int @ A) => (((min = A) => (min = (hAPP_int_int @ bit1 @ A))) & ((min = (hAPP_int_int @ bit1 @ A)) => (min = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357])). 120.83/55.33 thf(3626,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (z3mod @ A) @ B)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (z3mod @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3949_z3mod__def)). 120.83/55.33 thf(17488,plain,((! [A:$i,B:$i]: ((((hAPP_int_int @ (div_mod_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (hAPP_int_int @ (z3mod @ A) @ B)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (z3mod @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3626])). 120.83/55.33 thf(4710,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) @ one_one_int))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ B)))) @ one_one_int) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2318_zmod__number__of__Bit1)). 120.83/55.33 thf(21653,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) @ one_one_int))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B)))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ one_one_int)) @ (hAPP_int_int @ number_number_of_int @ B)))) @ one_one_int) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4710])). 120.83/55.33 thf(2141,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3144_of__nat__0__less__iff)). 120.83/55.33 thf(12312,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141])). 120.83/55.33 thf(59,axiom,((zero_zero_real = (hAPP_complex_real @ re @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4119_complex__Re__i)). 120.83/55.33 thf(5159,plain,((zero_zero_real = (hAPP_complex_real @ re @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 120.83/55.33 thf(1736,axiom,((! [A:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3143_of__nat__0__less__iff)). 120.83/55.33 thf(10941,plain,((! [A:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_n522471361de_int @ semiri1424489471de_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736])). 120.83/55.33 thf(4456,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2023_add__le__cancel__left)). 120.83/55.33 thf(20608,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4456])). 120.83/55.33 thf(772,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) => (zero_zero_real = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3348_real__sqrt__sum__squares__eq__cancel)). 120.83/55.33 thf(7557,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = A) => (zero_zero_real = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])). 120.83/55.33 thf(2879,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2123_mult__1__left)). 120.83/55.33 thf(14967,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ one_one_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2879])). 120.83/55.33 thf(669,axiom,((! [A:$i,B:$i]: ((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) <=> ((zero_zero_nat = A) & (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1613_add__is__0)). 120.83/55.33 thf(7184,plain,((! [A:$i,B:$i]: (((zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) => ((zero_zero_nat = A) & (zero_zero_nat = B))) & (((zero_zero_nat = A) & (zero_zero_nat = B)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])). 120.83/55.33 thf(403,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1735_real__le__linear)). 120.83/55.33 thf(6294,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 120.83/55.33 thf(1904,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2012_add__left__mono)). 120.83/55.33 thf(11557,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904])). 120.83/55.33 thf(350,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1561_le__add__iff1)). 120.83/55.33 thf(6114,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 120.83/55.33 thf(3999,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1384_mult__left__le__one__le)). 120.83/55.33 thf(18830,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ one_one_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3999])). 120.83/55.33 thf(3948,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((one_one_int = A) | (zero_zero_int = A)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_int__pos__lt__two__imp__zero__or__one)). 120.83/55.33 thf(18643,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => ((one_one_int = A) | (zero_zero_int = A)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3948])). 120.83/55.33 thf(3979,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_power__even__eq)). 120.83/55.33 thf(18759,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3979])). 120.83/55.33 thf(4723,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1986_add__0__left)). 120.83/55.33 thf(21702,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4723])). 120.83/55.33 thf(4908,axiom,((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2882_odd__one__int)). 120.83/55.33 thf(22337,plain,((~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4908])). 120.83/55.33 thf(4796,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_dvd__add)). 120.83/55.33 thf(21959,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4796])). 120.83/55.33 thf(2280,axiom,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2500_mod__by__1)). 120.83/55.33 thf(12820,plain,((! [A:$i]: ((hAPP_nat_nat @ (div_mod_nat @ A) @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280])). 120.83/55.33 thf(3904,axiom,((! [A:$i,B:$i]: ((zero_zero_int = (hAPP_int_int @ (standardRes @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2592_StandardRes__eq__zcong)). 120.83/55.33 thf(18506,plain,((! [A:$i,B:$i]: (((zero_zero_int = (hAPP_int_int @ (standardRes @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ zero_zero_int) @ A)) => (zero_zero_int = (hAPP_int_int @ (standardRes @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3904])). 120.83/55.33 thf(1260,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3056_less__add__Suc1)). 120.83/55.33 thf(9271,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260])). 120.83/55.33 thf(102,axiom,((! [A:$i]: ((natceiling @ (hAPP_nat_real @ real_nat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3639_natceiling__real__of__nat)). 120.83/55.33 thf(5290,plain,((! [A:$i]: ((natceiling @ (hAPP_nat_real @ real_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 120.83/55.33 thf(901,axiom,((! [A:$i]: ((zero_zero_real != A) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zero__less__power2)). 120.83/55.33 thf(8019,plain,((! [A:$i]: (((~ (zero_zero_real = A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (~ (zero_zero_real = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])). 120.83/55.33 thf(4082,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) <=> (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zero__eq__power2)). 120.83/55.33 thf(19212,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) => (A = zero_zero_int)) & ((A = zero_zero_int) => (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4082])). 120.83/55.33 thf(2139,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ one_one_nat)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.33 thf(12307,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ one_one_nat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139])). 120.83/55.33 thf(2018,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1659_nat__mult__1__right)). 120.83/55.33 thf(11903,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018])). 120.83/55.33 thf(1043,axiom,((! [A:$i,B:$i,C:$i]: (((A = B) <=> ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1285_power__inject__exp)). 120.83/55.33 thf(8510,plain,((! [A:$i,B:$i,C:$i]: ((((A = B) => ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B))) & (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ A) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) => (A = B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043])). 120.83/55.33 thf(1472,axiom,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.33 thf(10009,plain,((! [A:$i]: (A = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472])). 120.83/55.33 thf(3047,axiom,((! [A:$i]: ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1698_dvd_Oless__irrefl)). 120.83/55.33 thf(15533,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3047])). 120.83/55.33 thf(2915,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_right__distrib__number__of)). 120.83/55.33 thf(15091,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_i769753017umeral @ number1443263063umeral @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2915])). 120.83/55.33 thf(1333,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4433_powr__le__cancel__iff)). 120.83/55.33 thf(9541,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ C) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333])). 120.83/55.33 thf(1861,axiom,((! [A:$i]: ((zero_zero_rat = A) <=> (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_double__eq__0__iff)). 120.83/55.33 thf(11415,plain,((! [A:$i]: (((zero_zero_rat = A) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A))) & ((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) => (zero_zero_rat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861])). 120.83/55.33 thf(540,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) <= ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_dvdI)). 120.83/55.33 thf(6735,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_complex_bool @ (hAPP_c1403687985x_bool @ dvd_dvd_complex @ B) @ A)) | ~ ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])). 120.83/55.33 thf(3773,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1420_power__less__power__Suc)). 120.83/55.33 thf(18025,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3773])). 120.83/55.33 thf(47,axiom,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ re @ A))) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) = (hAPP_complex_complex @ uminus473333897omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4135_complex__minus__def)). 120.83/55.33 thf(5105,plain,((! [A:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ re @ A))) @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_complex_real @ im @ A))) = (hAPP_complex_complex @ uminus473333897omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 120.83/55.33 thf(3524,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) <=> (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1849_nat__eq__add__iff2)). 120.83/55.33 thf(17135,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E)) => ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) => (B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C))) & ((B = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3524])). 120.83/55.33 thf(2646,axiom,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2124_mult__1__left)). 120.83/55.33 thf(14159,plain,((! [A:$i]: (A = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ one_on1684967323de_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2646])). 120.83/55.33 thf(632,axiom,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3719_sin__pi__half)). 120.83/55.33 thf(7050,plain,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])). 120.83/55.33 thf(1157,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i,E:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ E)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)))) <=> ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2787_nat__mod__eq__iff)). 120.83/55.33 thf(8921,plain,((! [A:$i,B:$i,C:$i]: (((? [D:$i,E:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ E)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)))) => ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B))) & (((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = (hAPP_nat_nat @ (div_mod_nat @ C) @ B)) => (? [D:$i,E:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ E)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157])). 120.83/55.33 thf(1966,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 120.83/55.33 thf(11759,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966])). 120.83/55.33 thf(4056,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ (wset @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2223_wset__mem__mem)). 120.83/55.33 thf(19068,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ (hAPP_i1948725293t_bool @ (wset @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4056])). 120.83/55.33 thf(1142,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1422_power__less__power__Suc)). 120.83/55.33 thf(8869,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142])). 120.83/55.33 thf(4736,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ A) @ (posDivAlg @ B @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2799_posDivAlg__correct)). 120.83/55.33 thf(21757,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ B @ A) @ (posDivAlg @ B @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4736])). 120.83/55.33 thf(4359,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ D)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D))) <= ((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4526_zcong__cancel2)). 120.83/55.33 thf(20243,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ D)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ B)) @ D)))) | ~ ((hAPP_int_int @ (legacy_zgcd @ C) @ D) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4359])). 120.83/55.33 thf(2777,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2839_of__nat__Suc)). 120.83/55.33 thf(14600,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ one_one_nat) @ (hAPP_nat_nat @ semiri984289939at_nat @ A)) = (hAPP_nat_nat @ semiri984289939at_nat @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2777])). 120.83/55.33 thf(1891,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1305_power__add)). 120.83/55.33 thf(11522,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ B)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891])). 120.83/55.33 thf(2122,axiom,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ fequal_rat @ A) @ B)) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Rat__Orat_T)). 120.83/55.33 thf(12252,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ fequal_rat @ A) @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122])). 120.83/55.33 thf(533,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3683_cos__diff)). 120.83/55.33 thf(6714,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ sin @ A)) @ (hAPP_real_real @ sin @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 120.83/55.33 thf(4933,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1807_add__diff__add)). 120.83/55.33 thf(22411,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ C)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ D)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4933])). 120.83/55.33 thf(4009,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_power2__eq__square)). 120.83/55.33 thf(18865,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4009])). 120.83/55.33 thf(495,axiom,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_real @ real_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3635_abs__real__of__nat__cancel)). 120.83/55.33 thf(6590,plain,((! [A:$i]: ((hAPP_real_real @ abs_abs_real @ (hAPP_nat_real @ real_nat @ A)) = (hAPP_nat_real @ real_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 120.83/55.33 thf(3739,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2451_dvd__mod)). 120.83/55.33 thf(17910,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3739])). 120.83/55.33 thf(4335,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 120.83/55.33 thf(20170,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4335])). 120.83/55.33 thf(4316,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => (((! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ D))) <= (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ C))) <= (hBOOL @ (hAPP_int_bool @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2220_int__ge__induct)). 120.83/55.33 thf(20073,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ C)) => (((! [D:$i]: (((hBOOL @ (hAPP_int_bool @ A @ D)) => (hBOOL @ (hAPP_int_bool @ A @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ one_one_int)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ D)) | ~ (is_int @ D))) => (hBOOL @ (hAPP_int_bool @ A @ C))) | ~ (hBOOL @ (hAPP_int_bool @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4316])). 120.83/55.33 thf(1044,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4306_gcd__semilattice__nat_Oinf__commute)). 120.83/55.33 thf(8516,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044])). 120.83/55.33 thf(3265,axiom,((! [A:$i]: (((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) | (zero_zero_nat = A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3046_nat__lt__two__imp__zero__or__one)). 120.83/55.33 thf(16321,plain,((! [A:$i]: ((A = (hAPP_nat_nat @ suc @ zero_zero_nat)) | (zero_zero_nat = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3265])). 120.83/55.33 thf(4806,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1553_diff__bin__simps_I10_J)). 120.83/55.33 thf(21991,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4806])). 120.83/55.33 thf(2190,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ suc @ zero_zero_nat)) <=> (((zero_zero_nat = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))) | (((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3051_add__is__1)). 120.83/55.33 thf(12503,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ suc @ zero_zero_nat)) => (((zero_zero_nat = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))) | (((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = zero_zero_nat)))) & ((((zero_zero_nat = A) & (B = (hAPP_nat_nat @ suc @ zero_zero_nat))) | (((hAPP_nat_nat @ suc @ zero_zero_nat) = A) & (B = zero_zero_nat))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B) = (hAPP_nat_nat @ suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190])). 120.83/55.33 thf(1599,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_add__number__of__left)). 120.83/55.33 thf(10472,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599])). 120.83/55.33 thf(3375,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = zero_zero_nat) => ((zero_zero_nat = A) | (zero_zero_nat = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_divisors__zero)). 120.83/55.33 thf(16671,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B) = zero_zero_nat) => ((zero_zero_nat = A) | (zero_zero_nat = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3375])). 120.83/55.33 thf(2239,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1901_ab__semigroup__mult__class_Omult__ac_I1_J)). 120.83/55.33 thf(12679,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ C)) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239])). 120.83/55.33 thf(151,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A))) <= ((hAPP_real_real @ cos @ A) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3794_cos__zero__lemma)). 120.83/55.33 thf(5441,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (? [B:$i]: (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_nat_real @ real_nat @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) = A)) | ~ ((hAPP_real_real @ cos @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 120.83/55.33 thf(4224,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ D))) <= (! [E:$i]: ((is_int @ E) => ((! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (D != (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E))) <= (is_int @ F))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C))))))) <= (is_int @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5100_bset_I7_J)). 120.83/55.33 thf(19718,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) => (! [D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ D) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ D)) | ~ (! [E:$i]: ((is_int @ E) => (! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ B)) => (~ (D = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ F) @ E)))) | ~ (is_int @ F)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ E) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ C)))))) | ~ (is_int @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4224])). 120.83/55.33 thf(538,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ cOMBI_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U)). 120.83/55.33 thf(6729,plain,((! [A:$i]: (A = (hAPP_nat_nat @ cOMBI_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])). 120.83/55.33 thf(4926,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) <= ((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4660_normalize__denom__pos)). 120.83/55.33 thf(22392,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C)) | ~ ((normalize @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4926])). 120.83/55.33 thf(3665,axiom,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ pls))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3273_not__neg__number__of__Pls)). 120.83/55.33 thf(17649,plain,((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ pls))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3665])). 120.83/55.33 thf(695,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4305_gcd__commute__nat)). 120.83/55.33 thf(7278,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 120.83/55.33 thf(117,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)) @ D) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_combine__common__factor)). 120.83/55.33 thf(5339,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C)) @ B)) @ D) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 120.83/55.33 thf(1739,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) <=> ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3776_even__nat__equiv__def)). 120.83/55.33 thf(10956,plain,((! [A:$i]: (((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = zero_zero_nat)) & (((hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = zero_zero_nat) => (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739])). 120.83/55.33 thf(393,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real)) <=> (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_mult__le__0__iff)). 120.83/55.33 thf(6258,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))) & ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 120.83/55.33 thf(550,axiom,(((expi @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4001_expi__zero)). 120.83/55.33 thf(6765,plain,(((expi @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 120.83/55.33 thf(1398,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1862_add__pos__nonneg)). 120.83/55.33 thf(9752,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398])). 120.83/55.33 thf(3036,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1440_power__strict__increasing)). 120.83/55.33 thf(15493,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ A)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ C)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3036])). 120.83/55.33 thf(2509,axiom,(((collect_int @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ fEx_int) @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ cOMBB_int_bool_int) @ fequal_int)) @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = zEven)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5031_zEven__def)). 120.83/55.33 thf(13657,plain,(((collect_int @ (hAPP_f2119767738t_bool @ (hAPP_f423804115t_bool @ cOMBB_1418110531ol_int @ fEx_int) @ (hAPP_f1791153283t_bool @ (hAPP_f735247205t_bool @ cOMBC_983868720t_bool @ (hAPP_f1251097615t_bool @ (hAPP_f1475822739t_bool @ cOMBB_2027861294ol_int @ cOMBB_int_bool_int) @ fequal_int)) @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) = zEven)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509])). 120.83/55.33 thf(1770,axiom,((! [A:$i,B:$i]: (((zero_zero_rat = B) & (zero_zero_rat = A)) <=> (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_sum__power2__eq__zero__iff)). 120.83/55.33 thf(11067,plain,((! [A:$i,B:$i]: ((((zero_zero_rat = B) & (zero_zero_rat = A)) => (zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((zero_zero_rat = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((zero_zero_rat = B) & (zero_zero_rat = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770])). 120.83/55.33 thf(2657,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B))) <= ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4301_coprime__exp2__nat)). 120.83/55.33 thf(14191,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((one_one_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ D) @ B))) | ~ ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ D) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2657])). 120.83/55.33 thf(4503,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ A) & (is_int @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ B)) => (A = C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1460_zcong__zless__imp__eq)). 120.83/55.33 thf(20799,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ A) & (is_int @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ C) @ A) @ B)) => (A = C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4503])). 120.83/55.33 thf(1245,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2434_mod__add__self2)). 120.83/55.33 thf(9215,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245])). 120.83/55.33 thf(3070,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3000_int__mult)). 120.83/55.33 thf(15636,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ (hAPP_nat_int @ semiri1621563631at_int @ B)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3070])). 120.83/55.33 thf(2110,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((A = one_one_nat) | (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4172_prime__product)). 120.83/55.33 thf(12198,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((A = one_one_nat) | (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110])). 120.83/55.33 thf(1538,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => ((((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1369_mult__strict__mono_H)). 120.83/55.33 thf(10237,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ C) @ D)) => (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538])). 120.83/55.33 thf(3806,axiom,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1822_real__squared__diff__one__factored)). 120.83/55.33 thf(18142,plain,((! [A:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)) @ one_one_int) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3806])). 120.83/55.33 thf(28,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ uminus473333897omplex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ A)) @ (hAPP_real_real @ uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3963_complex__minus)). 120.83/55.33 thf(5036,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ uminus473333897omplex @ (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ A) @ B)) = (hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ uminus_uminus_real @ A)) @ (hAPP_real_real @ uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 120.83/55.33 thf(128,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real))) => (A = (natfloor @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3705_natfloor__eq)). 120.83/55.33 thf(5378,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ A)) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ A)) @ one_one_real))) => (A = (natfloor @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 120.83/55.33 thf(1938,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = A)) <= ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2788_mod__eq__0D)). 120.83/55.33 thf(11668,plain,((! [A:$i,B:$i]: (? [C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = A) | ~ ((hAPP_nat_nat @ (div_mod_nat @ A) @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938])). 120.83/55.33 thf(3334,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J)). 120.83/55.33 thf(16539,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ B) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3334])). 120.83/55.33 thf(3614,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_odd__less__0)). 120.83/55.33 thf(17443,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A)) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ one_one_int) @ A)) @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3614])). 120.83/55.33 thf(1300,axiom,((! [A:$i]: (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2991_power__0__Suc)). 120.83/55.33 thf(9414,plain,((! [A:$i]: (zero_zero_rat = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ zero_zero_rat) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300])). 120.83/55.33 thf(2955,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (archim1246769320r_real @ B)) @ (archim1246769320r_real @ A))) @ (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4034_le__mult__floor)). 120.83/55.33 thf(15213,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (archim1246769320r_real @ B)) @ (archim1246769320r_real @ A))) @ (archim1246769320r_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2955])). 120.83/55.33 thf(4175,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2652_div__prop2)). 120.83/55.33 thf(19541,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C)) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ C)) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4175])). 120.83/55.33 thf(1972,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_mult__nonpos__nonpos)). 120.83/55.33 thf(11779,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ A)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972])). 120.83/55.33 thf(522,axiom,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2340_semiring__div__class_Omod__div__equality_H)). 120.83/55.33 thf(6682,plain,((! [A:$i,B:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 120.83/55.33 thf(2380,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) <= (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))) | ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_split__mult__neg__le)). 120.83/55.33 thf(13194,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A)) @ zero_z126310315umeral)) | ~ (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ zero_z126310315umeral)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))) | ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ zero_z126310315umeral)) & (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380])). 120.83/55.33 thf(3896,axiom,((! [A:$i]: ((? [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) <=> (? [B:$i]: ((hBOOL @ (hAPP_int_bool @ A @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (is_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2987_transfer__int__nat__quantifiers_I2_J)). 120.83/55.33 thf(18467,plain,((! [A:$i]: (((? [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B)))) => (? [B:$i]: ((hBOOL @ (hAPP_int_bool @ A @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (is_int @ B)))) & ((? [B:$i]: ((hBOOL @ (hAPP_int_bool @ A @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) & (is_int @ B))) => (? [B:$i]: (hBOOL @ (hAPP_int_bool @ A @ (hAPP_nat_int @ semiri1621563631at_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3896])). 120.83/55.33 thf(2171,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))) @ (hAPP_nat_nat @ C @ D))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D)))))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ B)) @ (hAPP_nat_nat @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3263_dvd_Olift__Suc__mono__less)). 120.83/55.33 thf(12431,plain,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D))) @ (hAPP_nat_nat @ C @ D))) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ D)) @ (hAPP_nat_nat @ C @ (hAPP_nat_nat @ suc @ D)))))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ A)) @ (hAPP_nat_nat @ C @ B))) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ C @ B)) @ (hAPP_nat_nat @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171])). 120.83/55.33 thf(2312,axiom,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ succ @ (hAPP_int_int @ pred @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4039_succ__pred)). 120.83/55.33 thf(12944,plain,((! [A:$i]: ((is_int @ A) => (A = (hAPP_int_int @ succ @ (hAPP_int_int @ pred @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312])). 120.83/55.33 thf(211,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ sin @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3732_sin__monotone__2pi_H)). 120.83/55.33 thf(5642,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ sin @ B)) @ (hAPP_real_real @ sin @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 120.83/55.33 thf(836,axiom,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1985_add__0__left)). 120.83/55.33 thf(7808,plain,((! [A:$i]: (A = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ zero_z126310315umeral) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])). 120.83/55.33 thf(2056,axiom,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ one_on1684967323de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1225_zero__less__one)). 120.83/55.33 thf(12024,plain,((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ one_on1684967323de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056])). 120.83/55.33 thf(1757,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = zero_zero_real) <=> (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3483_real__add__minus__iff)). 120.83/55.33 thf(11028,plain,((! [A:$i,B:$i]: ((((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = zero_zero_real) => (A = B)) & ((A = B) => ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ uminus_uminus_real @ B)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757])). 120.83/55.33 thf(502,axiom,((semiri132038758t_real = real_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3643_real__eq__of__nat)). 120.83/55.33 thf(6612,plain,((semiri132038758t_real = real_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 120.83/55.33 thf(436,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_mult__dvd__mono)). 120.83/55.33 thf(6393,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ D) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 120.83/55.33 thf(3406,axiom,((! [A:$i]: (((zero_zero_nat != A) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral)) & (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ A) = one_on1645066479umeral) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1435_power__0__left)). 120.83/55.33 thf(16771,plain,((! [A:$i]: (((~ (zero_zero_nat = A)) => ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral)) & (((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ zero_z126310315umeral) @ A) = one_on1645066479umeral) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3406])). 120.83/55.33 thf(3875,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2748_nat__power__eq)). 120.83/55.33 thf(18391,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3875])). 120.83/55.33 thf(4197,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B)) <= ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ C) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2465_Residues_Oaux)). 120.83/55.33 thf(19625,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ C) @ B)) | ~ ((hAPP_int_int @ (div_mod_int @ A) @ B) = (hAPP_int_int @ (div_mod_int @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4197])). 120.83/55.33 thf(1417,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.33 thf(9827,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417])). 120.83/55.33 thf(1804,axiom,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1740_diff__0__eq__0)). 120.83/55.33 thf(11204,plain,((! [A:$i]: (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804])). 120.83/55.33 thf(3957,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_le__special_I2_J)). 120.83/55.33 thf(18670,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ bit1 @ pls)) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3957])). 120.83/55.33 thf(2736,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_power__mult__distrib)). 120.83/55.33 thf(14454,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ C) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2736])). 120.83/55.33 thf(4089,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ succ @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3297_add__Bit1__Bit1)). 120.83/55.33 thf(19237,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit1 @ B)) = (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ succ @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4089])). 120.83/55.33 thf(4530,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4987_gcd__abs__int)). 120.83/55.33 thf(20923,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ abs_abs_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4530])). 120.83/55.33 thf(4654,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2814_of__nat__double)). 120.83/55.33 thf(21436,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_rat @ semiri151668891at_rat @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4654])). 120.83/55.33 thf(600,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) <=> (C = D)) <= ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1960_diff__eq__diff__eq)). 120.83/55.33 thf(6929,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((A = B) => (C = D)) & ((C = D) => (A = B))) | ~ ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ C) @ D) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])). 120.83/55.33 thf(1887,axiom,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_semiring__mult__2__right)). 120.83/55.33 thf(11509,plain,((! [A:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887])). 120.83/55.33 thf(1932,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5184_max__number__of__Suc)). 120.83/55.33 thf(11649,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_max_nat @ A) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932])). 120.83/55.33 thf(1642,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mult__number__of__left)). 120.83/55.33 thf(10622,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642])). 120.83/55.33 thf(699,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1592_nat__add__left__commute)). 120.83/55.33 thf(7291,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 120.83/55.33 thf(606,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3482_real__minus__mult__self__le)). 120.83/55.33 thf(6952,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ A))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])). 120.83/55.33 thf(3594,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2573_dvd__mult__div__cancel)). 120.83/55.33 thf(17384,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B)) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3594])). 120.83/55.33 thf(2928,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1809_add__diff__add)). 120.83/55.33 thf(15128,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ C)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ B) @ D)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2928])). 120.83/55.33 thf(4562,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_zle__add1__eq__le)). 120.83/55.33 thf(21104,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4562])). 120.83/55.33 thf(2805,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4388_real__of__int__le__iff)). 120.83/55.33 thf(14717,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ (hAPP_int_real @ real_int @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2805])). 120.83/55.33 thf(2895,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3135_one__le__mult__iff)). 120.83/55.33 thf(15012,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2895])). 120.83/55.33 thf(63,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3438_ln__le__cancel__iff)). 120.83/55.33 thf(5176,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ B)) @ (hAPP_real_real @ ln @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 120.83/55.33 thf(1298,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ D)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_power__le__dvd)). 120.83/55.33 thf(9409,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ C)) @ D)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ A)) @ D)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298])). 120.83/55.33 thf(1975,axiom,((! [A:$i,B:$i]: ((A != B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ fequal_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T)). 120.83/55.33 thf(11784,plain,((! [A:$i,B:$i]: (~ (A = B) | (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ fequal_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975])). 120.83/55.33 thf(4758,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i]: (((! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F) != E)) <= (is_int @ G)))) <= (is_int @ F))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D)) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A))))) <= (is_int @ E))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5104_bset_I9_J)). 120.83/55.33 thf(21836,plain,((! [A:$i,B:$i,C:$i,D:$i]: (! [E:$i]: (((! [F:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ F) @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ one_one_int) @ D))) => (! [G:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ G) @ B)) => (~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ G) @ F) = E))) | ~ (is_int @ G)))) | ~ (is_int @ F))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ E) @ D)) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ E) @ A))))) | ~ (is_int @ E)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4758])). 120.83/55.33 thf(1567,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_add__number__of__left)). 120.83/55.33 thf(10355,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ A)) @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ B)) @ C)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567])). 120.83/55.33 thf(4210,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2526_neg__mod__bound)). 120.83/55.33 thf(19674,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_int_int @ (div_mod_int @ A) @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4210])). 120.83/55.33 thf(3953,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1778081398nt_int @ (hAPP_f2004554147nt_int @ (hAPP_f1228585167nt_int @ cOMBB_1102189010nt_int @ A) @ B) @ C) = (hAPP_f1574055885nt_int @ A @ (hAPP_int_fun_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___024)). 120.83/55.33 thf(18660,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1778081398nt_int @ (hAPP_f2004554147nt_int @ (hAPP_f1228585167nt_int @ cOMBB_1102189010nt_int @ A) @ B) @ C) = (hAPP_f1574055885nt_int @ A @ (hAPP_int_fun_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3953])). 120.83/55.33 thf(1850,axiom,((! [A:$i]: ((hAPP_int_nat @ nat @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4919_card__atLeastZeroLessThan__int)). 120.83/55.33 thf(11377,plain,((! [A:$i]: ((hAPP_int_nat @ nat @ A) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_at641636577an_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850])). 120.83/55.33 thf(3984,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((((negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) => ((negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ B)) @ (negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2668_negDivAlg__eqn__number__of)). 120.83/55.33 thf(18776,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ B))) => ((((negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))) => ((negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ number_number_of_int @ B)) = (hAPP_P1975530577nt_int @ (adjust @ (hAPP_int_int @ number_number_of_int @ B)) @ (negDivAlg @ (hAPP_int_int @ number_number_of_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ number_number_of_int @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3984])). 120.83/55.33 thf(1778,axiom,((! [A:$i]: (((A != zero_zero_nat) => ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A) = zero_zero_real)) & (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A) = one_one_real) <= (zero_zero_nat = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1434_power__0__left)). 120.83/55.33 thf(11114,plain,((! [A:$i]: (((~ (A = zero_zero_nat)) => ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A) = zero_zero_real)) & (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ A) = one_one_real) | ~ (zero_zero_nat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778])). 120.83/55.33 thf(1535,axiom,((! [A:$i]: ((A = zero_zero_rat) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ zero_zero_rat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_dvd__0__left)). 120.83/55.33 thf(10224,plain,((! [A:$i]: ((A = zero_zero_rat) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ zero_zero_rat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535])). 120.83/55.33 thf(839,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_mult__numeral__1)). 120.83/55.33 thf(7819,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ pls))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[839])). 120.83/55.33 thf(2626,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2151_add__increasing2)). 120.83/55.33 thf(14087,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ C))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2626])). 120.83/55.33 thf(639,axiom,((! [A:$i]: ((? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ B)) @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3750_reals__Archimedean6a)). 120.83/55.33 thf(7076,plain,((! [A:$i]: (? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ suc @ B)))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_nat_real @ real_nat @ B)) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 120.83/55.33 thf(4398,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ iszero_int @ (hAPP_int_int @ number_number_of_int @ A))) <=> (hBOOL @ (hAPP_rat_bool @ iszero_rat @ (hAPP_int_rat @ number_number_of_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4636_iszero__rat)). 120.83/55.33 thf(20397,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ iszero_int @ (hAPP_int_int @ number_number_of_int @ A))) => (hBOOL @ (hAPP_rat_bool @ iszero_rat @ (hAPP_int_rat @ number_number_of_rat @ A)))) & ((hBOOL @ (hAPP_rat_bool @ iszero_rat @ (hAPP_int_rat @ number_number_of_rat @ A))) => (hBOOL @ (hAPP_int_bool @ iszero_int @ (hAPP_int_int @ number_number_of_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4398])). 120.83/55.33 thf(1500,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1915_add__imp__eq)). 120.83/55.33 thf(10092,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500])). 120.83/55.33 thf(1239,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A) = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2716_le__mod__geq)). 120.83/55.33 thf(9198,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ A) = (hAPP_nat_nat @ (div_mod_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239])). 120.83/55.33 thf(3778,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ pred @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4051_Suc__diff__number__of)). 120.83/55.33 thf(18042,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ pls) @ B)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ pred @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3778])). 120.83/55.33 thf(4669,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ (hAPP_i1948725293t_bool @ norRRset @ C))) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4592_RRset2norRR__correct2)). 120.83/55.33 thf(21475,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ (hAPP_i1948725293t_bool @ norRRset @ C))) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4669])). 120.83/55.33 thf(4828,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))) <= (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2890_Parity_Oeven__plus__even)). 120.83/55.33 thf(22079,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ even_odd_even_int @ A)) => (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)))) | ~ (hBOOL @ (hAPP_int_bool @ even_odd_even_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4828])). 120.83/55.33 thf(3602,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2879_mod__Suc__eq__Suc__mod)). 120.83/55.33 thf(17409,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3602])). 120.83/55.33 thf(97,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C) = A) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_dvdI)). 120.83/55.33 thf(5275,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C) = A) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ dvd_dvd_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 120.83/55.33 thf(584,axiom,((! [A:$i]: ((hAPP_real_real @ inverse_inverse_real @ (ratreal @ A)) = (ratreal @ (hAPP_rat_rat @ inverse_inverse_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4706_real__inverse__code)). 120.83/55.33 thf(6874,plain,((! [A:$i]: ((hAPP_real_real @ inverse_inverse_real @ (ratreal @ A)) = (ratreal @ (hAPP_rat_rat @ inverse_inverse_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 120.83/55.33 thf(4663,axiom,((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_qf1pt)). 120.83/55.33 thf(21461,plain,((hBOOL @ (hAPP_int_bool @ twoSqu1770640450sum2sq @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ t)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4663])). 120.83/55.33 thf(4414,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f720654810t_bool @ (hAPP_f908327869t_bool @ cOMBB_1290694363ol_int @ A) @ B) @ C) = (hAPP_f429935748t_bool @ A @ (hAPP_int_fun_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc__)). 120.83/55.33 thf(20461,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i1948725293t_bool @ (hAPP_f720654810t_bool @ (hAPP_f908327869t_bool @ cOMBB_1290694363ol_int @ A) @ B) @ C) = (hAPP_f429935748t_bool @ A @ (hAPP_int_fun_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4414])). 120.83/55.33 thf(4717,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2171_double__add__le__zero__iff__single__add__le__zero)). 120.83/55.33 thf(21680,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4717])). 120.83/55.33 thf(2050,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__number__of__left)). 120.83/55.33 thf(12002,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050])). 120.83/55.33 thf(2492,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_less__special_I3_J)). 120.83/55.33 thf(13599,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_int_real @ number267125858f_real @ A)) @ zero_zero_real)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ pls)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2492])). 120.83/55.33 thf(768,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_mult__pos__neg)). 120.83/55.33 thf(7538,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 120.83/55.33 thf(4707,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (one_one_int = (hAPP_int_int @ zfact @ A))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) = (hAPP_int_int @ zfact @ A)) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2213_zfact_Osimps)). 120.83/55.33 thf(21634,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)) => (one_one_int = (hAPP_int_int @ zfact @ A))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ zfact @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))) = (hAPP_int_int @ zfact @ A)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4707])). 120.83/55.33 thf(1282,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ real_nat @ (natfloor @ B)) = B) => ((natfloor @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (natfloor @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3678_natfloor__power)). 120.83/55.33 thf(9367,plain,((! [A:$i,B:$i]: (((hAPP_nat_real @ real_nat @ (natfloor @ B)) = B) => ((natfloor @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (natfloor @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282])). 120.83/55.33 thf(3580,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ one_on1684967323de_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1261_less__add__one)). 120.83/55.33 thf(17340,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ one_on1684967323de_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3580])). 120.83/55.33 thf(74,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ C @ (hAPP_real_real @ D @ E)) @ F)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ E)) => ((((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ D @ E) @ (hAPP_real_real @ inverse_inverse_real @ F)))) <= (! [G:$i]: ((G = (hAPP_real_real @ C @ (hAPP_real_real @ D @ G))) <= ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ G)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ G) @ A)))))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ A)))) <= (F != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5175_DERIV__inverse__function)). 120.83/55.33 thf(5204,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ C @ (hAPP_real_real @ D @ E)) @ F)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ E)) => (((hBOOL @ (hAPP_real_bool @ (isCont_real_real @ D) @ E)) => (hBOOL @ (hAPP_real_bool @ (deriv_real @ D @ E) @ (hAPP_real_real @ inverse_inverse_real @ F)))) | ~ (! [G:$i]: ((G = (hAPP_real_real @ C @ (hAPP_real_real @ D @ G))) | ~ ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ G)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ G) @ A))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ A)))) | (F = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 120.83/55.33 thf(4220,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((! [D:$i,E:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) <= ((~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ E)))))) <= ((is_int @ D) & (is_int @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2785_posDivAlg_Opinduct)). 120.83/55.33 thf(19706,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ B) @ C))) => ((! [D:$i,E:$i]: (((hBOOL @ (hAPP_P603027463t_bool @ (accp_P2006205492nt_int @ posDivAlg_rel) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ D) @ E))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ E)) | ~ ((~ ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ E) @ zero_zero_int)) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ D) @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ E)))))) | ~ ((is_int @ D) & (is_int @ E)))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ A @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4220])). 120.83/55.33 thf(1252,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2153_add__increasing)). 120.83/55.33 thf(9235,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ C) @ B)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252])). 120.83/55.33 thf(3495,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ one_on1684967323de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1406_power__decreasing)). 120.83/55.33 thf(17056,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ one_on1684967323de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ C)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ B)))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3495])). 120.83/55.33 thf(1412,axiom,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3547_neg__zminus__int)). 120.83/55.33 thf(9810,plain,((! [A:$i]: (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412])). 120.83/55.33 thf(4936,axiom,((! [A:$i,B:$i]: ((((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2746_nat__diff__distrib)). 120.83/55.33 thf(22426,plain,((! [A:$i,B:$i]: (((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ nat @ A)) @ (hAPP_int_nat @ nat @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ B) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4936])). 120.83/55.33 thf(262,axiom,((! [A:$i]: ((archim1246769320r_real @ (ratreal @ A)) = (archim791455193or_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4682_real__floor__code)). 120.83/55.33 thf(5803,plain,((! [A:$i]: ((archim1246769320r_real @ (ratreal @ A)) = (archim791455193or_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 120.83/55.33 thf(2828,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1571_less__add__iff1)). 120.83/55.33 thf(14797,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C)) @ E)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2828])). 120.83/55.33 thf(3317,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1472_power__Suc__less)). 120.83/55.33 thf(16479,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ one_one_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ B) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3317])). 120.83/55.33 thf(3834,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ B)) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A)) <= (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3284_power__nat__number__of)). 120.83/55.33 thf(18227,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A) = (hAPP_int_nat @ nat @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ B)) @ A))) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ A) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ zero_zero_nat) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3834])). 120.83/55.33 thf(4517,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => ((B = C) <= ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1923_add__left__imp__eq)). 120.83/55.33 thf(20859,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ B) & (is_int @ C)) => ((B = C) | ~ ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ C) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4517])). 120.83/55.33 thf(2697,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ pred @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4038_nat__number__of__diff__1)). 120.83/55.33 thf(14325,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls)) => (zero_zero_nat = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat))) & ((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ pls))) => ((hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ pred @ A)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2697])). 120.83/55.33 thf(1793,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1758_diff__mult__distrib2)). 120.83/55.33 thf(11177,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793])). 120.83/55.33 thf(719,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4358_gcd__diff2__nat)). 120.83/55.33 thf(7352,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A)) @ B) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])). 120.83/55.33 thf(3032,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5144_SetInterval_Otransfer__int__nat__set__function__closures)). 120.83/55.33 thf(15484,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ nat_nat_set @ (hAPP_i1948725293t_bool @ (ord_at875362053st_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ nat_is_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3032])). 120.83/55.33 thf(2172,axiom,((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1218_not__one__le__zero)). 120.83/55.33 thf(12435,plain,((~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172])). 120.83/55.33 thf(345,axiom,((one_one_real = (hAPP_complex_real @ im @ ii))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4095_complex__Im__i)). 120.83/55.33 thf(6099,plain,((one_one_real = (hAPP_complex_real @ im @ ii))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 120.83/55.33 thf(2754,axiom,((! [A:$i,B:$i]: (((B = zero_zero_real) & (A = zero_zero_real)) <=> (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_sum__power2__eq__zero__iff)). 120.83/55.33 thf(14514,plain,((! [A:$i,B:$i]: ((((B = zero_zero_real) & (A = zero_zero_real)) => (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) & ((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) => ((B = zero_zero_real) & (A = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2754])). 120.83/55.33 thf(3079,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2137_diff__add__cancel)). 120.83/55.33 thf(15662,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ minus_minus_complex @ A) @ B)) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3079])). 120.83/55.33 thf(3763,axiom,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (A = (hAPP_int_int @ (legacy_zgcd @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4499_zgcd__self)). 120.83/55.33 thf(17993,plain,((! [A:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => (A = (hAPP_int_int @ (legacy_zgcd @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3763])). 120.83/55.33 thf(3452,axiom,((! [A:$i,B:$i]: ((zero_z126310315umeral != B) => (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A) != zero_z126310315umeral) <= (A != zero_z126310315umeral))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_no__zero__divisors)). 120.83/55.33 thf(16908,plain,((! [A:$i,B:$i]: ((~ (zero_z126310315umeral = B)) => (~ ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A) = zero_z126310315umeral) | (A = zero_z126310315umeral))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3452])). 120.83/55.33 thf(714,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4071_cnj_Oadd)). 120.83/55.34 thf(7338,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B)) = (hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 120.83/55.34 thf(2033,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3927_real__root__strict__decreasing)). 120.83/55.34 thf(11953,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033])). 120.83/55.34 thf(4313,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4968_gcd__add1__int)). 120.83/55.34 thf(20058,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4313])). 120.83/55.34 thf(1994,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ one_on1684967323de_int)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 120.83/55.34 thf(11839,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ one_on1684967323de_int)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994])). 120.83/55.34 thf(218,axiom,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3480_real__sqrt__minus)). 120.83/55.34 thf(5668,plain,((! [A:$i]: ((hAPP_real_real @ sqrt @ (hAPP_real_real @ uminus_uminus_real @ A)) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 120.83/55.34 thf(2953,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ prime @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4187_prime__coprime__lt)). 120.83/55.34 thf(15209,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ prime @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2953])). 120.83/55.34 thf(360,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) <= (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_split__mult__pos__le)). 120.83/55.34 thf(6155,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ A))) | ~ (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) | ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ zero_zero_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 120.83/55.34 thf(1788,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zEven)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2895_even__times__either)). 120.83/55.34 thf(11144,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A)) @ zEven)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788])). 120.83/55.34 thf(3169,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1543_eq__add__iff1)). 120.83/55.34 thf(15970,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C) = E)) & (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ minus_minus_rat @ A) @ D)) @ B)) @ C) = E) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ D) @ B)) @ E) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3169])). 120.83/55.34 thf(565,axiom,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ uminus_uminus_real @ A))) & ((A = (hAPP_real_real @ abs_abs_real @ A)) <= (~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3495_real__abs__def)). 120.83/55.34 thf(6807,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)) => ((hAPP_real_real @ abs_abs_real @ A) = (hAPP_real_real @ uminus_uminus_real @ A))) & ((A = (hAPP_real_real @ abs_abs_real @ A)) | (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])). 120.83/55.34 thf(414,axiom,((! [A:$i]: ((hAPP_int_complex @ ring_11397209091omplex @ A) = (hAPP_int_complex @ number528085621omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4584_complex__number__of__def)). 120.83/55.34 thf(6329,plain,((! [A:$i]: ((hAPP_int_complex @ ring_11397209091omplex @ A) = (hAPP_int_complex @ number528085621omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 120.83/55.34 thf(1481,axiom,((! [A:$i]: (((one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ A))) <= (zero_zero_nat != (hAPP_int_nat @ number_number_of_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_power__0__left__number__of)). 120.83/55.34 thf(10032,plain,((! [A:$i]: (((one_one_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ A))) | ~ ((hAPP_int_nat @ number_number_of_nat @ A) = zero_zero_nat)) & ((zero_zero_real = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ zero_zero_real) @ (hAPP_int_nat @ number_number_of_nat @ A))) | (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481])). 120.83/55.34 thf(263,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((zero_zero_real = D) <= (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ B @ C)) @ (hAPP_real_real @ B @ E))))))) <= (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3884_DERIV__local__min)). 120.83/55.34 thf(5806,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((zero_zero_real = D) | ~ (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ abs_abs_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ C) @ E))) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ B @ C)) @ (hAPP_real_real @ B @ E))))))) | ~ (hBOOL @ (hAPP_real_bool @ (deriv_real @ B @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 120.83/55.34 thf(2116,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_le__number__of__eq__not__less)). 120.83/55.34 thf(12220,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ number_number_of_nat @ B)) @ (hAPP_int_nat @ number_number_of_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116])). 120.83/55.34 thf(4529,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E))) @ C))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_zdvd__period)). 120.83/55.34 thf(20920,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E))) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ E))) @ C))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4529])). 120.83/55.34 thf(2292,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3139_nat__one__le__power)). 120.83/55.34 thf(12872,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ suc @ zero_zero_nat)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292])). 120.83/55.34 thf(4689,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2095_diff__eq__diff__less)). 120.83/55.34 thf(21541,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ C) @ D)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4689])). 120.83/55.34 thf(449,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ sin) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5164_isCont__sin)). 120.83/55.34 thf(6435,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (isCont_real_real @ sin) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 120.83/55.34 thf(2035,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ zero_zero_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_mult__nonneg__nonpos2)). 120.83/55.34 thf(11958,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ zero_zero_nat))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035])). 120.83/55.34 thf(3133,axiom,((! [A:$i,B:$i,C:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C))) => ((A = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) <= (B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3899_odd__real__root__unique)). 120.83/55.34 thf(15845,plain,((! [A:$i,B:$i,C:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ C))) => ((A = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ B)) | ~ (B = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3133])). 120.83/55.34 thf(3226,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ pls)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_add__numeral__0)). 120.83/55.34 thf(16190,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ (hAPP_int_complex @ number528085621omplex @ pls)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3226])). 120.83/55.34 thf(2528,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2818_zero__less__Suc)). 120.83/55.34 thf(13728,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2528])). 120.83/55.34 thf(1845,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)) => (? [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) & ! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ E))) @ (hAPP_real_real @ A @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3889_DERIV__neg__dec__right)). 120.83/55.34 thf(11358,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ C) @ zero_zero_real)) => (? [D:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)) & ! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ E))) @ (hAPP_real_real @ A @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845])). 120.83/55.34 thf(3855,axiom,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_power__m1__even)). 120.83/55.34 thf(18323,plain,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3855])). 120.83/55.34 thf(905,axiom,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3436_nat__abs__mult__distrib)). 120.83/55.34 thf(8034,plain,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ A))) @ (hAPP_int_nat @ nat @ (hAPP_int_int @ abs_abs_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])). 120.83/55.34 thf(377,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_mult__zero__right)). 120.83/55.34 thf(6209,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 120.83/55.34 thf(4799,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2651_zmod__number__of__Bit0)). 120.83/55.34 thf(21971,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A))) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ B))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4799])). 120.83/55.34 thf(428,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_mult__left__mono)). 120.83/55.34 thf(6373,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ C)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 120.83/55.34 thf(3200,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1629_add__less__mono1)). 120.83/55.34 thf(16081,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3200])). 120.83/55.34 thf(432,axiom,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3722_sin__45)). 120.83/55.34 thf(6383,plain,(((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_real_real @ sqrt @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 120.83/55.34 thf(4612,axiom,((! [A:$i,B:$i]: ? [C:$i]: (! [D:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ D) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ C) @ D))) & (is_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2273_pinf_I9_J)). 120.83/55.34 thf(21277,plain,((? [A:$i]: (is_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4612])). 120.83/55.34 thf(1325,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1879_add__strict__increasing2)). 120.83/55.34 thf(9504,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ C)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325])). 120.83/55.34 thf(3648,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ B) => (((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E))) <= ((xzgcd @ A @ E) = (hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4199_xzgcd__linear)). 120.83/55.34 thf(17572,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((is_int @ B) => ((B = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ C) @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ D) @ E))) | ~ ((xzgcd @ A @ E) = (hAPP_P408881810nt_int @ (hAPP_i1730167831nt_int @ produc282740534nt_int @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3648])). 120.83/55.34 thf(310,axiom,((! [A:$i]: (A = (hAPP_complex_real @ re @ (of_real_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4114_Re__complex__of__real)). 120.83/55.34 thf(5975,plain,((! [A:$i]: (A = (hAPP_complex_real @ re @ (of_real_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 120.83/55.34 thf(4677,axiom,((! [A:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ one_one_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4223_div__pos__neg__1__number__of)). 120.83/55.34 thf(21500,plain,((! [A:$i]: (((hAPP_P1175774780nt_int @ product_fst_int_int @ (hAPP_P1975530577nt_int @ negateSnd @ (negDivAlg @ (hAPP_int_int @ uminus_uminus_int @ one_one_int) @ (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ one_one_int) @ (hAPP_int_int @ number_number_of_int @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ A)) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4677])). 120.83/55.34 thf(3987,axiom,((! [A:$i]: ((hAPP_i1948725293t_bool @ (bnorRset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ A) = (hAPP_i1948725293t_bool @ norRRset @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4575_norRRset__def)). 120.83/55.34 thf(18791,plain,((! [A:$i]: ((hAPP_i1948725293t_bool @ (bnorRset @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) @ A) = (hAPP_i1948725293t_bool @ norRRset @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3987])). 120.83/55.34 thf(4508,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A)))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1506_number__of1)). 120.83/55.34 thf(20827,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ A)))) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ A))))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ number_number_of_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4508])). 120.83/55.34 thf(3897,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ bit1 @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_mult__Bit1)). 120.83/55.34 thf(18474,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ bit1 @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3897])). 120.83/55.34 thf(461,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3566_cos__monotone__0__pi_H)). 120.83/55.34 thf(6473,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ cos @ A)) @ (hAPP_real_real @ cos @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ pi)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 120.83/55.34 thf(1270,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1873_add__strict__increasing)). 120.83/55.34 thf(9314,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ C) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B)) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270])). 120.83/55.34 thf(2201,axiom,((! [A:$i]: (zero_zero_nat != (hAPP_nat_nat @ suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2850_nat_Osimps_I3_J)). 120.83/55.34 thf(12560,plain,((! [A:$i]: ~ (zero_zero_nat = (hAPP_nat_nat @ suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201])). 120.83/55.34 thf(1439,axiom,((one_one_complex = (hAPP_nat_complex @ semiri2020571505omplex @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2969_of__nat__1)). 120.83/55.34 thf(9895,plain,((one_one_complex = (hAPP_nat_complex @ semiri2020571505omplex @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439])). 120.83/55.34 thf(637,axiom,((! [A:$i]: (A = (natfloor @ (hAPP_nat_real @ real_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3638_natfloor__real__of__nat)). 120.83/55.34 thf(7071,plain,((! [A:$i]: (A = (natfloor @ (hAPP_nat_real @ real_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 120.83/55.34 thf(4483,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_zcong__zpower)). 120.83/55.34 thf(20735,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ B) @ C) @ D)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ C) @ A)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4483])). 120.83/55.34 thf(4187,axiom,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_numeral__1__eq__1)). 120.83/55.34 thf(19573,plain,((one_one_int = (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ pls)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4187])). 120.83/55.34 thf(3209,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zEven))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2898_even__diff)). 120.83/55.34 thf(16110,plain,((! [A:$i,B:$i]: (((((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)))) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zEven))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ zEven)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3209])). 120.83/55.34 thf(98,axiom,((one_one_real = (hAPP_real_real @ cos @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3563_cos__zero)). 120.83/55.34 thf(5280,plain,((one_one_real = (hAPP_real_real @ cos @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 120.83/55.34 thf(4599,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_bool @ (hAPP_i16292313t_bool @ A @ C) @ B) = (hAPP_int_bool @ (hAPP_r1900510169t_bool @ (hAPP_f1480506641t_bool @ cOMBC_int_rat_bool @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Rat__Orat_000tc__HOL__Obool_U)). 120.83/55.34 thf(21236,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_rat_bool @ (hAPP_i16292313t_bool @ A @ C) @ B) = (hAPP_int_bool @ (hAPP_r1900510169t_bool @ (hAPP_f1480506641t_bool @ cOMBC_int_rat_bool @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4599])). 120.83/55.34 thf(1309,axiom,((! [A:$i]: ((A = one_one_nat) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4024_coprime__0)). 120.83/55.34 thf(9446,plain,((! [A:$i]: (((A = one_one_nat) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ zero_zero_nat))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ coprime @ A) @ zero_zero_nat)) => (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309])). 120.83/55.34 thf(4196,axiom,((! [A:$i,B:$i]: ((((A = zero_zero_int) & (zero_zero_nat != B)) <=> (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1289_power__eq__0__iff)). 120.83/55.34 thf(19614,plain,((! [A:$i,B:$i]: (((((A = zero_zero_int) & ~ (zero_zero_nat = B)) => (zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B))) & ((zero_zero_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) => ((A = zero_zero_int) & ~ (zero_zero_nat = B)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4196])). 120.83/55.34 thf(2870,axiom,((! [A:$i,B:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_nat_real @ real_nat @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4459_powr__realpow)). 120.83/55.34 thf(14935,plain,((! [A:$i,B:$i]: (((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ B) @ (hAPP_nat_real @ real_nat @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2870])). 120.83/55.34 thf(4834,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2811_of__nat__double)). 120.83/55.34 thf(22094,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) => ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ A))) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ A))) @ (hAPP_nat_real @ semiri132038758t_real @ (hAPP_int_nat @ nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4834])). 120.83/55.34 thf(222,axiom,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3739_minus__sin__cos__eq)). 120.83/55.34 thf(5681,plain,((! [A:$i]: ((hAPP_real_real @ cos @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) = (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ sin @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 120.83/55.34 thf(4264,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 120.83/55.34 thf(19891,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4264])). 120.83/55.34 thf(4355,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ d22set @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2267_d22set__g__1)). 120.83/55.34 thf(20231,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ d22set @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4355])). 120.83/55.34 thf(34,axiom,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4134_complex__add__def)). 120.83/55.34 thf(5060,plain,((! [A:$i,B:$i]: ((hAPP_real_complex @ (hAPP_r265291036omplex @ complex @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ re @ A)) @ (hAPP_complex_real @ re @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_complex_real @ im @ A)) @ (hAPP_complex_real @ im @ B))) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 120.83/55.34 thf(728,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 120.83/55.34 thf(7387,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ C)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ D)) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])). 120.83/55.34 thf(2682,axiom,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1981_add__0)). 120.83/55.34 thf(14269,plain,((! [A:$i]: (A = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2682])). 120.83/55.34 thf(2793,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1409_power__le__imp__le__exp)). 120.83/55.34 thf(14672,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2793])). 120.83/55.34 thf(1833,axiom,((! [A:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (one_one_real = (hAPP_real_real @ sgn_sgn_real @ A))) & ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) => ((hAPP_real_real @ uminus_uminus_real @ one_one_real) = (hAPP_real_real @ sgn_sgn_real @ A)))) <= (zero_zero_real != A)) & ((zero_zero_real = (hAPP_real_real @ sgn_sgn_real @ A)) <= (zero_zero_real = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3575_real__sgn__def)). 120.83/55.34 thf(11309,plain,((! [A:$i]: (((((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => (one_one_real = (hAPP_real_real @ sgn_sgn_real @ A))) & ((~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) => ((hAPP_real_real @ uminus_uminus_real @ one_one_real) = (hAPP_real_real @ sgn_sgn_real @ A)))) | (zero_zero_real = A)) & ((zero_zero_real = (hAPP_real_real @ sgn_sgn_real @ A)) | ~ (zero_zero_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833])). 120.83/55.34 thf(251,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2305_mult_Odiff__right)). 120.83/55.34 thf(5768,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 120.83/55.34 thf(206,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real)) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3841_exp__le__one__iff)). 120.83/55.34 thf(5623,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ zero_zero_real)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ exp_real @ A)) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 120.83/55.34 thf(3970,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) <=> ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2619_zdvd__iff__zmod__eq__0__number__of)). 120.83/55.34 thf(18719,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))) => ((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)) = zero_zero_int)) & (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ B)) @ (hAPP_int_int @ number_number_of_int @ A)) = zero_zero_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ number_number_of_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3970])). 120.83/55.34 thf(2560,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4331_gcd__semilattice__nat_Oinf__le1)). 120.83/55.34 thf(13827,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2560])). 120.83/55.34 thf(3094,axiom,((! [A:$i,B:$i]: (((A = B) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1707_dvd_Ole__imp__less__or__eq)). 120.83/55.34 thf(15709,plain,((! [A:$i,B:$i]: ((A = B) | ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3094])). 120.83/55.34 thf(1878,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3772_even__nat__plus__one__div__two)). 120.83/55.34 thf(11477,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ suc @ A)) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878])). 120.83/55.34 thf(1795,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3924_real__root__decreasing)). 120.83/55.34 thf(11182,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ C)) => (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ A)) @ (hAPP_real_real @ (hAPP_n546711566l_real @ root @ C) @ A)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795])). 120.83/55.34 thf(253,axiom,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ invers1449016382omplex @ A)) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_complex_complex @ cnj @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4064_complex__cnj__inverse)). 120.83/55.34 thf(5774,plain,((! [A:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ invers1449016382omplex @ A)) = (hAPP_complex_complex @ invers1449016382omplex @ (hAPP_complex_complex @ cnj @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 120.83/55.34 thf(455,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A)) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3745_arcsin)). 120.83/55.34 thf(6452,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)) => ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & ((hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A)) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 120.83/55.34 thf(4387,axiom,((! [A:$i,B:$i]: ((((hAPP_int_int @ bit1 @ B) = (hAPP_int_int @ bit1 @ A)) <=> (B = A)) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_rel__simps_I51_J)). 120.83/55.34 thf(20339,plain,((! [A:$i,B:$i]: (((((hAPP_int_int @ bit1 @ B) = (hAPP_int_int @ bit1 @ A)) => (B = A)) & ((B = A) => ((hAPP_int_int @ bit1 @ B) = (hAPP_int_int @ bit1 @ A)))) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4387])). 120.83/55.34 thf(268,axiom,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (A = (hAPP_real_real @ tan @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3628_lemma__tan__total1)). 120.83/55.34 thf(5821,plain,((! [A:$i]: ? [B:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) & (A = (hAPP_real_real @ tan @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 120.83/55.34 thf(2778,axiom,((! [A:$i,B:$i]: ((~ ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) <=> (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))))) <=> (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3755_odd__add)). 120.83/55.34 thf(14603,plain,((! [A:$i,B:$i]: (((~ (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B))))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)))) => (~ (((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B)))) & ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2778])). 120.83/55.34 thf(2756,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3381_natfloor__add__number__of)). 120.83/55.34 thf(14528,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (natfloor @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B)) = (natfloor @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2756])). 120.83/55.34 thf(1836,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5120_min__Suc__number__of)). 120.83/55.34 thf(11330,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_int_nat @ number_number_of_nat @ A)) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ (hAPP_b992065680at_nat @ if_nat @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ zero_zero_nat) @ (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836])). 120.83/55.34 thf(1053,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1608_less__nat__zero__code)). 120.83/55.34 thf(8548,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053])). 120.83/55.34 thf(1614,axiom,((! [A:$i]: ((is_int @ A) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ zero_zero_int) = zero_zero_int) & (A = (hAPP_int_int @ (div_mod_int @ A) @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2330_DIVISION__BY__ZERO)). 120.83/55.34 thf(10535,plain,((! [A:$i]: ((is_int @ A) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ zero_zero_int) = zero_zero_int) & (A = (hAPP_int_int @ (div_mod_int @ A) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614])). 120.83/55.34 thf(1590,axiom,((! [A:$i,B:$i]: ((A = zero_zero_rat) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_even__power__le__0__imp__0)). 120.83/55.34 thf(10440,plain,((! [A:$i,B:$i]: ((A = zero_zero_rat) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590])). 120.83/55.34 thf(4780,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 120.83/55.34 thf(21913,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4780])). 120.83/55.34 thf(158,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3831_real__divide__def)). 120.83/55.34 thf(5468,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ B) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 120.83/55.34 thf(688,axiom,((! [A:$i,B:$i]: ? [C:$i]: ! [D:$i]: (((~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B)))) <=> (~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ A) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2256_pinf_I10_J)). 120.83/55.34 thf(7263,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])). 120.83/55.34 thf(4341,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_power2__le__imp__le)). 120.83/55.34 thf(20190,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ B))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4341])). 120.83/55.34 thf(283,axiom,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4102_complex__Im__of__nat)). 120.83/55.34 thf(5891,plain,((! [A:$i]: ((hAPP_complex_real @ im @ (hAPP_nat_complex @ semiri2020571505omplex @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 120.83/55.34 thf(1109,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3842_exp__gt__one)). 120.83/55.34 thf(8773,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ one_one_real) @ (hAPP_real_real @ exp_real @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109])). 120.83/55.34 thf(2518,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_on1645066479umeral = A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1492_dvd__power)). 120.83/55.34 thf(13678,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_on1645066479umeral = A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518])). 120.83/55.34 thf(2028,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 120.83/55.34 thf(11935,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028])). 120.83/55.34 thf(4741,axiom,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4628_card__greaterThanLessThan__int)). 120.83/55.34 thf(21773,plain,((! [A:$i,B:$i]: ((hAPP_int_nat @ nat @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ one_one_int))) = (hAPP_f957591787ol_nat @ finite_card_int @ (hAPP_i1948725293t_bool @ (ord_gr1297742076an_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4741])). 120.83/55.34 thf(348,axiom,((! [A:$i,B:$i]: (B = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2344_mod__div__equality2)). 120.83/55.34 thf(6109,plain,((! [A:$i,B:$i]: (B = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A))) @ (hAPP_C498520661umeral @ (div_mo1740067990umeral @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 120.83/55.34 thf(1283,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3069_Suc__mult__le__cancel1)). 120.83/55.34 thf(9370,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ suc @ A)) @ C))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283])). 120.83/55.34 thf(1687,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1352_mult__right__less__imp__less)). 120.83/55.34 thf(10773,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ B))) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687])). 120.83/55.34 thf(1200,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2179_add__neg__neg)). 120.83/55.34 thf(9066,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ A)) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ zero_zero_nat)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200])). 120.83/55.34 thf(1619,axiom,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3125_zdiff__int)). 120.83/55.34 thf(10552,plain,((! [A:$i,B:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ semiri1621563631at_int @ B)) @ (hAPP_nat_int @ semiri1621563631at_int @ A)) = (hAPP_nat_int @ semiri1621563631at_int @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619])). 120.83/55.34 thf(3787,axiom,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (legacy_zgcd @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4507_zgcd__0)). 120.83/55.34 thf(18070,plain,((! [A:$i]: ((hAPP_int_int @ abs_abs_int @ A) = (hAPP_int_int @ (legacy_zgcd @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3787])). 120.83/55.34 thf(666,axiom,((! [A:$i]: ((? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3795_odd__square)). 120.83/55.34 thf(7176,plain,((! [A:$i]: (? [B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ B)) @ one_one_nat) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) | (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])). 120.83/55.34 thf(2354,axiom,((! [A:$i]: ((posDivAlg @ zero_zero_int @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2730_posDivAlg__0)). 120.83/55.34 thf(13092,plain,((! [A:$i]: ((posDivAlg @ zero_zero_int @ A) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354])). 120.83/55.34 thf(4133,axiom,((! [A:$i]: (min != (hAPP_int_int @ bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_rel__simps_I42_J)). 120.83/55.34 thf(19400,plain,((! [A:$i]: ~ (min = (hAPP_int_int @ bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4133])). 120.83/55.34 thf(3131,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2930_of__nat__less__imp__less)). 120.83/55.34 thf(15840,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ semiri151668891at_rat @ A)) @ (hAPP_nat_rat @ semiri151668891at_rat @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3131])). 120.83/55.34 thf(2521,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A) = B) <=> ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ B)) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4326_gcd__unique__nat)). 120.83/55.34 thf(13689,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A) = B) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ B)) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ A)))))) & (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ B)) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ C)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ A))))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ C) @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2521])). 120.83/55.34 thf(3716,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ A)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_nat_int @ semiri1621563631at_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3189_nat__less__iff)). 120.83/55.34 thf(17821,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_nat_int @ semiri1621563631at_int @ A)))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ (hAPP_nat_int @ semiri1621563631at_int @ A))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_int_nat @ nat @ B)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3716])). 120.83/55.34 thf(2006,axiom,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_nat_nat @ suc @ A)) = zero_z891286103de_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2992_power__0__Suc)). 120.83/55.34 thf(11875,plain,((! [A:$i]: ((hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ zero_z891286103de_int) @ (hAPP_nat_nat @ suc @ A)) = zero_z891286103de_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006])). 120.83/55.34 thf(4873,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_less__int__code_I15_J)). 120.83/55.34 thf(22215,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ bit1 @ A)) @ (hAPP_int_int @ bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4873])). 120.83/55.34 thf(978,axiom,((! [A:$i]: ((A = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ uminus_uminus_int @ A))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3518_zminus__zminus)). 120.83/55.34 thf(8305,plain,((! [A:$i]: ((A = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ uminus_uminus_int @ A))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[978])). 120.83/55.34 thf(3022,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_zero__less__mult__pos2)). 120.83/55.34 thf(15457,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ B)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3022])). 120.83/55.34 thf(4432,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ fact_fact_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4288_fact__reduce__int)). 120.83/55.34 thf(20531,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => ((hAPP_int_int @ fact_fact_int @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ fact_fact_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4432])). 120.83/55.34 thf(2633,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1945_ab__semigroup__add__class_Oadd__ac_I1_J)). 120.83/55.34 thf(14114,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2633])). 120.83/55.34 thf(1628,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((((hAPP_int_int @ (div_mod_int @ A) @ B) = D) <= (zero_zero_int != B)) <= (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D)))) <= ((is_int @ D) & (is_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2796_divmod__int__rel__mod)). 120.83/55.34 thf(10586,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP_int_int @ (div_mod_int @ A) @ B) = D) | (zero_zero_int = B) | ~ (hBOOL @ (hAPP_P603027463t_bool @ (divmod_int_rel @ A @ B) @ (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ C) @ D))) | ~ ((is_int @ D) & (is_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628])). 120.83/55.34 thf(702,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ B @ A)) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C)) => (~ (hBOOL @ (hAPP_nat_bool @ B @ D)))) & (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ one_one_nat)))))) <= (~ (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1691_ex__least__nat__less)). 120.83/55.34 thf(7299,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ B @ A)) => (? [C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ C)) => (~ (hBOOL @ (hAPP_nat_bool @ B @ D)))) & (hBOOL @ (hAPP_nat_bool @ B @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ C) @ one_one_nat)))))) | (hBOOL @ (hAPP_nat_bool @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 120.83/55.34 thf(3060,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3332_real__sqrt__ge__1__iff)). 120.83/55.34 thf(15597,plain,((! [A:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ A)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ one_one_real) @ (hAPP_real_real @ sqrt @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3060])). 120.83/55.34 thf(3724,axiom,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1296_power__0)). 120.83/55.34 thf(17849,plain,((! [A:$i]: (one_one_int = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3724])). 120.83/55.34 thf(1920,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1274_power__increasing)). 120.83/55.34 thf(11616,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ one_on1645066479umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920])). 120.83/55.34 thf(562,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((A = (hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3744_arcsin__pi)). 120.83/55.34 thf(6797,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ number267125858f_real @ min)) @ A)) => (((A = (hAPP_real_real @ sin @ (hAPP_real_real @ arcsin @ A))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ arcsin @ A)) @ pi)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ uminus_uminus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ (hAPP_real_real @ arcsin @ A)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])). 120.83/55.34 thf(3362,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((one_one_real = (hAPP_real_real @ (log @ A) @ A)) <= (one_one_real != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3867_log__eq__one)). 120.83/55.34 thf(16622,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) => ((one_one_real = (hAPP_real_real @ (log @ A) @ A)) | (one_one_real = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3362])). 120.83/55.34 thf(4720,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ A) @ B)) | (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Int__Oint_T)). 120.83/55.34 thf(21693,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ fequal_int @ A) @ B)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4720])). 120.83/55.34 thf(2993,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zOdd)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3092_IntNatAux_Oeven__plus__odd)). 120.83/55.34 thf(15359,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ B) @ zEven)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zOdd)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A)) @ zOdd)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2993])). 120.83/55.34 thf(2559,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2476_div__0)). 120.83/55.34 thf(13824,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ zero_z126310315umeral) @ A) = zero_z126310315umeral))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2559])). 120.83/55.34 thf(3679,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (div_mod_int @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5136_Divides_Otransfer__int__nat__function__closures_I2_J)). 120.83/55.34 thf(17701,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ B)) => ((hBOOL @ (hAPP_int_bool @ nat_is_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_is_nat @ (hAPP_int_int @ (div_mod_int @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3679])). 120.83/55.34 thf(4340,axiom,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_zadd__0)). 120.83/55.34 thf(20187,plain,((! [A:$i]: ((A = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int) @ A)) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4340])). 120.83/55.34 thf(2026,axiom,((! [A:$i,B:$i]: ((A = B) <=> ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2835_nat_Oinject)). 120.83/55.34 thf(11925,plain,((! [A:$i,B:$i]: (((A = B) => ((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ suc @ B))) & (((hAPP_nat_nat @ suc @ A) = (hAPP_nat_nat @ suc @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026])). 120.83/55.34 thf(774,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3036_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 120.83/55.34 thf(7563,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])). 120.83/55.34 thf(1138,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (A = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3901_odd__real__root__power__cancel)). 120.83/55.34 thf(8857,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ B))) => (A = (hAPP_real_real @ (hAPP_n546711566l_real @ root @ B) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138])). 120.83/55.34 thf(160,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: ((B = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D))) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3947_polar__ex2)). 120.83/55.34 thf(5473,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: ((B = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ sin @ D))) & ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ cos @ D)) = A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 120.83/55.34 thf(4039,axiom,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => ((C = A) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1930_add__right__cancel)). 120.83/55.34 thf(18973,plain,((! [A:$i,B:$i,C:$i]: (((is_int @ C) & (is_int @ A)) => (((C = A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ C) @ B) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B)) => (C = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4039])). 120.83/55.34 thf(1175,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3119_power__gt1)). 120.83/55.34 thf(8978,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ B) @ (hAPP_nat_nat @ suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175])). 120.83/55.34 thf(1754,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2288_mult_Ozero__right)). 120.83/55.34 thf(11021,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ A) @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754])). 120.83/55.34 thf(3694,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int = A) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1975_double__zero__sym)). 120.83/55.34 thf(17746,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_int = A) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = zero_zero_int)) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ A) = zero_zero_int) => (zero_zero_int = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3694])). 120.83/55.34 thf(3620,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((((zero_zero_int = B) & (zero_zero_int = A)) <=> ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A) = zero_zero_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2160_add__nonneg__eq__0__iff)). 120.83/55.34 thf(17469,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((((zero_zero_int = B) & (zero_zero_int = A)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A) = zero_zero_int)) & (((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ A) = zero_zero_int) => ((zero_zero_int = B) & (zero_zero_int = A)))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3620])). 120.83/55.34 thf(2095,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_dvd__mult)). 120.83/55.34 thf(12144,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ dvd_dvd_rat @ B) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095])). 120.83/55.34 thf(119,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2299_mult__left_Odiff)). 120.83/55.34 thf(5344,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ A) @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 120.83/55.34 thf(1036,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2426_mod__add__right__eq)). 120.83/55.34 thf(8493,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (div_mod_nat @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036])). 120.83/55.34 thf(3805,axiom,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4518_zrelprime__dvd__mult)). 120.83/55.34 thf(18139,plain,((! [A:$i,B:$i,C:$i]: ((one_one_int = (hAPP_int_int @ (legacy_zgcd @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3805])). 120.83/55.34 thf(4863,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.34 thf(22189,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ B) @ one_one_int)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4863])). 120.83/55.34 thf(4400,axiom,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3459_abs__power2__distrib)). 120.83/55.34 thf(20404,plain,((! [A:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ abs_abs_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4400])). 120.83/55.34 thf(4484,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ C) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2467_zdvd__zmod)). 120.83/55.34 thf(20737,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (div_mod_int @ C) @ A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4484])). 120.83/55.34 thf(2891,axiom,((! [A:$i]: ((zero_zero_complex = A) <=> (zero_zero_complex = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1898_zero__reorient)). 120.83/55.34 thf(15003,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2891])). 120.83/55.34 thf(671,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((A = C) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))) <= ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3106_power__inject__base)). 120.83/55.34 thf(7195,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) => ((A = C) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ C)))) | ~ ((hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 120.83/55.34 thf(647,axiom,((! [A:$i,B:$i]: (((B != A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1633_nat__less__le)). 120.83/55.34 thf(7103,plain,((! [A:$i,B:$i]: (((~ (B = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (~ (B = A) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])). 120.83/55.34 thf(4162,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3024_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 120.83/55.34 thf(19496,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4162])). 120.83/55.34 thf(580,axiom,((! [A:$i]: ((hAPP_real_real @ sgn_sgn_real @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ abs_abs_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3565_real__sgn__eq)). 120.83/55.34 thf(6864,plain,((! [A:$i]: ((hAPP_real_real @ sgn_sgn_real @ A) = (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ A) @ (hAPP_real_real @ abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 120.83/55.34 thf(4029,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_power2__less__0)). 120.83/55.34 thf(18939,plain,((! [A:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4029])). 120.83/55.34 thf(1430,axiom,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4322_gcd__proj2__if__dvd__nat)). 120.83/55.34 thf(9870,plain,((! [A:$i,B:$i]: ((A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ B) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430])). 120.83/55.34 thf(4814,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2504_mod__mult__self1)). 120.83/55.34 thf(22022,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (div_mod_int @ A) @ C) = (hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ C))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4814])). 120.83/55.34 thf(1577,axiom,((! [A:$i,B:$i]: (((? [C:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1828_realpow__pos__nth)). 120.83/55.34 thf(10389,plain,((! [A:$i,B:$i]: (? [C:$i]: ((A = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ C) @ B)) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577])). 120.83/55.34 thf(1575,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ zero_zero_rat) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 120.83/55.34 thf(10383,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ zero_zero_rat) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575])). 120.83/55.34 thf(3378,axiom,((! [A:$i,B:$i]: (((one_one_nat = A) | (B = zero_zero_nat)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1821_exp__eq__1)). 120.83/55.34 thf(16679,plain,((! [A:$i,B:$i]: ((((one_one_nat = A) | (B = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat)) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B) = one_one_nat) => ((one_one_nat = A) | (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3378])). 120.83/55.34 thf(1115,axiom,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1990_add__0__left)). 120.83/55.34 thf(8786,plain,((! [A:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ zero_z891286103de_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115])). 120.83/55.34 thf(4522,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => ((A != zero_zero_int) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)))) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_zdvd__mult__cancel)). 120.83/55.34 thf(20884,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => ((~ (A = zero_zero_int)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C)))) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4522])). 120.83/55.34 thf(3234,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2188_add__pos__pos)). 120.83/55.34 thf(16224,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3234])). 120.83/55.34 thf(2546,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (archim856651990g_real @ A)) @ B) = (archim856651990g_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4427_ceiling__add)). 120.83/55.34 thf(13792,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (archim856651990g_real @ A)) @ B) = (archim856651990g_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_int_real @ real_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2546])). 120.83/55.34 thf(4088,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ pred @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4042_le__iff__pred__less)). 120.83/55.34 thf(19232,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ pred @ A)) @ B))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ pred @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4088])). 120.83/55.34 thf(1454,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ one_on1684967323de_int)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 120.83/55.34 thf(9954,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ one_on1684967323de_int)) @ A) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454])). 120.83/55.34 thf(4555,axiom,((! [A:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2663_zmod__minus1)). 120.83/55.34 thf(21076,plain,((! [A:$i]: (((hAPP_int_int @ (div_mod_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ one_one_int)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4555])). 120.83/55.34 thf(2794,axiom,((! [A:$i]: ((zero_zero_rat = A) <=> (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1900_zero__reorient)). 120.83/55.34 thf(14674,plain,((! [A:$i]: (((zero_zero_rat = A) => (A = zero_zero_rat)) & ((A = zero_zero_rat) => (zero_zero_rat = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2794])). 120.83/55.34 thf(1498,axiom,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))) <= (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3411_natceiling__le__eq__number__of)). 120.83/55.34 thf(10086,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ number267125858f_real @ B)))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_int_real @ number267125858f_real @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (natceiling @ A)) @ (hAPP_int_nat @ number_number_of_nat @ B))))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A)) | (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498])). 120.83/55.34 thf(4860,axiom,((! [A:$i]: ((((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ A) = one_one_int) <= (A != zero_zero_int)) <= (is_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2523_zdiv__self)). 120.83/55.34 thf(22183,plain,((! [A:$i]: (((hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ A) = one_one_int) | (A = zero_zero_int) | ~ (is_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4860])). 120.83/55.34 thf(1571,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4721_Fract__less__one__iff)). 120.83/55.34 thf(10372,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)) @ one_one_rat)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571])). 120.83/55.34 thf(2847,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1748_Nat_Odiff__le__self)). 120.83/55.34 thf(14858,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2847])). 120.83/55.34 thf(4416,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_one_int = A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1496_dvd__power)). 120.83/55.34 thf(20471,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) | (one_one_int = A)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4416])). 120.83/55.34 thf(3624,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) @ one_one_int)) @ C))) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3464_decr__lemma)). 120.83/55.34 thf(17484,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ abs_abs_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) @ one_one_int)) @ C))) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3624])). 120.83/55.34 thf(1087,axiom,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_dvd__refl)). 120.83/55.34 thf(8702,plain,((! [A:$i]: (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087])). 120.83/55.34 thf(4541,axiom,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096)). 120.83/55.34 thf(20977,plain,((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ m)) @ one_one_int)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ s) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4541])). 120.83/55.34 thf(194,axiom,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (hAPP_int_real @ real_int @ A)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4399_real__of__int__minus)). 120.83/55.34 thf(5591,plain,((! [A:$i]: ((hAPP_real_real @ uminus_uminus_real @ (hAPP_int_real @ real_int @ A)) = (hAPP_int_real @ real_int @ (hAPP_int_int @ uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 120.83/55.34 thf(2331,axiom,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3470_pi__half__gt__zero)). 120.83/55.34 thf(13016,plain,((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ pi) @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331])). 120.83/55.34 thf(1602,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)) <=> (one_one_nat = A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1573_dvd__mult__cancel2)). 120.83/55.34 thf(10492,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)) => (one_one_nat = A)) & ((one_one_nat = A) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602])). 120.83/55.34 thf(2112,axiom,((! [A:$i]: ((zero_z891286103de_int = A) <=> (A = zero_z891286103de_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1899_zero__reorient)). 120.83/55.34 thf(12203,plain,((! [A:$i]: (((zero_z891286103de_int = A) => (A = zero_z891286103de_int)) & ((A = zero_z891286103de_int) => (zero_z891286103de_int = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112])). 120.83/55.34 thf(2757,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = one_one_int) <=> (((one_one_int = A) & (one_one_int = B)) | (((hAPP_int_int @ number_number_of_int @ min) = A) & (B = (hAPP_int_int @ number_number_of_int @ min)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_zmult__eq__1__iff)). 120.83/55.34 thf(14531,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => ((((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = one_one_int) => (((one_one_int = A) & (one_one_int = B)) | (((hAPP_int_int @ number_number_of_int @ min) = A) & (B = (hAPP_int_int @ number_number_of_int @ min))))) & ((((one_one_int = A) & (one_one_int = B)) | (((hAPP_int_int @ number_number_of_int @ min) = A) & (B = (hAPP_int_int @ number_number_of_int @ min)))) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B) = one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2757])). 120.83/55.34 thf(1700,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1729_real__zero__not__eq__one)). 120.83/55.34 thf(10813,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700])). 120.83/55.34 thf(765,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2562_dvd__div__mult)). 120.83/55.34 thf(7531,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ C) @ A)) @ B) = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ C) @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])). 120.83/55.34 thf(183,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J)). 120.83/55.34 thf(5542,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ D)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 120.83/55.34 thf(2319,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4994_gcd__mult__distrib__int)). 120.83/55.34 thf(12965,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ abs_abs_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ gcd_gcd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319])). 120.83/55.34 thf(1598,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ suc @ A) = (hAPP_int_nat @ number_number_of_nat @ B)) <=> (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4778_Suc__eq__number__of)). 120.83/55.34 thf(10460,plain,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ A) = (hAPP_int_nat @ number_number_of_nat @ B)) => (~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))) = A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))))) => ((hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ B))) = A))) => ((hAPP_nat_nat @ suc @ A) = (hAPP_int_nat @ number_number_of_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598])). 120.83/55.34 thf(1525,axiom,((! [A:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2191_double__add__less__zero__iff__single__add__less__zero)). 120.83/55.34 thf(10187,plain,((! [A:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ A) @ zero_zero_rat)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)) @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525])). 120.83/55.34 thf(2671,axiom,((! [A:$i,B:$i]: ((is_int @ B) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2342_mod__div__equality2)). 120.83/55.34 thf(14237,plain,((! [A:$i,B:$i]: ((is_int @ B) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ A))) @ (hAPP_int_int @ (div_mod_int @ B) @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2671])). 120.83/55.34 thf(4497,axiom,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) => ((((norm_frac @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int)) <= ((A = zero_zero_int) | (B = zero_zero_int))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) = (norm_frac @ A @ B)) <= (~ ((B = zero_zero_int) | (zero_zero_int = A)))))) & (((norm_frac @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (norm_frac @ A @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4807_norm__frac_Osimps)). 120.83/55.34 thf(20776,plain,((! [A:$i,B:$i]: (((is_int @ B) & (is_int @ A)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))) => ((((norm_frac @ A @ B) = (hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ zero_zero_int) @ one_one_int)) | ~ ((A = zero_zero_int) | (B = zero_zero_int))) & (((hAPP_i1524277240nt_int @ (hAPP_i1584592887nt_int @ product_Pair_int_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ div_div_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ int_gcd @ A) @ B))) = (norm_frac @ A @ B)) | (B = zero_zero_int) | (zero_zero_int = A)))) & (((norm_frac @ (hAPP_int_int @ uminus_uminus_int @ A) @ (hAPP_int_int @ uminus_uminus_int @ B)) = (norm_frac @ A @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4497])). 120.83/55.34 thf(2386,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2206_add__less__le__mono)). 120.83/55.34 thf(13215,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ C) @ D)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ A)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386])). 120.83/55.34 thf(314,axiom,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2345_mod__div__equality2)). 120.83/55.34 thf(5986,plain,((! [A:$i,B:$i]: ((hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ B) @ A))) @ (hAPP_Q1762011733de_int @ (div_mo231679042de_int @ B) @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 120.83/55.34 thf(1855,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_left__distrib__number__of)). 120.83/55.34 thf(11397,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ C))) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ (hAPP_int_nat @ number_number_of_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855])). 120.83/55.34 thf(361,axiom,((! [A:$i,B:$i]: ((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) => ((zero_zero_real = A) | (zero_zero_real = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_divisors__zero)). 120.83/55.34 thf(6158,plain,((! [A:$i,B:$i]: ((zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) => ((zero_zero_real = A) | (zero_zero_real = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 120.83/55.34 thf(965,axiom,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ one_on1645066479umeral) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ B)) <= (B != zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2630_div__add__self1)). 120.83/55.34 thf(8245,plain,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ A) @ B)) @ one_on1645066479umeral) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A)) @ B)) | (B = zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[965])). 120.83/55.34 thf(2861,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1725_dvd_Oless__le__trans)). 120.83/55.34 thf(14899,plain,((! [A:$i,B:$i,C:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2861])). 120.83/55.34 thf(1735,axiom,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => (one_one_nat = (hAPP_nat_nat @ suc @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ suc @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3300_Suc__nat__number__of)). 120.83/55.34 thf(10934,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A))) => (one_one_nat = (hAPP_nat_nat @ suc @ (hAPP_int_nat @ number_number_of_nat @ A)))) & ((~ (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ A)))) => ((hAPP_nat_nat @ suc @ (hAPP_int_nat @ number_number_of_nat @ A)) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ succ @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735])). 120.83/55.34 thf(2938,axiom,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3455_ln__add__one__self__le__self)). 120.83/55.34 thf(15166,plain,((! [A:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ ln @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ A))) @ A)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2938])). 120.83/55.34 thf(228,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2293_mult__right_Oadd)). 120.83/55.34 thf(5707,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 120.83/55.34 thf(4060,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_dvd__triv__left)). 120.83/55.34 thf(19116,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4060])). 120.83/55.34 thf(3589,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1885_add__neg__nonpos)). 120.83/55.34 thf(17372,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ B) @ zero_z891286103de_int)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le258702272de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ plus_p1446045655de_int @ B) @ A)) @ zero_z891286103de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3589])). 120.83/55.34 thf(1825,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 120.83/55.34 thf(11281,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ one_one_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825])). 120.83/55.34 thf(4910,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_pos__zmult__pos)). 120.83/55.34 thf(22341,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ B) @ A))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4910])). 120.83/55.34 thf(2207,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B)))) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1419_power__increasing__iff)). 120.83/55.34 thf(12579,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ A)) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ one_one_rat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207])). 120.83/55.34 thf(848,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zEven)) <=> (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3148_power__preserves__even)). 120.83/55.34 thf(7848,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B)) => (((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven))) & ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ zEven)) => (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) @ zEven))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[848])). 120.83/55.34 thf(2404,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2067_add__less__cancel__left)). 120.83/55.34 thf(13289,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ B) @ C)) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404])). 120.83/55.34 thf(156,axiom,((! [A:$i]: ((rcis @ zero_zero_real @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4261_rcis__zero__mod)). 120.83/55.34 thf(5458,plain,((! [A:$i]: ((rcis @ zero_zero_real @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 120.83/55.34 thf(2849,axiom,((! [A:$i,B:$i]: ((~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1720_dvd_Oless__imp__not__less)). 120.83/55.34 thf(14863,plain,((! [A:$i,B:$i]: (~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B)) & ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2849])). 120.83/55.34 thf(3829,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1500_neg__one__power__eq__mod__m)). 120.83/55.34 thf(18214,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ C)) => (((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A) = (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ number_number_of_int @ min)) @ B)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3829])). 120.83/55.34 thf(3595,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3117_power__gt1)). 120.83/55.34 thf(17387,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ B) @ (hAPP_nat_nat @ suc @ A)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ one_on1645066479umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3595])). 120.83/55.34 thf(4427,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1574_add__number__of__diff1)). 120.83/55.34 thf(20505,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4427])). 120.83/55.34 thf(2538,axiom,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_nat_nat @ suc @ A)) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2993_power__0__Suc)). 120.83/55.34 thf(13760,plain,((! [A:$i]: ((hAPP_nat_complex @ (hAPP_c1088319240omplex @ power_power_complex @ zero_zero_complex) @ (hAPP_nat_nat @ suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2538])). 120.83/55.34 thf(2475,axiom,((~ (hBOOL @ (hAPP_nat_bool @ prime @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4164_prime__1)). 120.83/55.34 thf(13534,plain,((~ (hBOOL @ (hAPP_nat_bool @ prime @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2475])). 120.83/55.34 thf(1407,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ C) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 120.83/55.34 thf(9784,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ B)) @ C) = (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407])). 120.83/55.34 thf(2832,axiom,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3810_fact__ge__one__nat)). 120.83/55.34 thf(14811,plain,((! [A:$i]: (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ one_one_nat) @ (hAPP_nat_nat @ fact_fact_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2832])). 120.83/55.34 thf(4939,axiom,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ B) @ A) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4495_zgcd__commute)). 120.83/55.34 thf(22436,plain,((! [A:$i,B:$i]: ((hAPP_int_int @ (legacy_zgcd @ B) @ A) = (hAPP_int_int @ (legacy_zgcd @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4939])). 120.83/55.34 thf(2727,axiom,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1987_add__0__left)). 120.83/55.34 thf(14426,plain,((! [A:$i]: (A = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2727])). 120.83/55.34 thf(358,axiom,((! [A:$i]: ((A = (hAPP_real_real @ exp_real @ (hAPP_real_real @ ln @ A))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3848_exp__ln)). 120.83/55.34 thf(6145,plain,((! [A:$i]: ((A = (hAPP_real_real @ exp_real @ (hAPP_real_real @ ln @ A))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 120.83/55.34 thf(2998,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_mult__pos__pos)). 120.83/55.34 thf(15381,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2998])). 120.83/55.34 thf(3519,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1719_dvd_Oless__imp__le)). 120.83/55.34 thf(17123,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ A)) & (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3519])). 120.83/55.34 thf(1098,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4717_zero__less__Fract__iff)). 120.83/55.34 thf(8741,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ B)) => (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ zero_zero_int) @ A)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ zero_zero_rat) @ (hAPP_int_rat @ (hAPP_int_fun_int_rat @ fract @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098])). 120.83/55.34 thf(2663,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1850_nat__diff__add__eq2)). 120.83/55.34 thf(14210,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ E) @ D)) @ A)) @ C)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ E) @ A)) @ C))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2663])). 120.83/55.34 thf(3228,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1770_diff__add__assoc)). 120.83/55.34 thf(16203,plain,((! [A:$i,B:$i,C:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ C) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ A) @ C)) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3228])). 120.83/55.34 thf(3958,axiom,(((hAPP_int_int @ fact_fact_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4273_fact__1__int)). 120.83/55.34 thf(18675,plain,(((hAPP_int_int @ fact_fact_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3958])). 120.83/55.34 thf(257,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))) @ (hAPP_complex_real @ norm_norm_complex @ A))) @ (hAPP_complex_real @ norm_norm_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3369_complex__mod__triangle__ineq2)). 120.83/55.34 thf(5788,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ minus_minus_real @ (hAPP_complex_real @ norm_norm_complex @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ plus_plus_complex @ A) @ B))) @ (hAPP_complex_real @ norm_norm_complex @ A))) @ (hAPP_complex_real @ norm_norm_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 120.83/55.34 thf(91,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_mult__zero__left)). 120.83/55.34 thf(5261,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 120.83/55.34 thf(948,axiom,((! [A:$i,B:$i]: (((hAPP_i1732201573de_int @ number1226105091de_int @ A) = B) <=> ((hAPP_i1732201573de_int @ number1226105091de_int @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_number__of__reorient)). 120.83/55.34 thf(8179,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])). 120.83/55.34 thf(149,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (A = B)) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1730_real__le__antisym)). 120.83/55.34 thf(5436,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ B) @ A)) => (A = B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 120.83/55.34 thf(1728,axiom,((! [A:$i]: ((A != zero_zero_nat) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ A) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2554_div__self)). 120.83/55.34 thf(10900,plain,((! [A:$i]: ((~ (A = zero_zero_nat)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728])). 120.83/55.34 thf(2943,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1764_add__diff__inverse)). 120.83/55.34 thf(15181,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B))) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ plus_plus_nat @ B) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2943])). 120.83/55.34 thf(4918,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1336_mult__left__less__imp__less)). 120.83/55.34 thf(22362,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ B)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) => ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4918])). 120.83/55.34 thf(3034,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_dvd__mult__right)). 120.83/55.34 thf(15489,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ B) @ C)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3034])). 120.83/55.34 thf(697,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) <=> (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2064_add__less__cancel__left)). 120.83/55.34 thf(7284,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C)))) & ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C))) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])). 120.83/55.34 thf(4488,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_dvd__mult)). 120.83/55.34 thf(20744,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ A) @ C))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4488])). 120.83/55.34 thf(1731,axiom,((! [A:$i,B:$i,C:$i]: (((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)) <= (C = B))) <= ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1590_nat__less__cases)). 120.83/55.34 thf(10916,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B))) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)) | ~ (C = B)) | ~ ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ B) @ C)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731])). 120.83/55.34 thf(3501,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2003_add__le__imp__le__right)). 120.83/55.34 thf(17076,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ A) @ C)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3501])). 120.83/55.34 thf(2466,axiom,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ real_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4391_real__of__int__power)). 120.83/55.34 thf(13510,plain,((! [A:$i,B:$i]: ((hAPP_int_real @ real_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_int_real @ real_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2466])). 120.83/55.34 thf(2701,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ suc @ A)) @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4347_coprime__Suc__nat)). 120.83/55.34 thf(14340,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ (hAPP_nat_nat @ suc @ A)) @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2701])). 120.83/55.34 thf(2185,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 120.83/55.34 thf(12488,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ B)) @ C) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185])). 120.83/55.34 thf(2930,axiom,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = A) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4323_gcd__proj1__if__dvd__nat)). 120.83/55.34 thf(15134,plain,((! [A:$i,B:$i]: (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ gcd_gcd_nat @ A) @ B) = A) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2930])). 120.83/55.34 thf(1288,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2183_add__pos__pos)). 120.83/55.34 thf(9385,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le1304079648umeral @ zero_z126310315umeral) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288])). 120.83/55.34 thf(2029,axiom,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A)) @ A) = B) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2565_dvd__div__mult__self)). 120.83/55.34 thf(11938,plain,((! [A:$i,B:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ div_di1218280263umeral @ B) @ A)) @ A) = B) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029])). 120.83/55.34 thf(2343,axiom,((! [A:$i]: (A = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 120.83/55.34 thf(13053,plain,((! [A:$i]: (A = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343])). 120.83/55.34 thf(551,axiom,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3717_sin__two__pi)). 120.83/55.34 thf(6767,plain,(((hAPP_real_real @ sin @ (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ (hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ pi)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])). 120.83/55.34 thf(3913,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (zero_zero_int = (hAPP_int_int @ fact_fact_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4275_fact__neg__int)). 120.83/55.34 thf(18534,plain,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ A) @ zero_zero_int)) => (zero_zero_int = (hAPP_int_int @ fact_fact_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3913])). 120.83/55.34 thf(1964,axiom,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2286_mult__left_Ozero)). 120.83/55.34 thf(11754,plain,((! [A:$i]: ((hAPP_complex_complex @ (hAPP_c172932010omplex @ times_times_complex @ zero_zero_complex) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964])). 120.83/55.34 thf(1434,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_mult__mono_H)). 120.83/55.34 thf(9880,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ B)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ C) @ A)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ D) @ B))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434])). 120.83/55.34 thf(910,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) <=> (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2069_add__less__cancel__left)). 120.83/55.34 thf(8055,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C)))) & ((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ C))) => (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[910])). 120.83/55.34 thf(3371,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_power__mult)). 120.83/55.34 thf(16659,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3371])). 120.83/55.34 thf(4732,axiom,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2715_nat__number__of)). 120.83/55.34 thf(21744,plain,((! [A:$i]: ((hAPP_int_nat @ number_number_of_nat @ A) = (hAPP_int_nat @ nat @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4732])). 120.83/55.34 thf(4203,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_i744251628nt_int @ (hAPP_f836602773nt_int @ (hAPP_f888249301nt_int @ cOMBB_1875755114nt_int @ A) @ B) @ C) = (hAPP_f747162069nt_int @ A @ (hAPP_int_fun_int_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__fun_Itc___023)). 120.83/55.34 thf(19642,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_i744251628nt_int @ (hAPP_f836602773nt_int @ (hAPP_f888249301nt_int @ cOMBB_1875755114nt_int @ A) @ B) @ C) = (hAPP_f747162069nt_int @ A @ (hAPP_int_fun_int_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4203])). 120.83/55.34 thf(3535,axiom,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sr @ B))) => ((hAPP_int_int @ (standardRes @ B) @ A) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2335_StandardRes__SR__prop)). 120.83/55.34 thf(17167,plain,((! [A:$i,B:$i]: ((is_int @ A) => ((hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ (hAPP_i1948725293t_bool @ sr @ B))) => ((hAPP_int_int @ (standardRes @ B) @ A) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3535])). 120.83/55.34 thf(1396,axiom,(((hAPP_n522471361de_int @ semiri1424489471de_int @ one_one_nat) = one_on1684967323de_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2968_of__nat__1)). 120.83/55.34 thf(9748,plain,(((hAPP_n522471361de_int @ semiri1424489471de_int @ one_one_nat) = one_on1684967323de_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396])). 120.83/55.34 thf(969,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => ((? [D:$i]: (! [E:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ E)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D)))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3890_DERIV__pos__inc__right)). 120.83/55.34 thf(8264,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (deriv_real @ A @ B) @ C)) => (? [D:$i]: (! [E:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ (hAPP_real_real @ A @ B)) @ (hAPP_real_real @ A @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ B) @ E)))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ E) @ D)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ E))) & (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ D))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])). 120.83/55.34 thf(548,axiom,((zero_zero_real = (hAPP_nat_real @ real_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3646_real__of__nat__zero)). 120.83/55.34 thf(6761,plain,((zero_zero_real = (hAPP_nat_real @ real_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 120.83/55.34 thf(1318,axiom,((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3760_odd__1__nat)). 120.83/55.34 thf(9479,plain,((~ (hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318])). 120.83/55.34 thf(1738,axiom,((! [A:$i,B:$i]: ((((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) != B) => ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) & ((B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3079_mod__Suc)). 120.83/55.34 thf(10949,plain,((! [A:$i,B:$i]: (((~ ((hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) = B)) => ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B) = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)))) & ((B = (hAPP_nat_nat @ suc @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) => (zero_zero_nat = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ suc @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738])). 120.83/55.34 thf(2423,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_mult__pos__neg)). 120.83/55.34 thf(13353,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ A) @ zero_z891286103de_int)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) @ zero_z891286103de_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423])). 120.83/55.34 thf(1170,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2165_add__nonneg__nonneg)). 120.83/55.34 thf(8966,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170])). 120.83/55.34 thf(4076,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ C)) <= (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B))) <= (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4593_RRset2norRR__correct1)). 120.83/55.34 thf(19193,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ (hAPP_int_int @ (rRset2norRR @ B @ C) @ A)) @ C)) | ~ (hBOOL @ (hAPP_f448129468l_bool @ (hAPP_i2112223885l_bool @ member_int @ A) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (is_RRset @ B) @ C)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ one_one_int) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4076])). 120.83/55.34 thf(2596,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2398_zmod__simps_I4_J)). 120.83/55.34 thf(13962,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B)) @ C)) @ B) = (hAPP_nat_nat @ (div_mod_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2596])). 120.83/55.34 thf(3336,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4174_prime__divexp)). 120.83/55.34 thf(16543,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_nat_bool @ prime @ C)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3336])). 120.83/55.34 thf(690,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_mult__left__mono)). 120.83/55.34 thf(7267,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ B)) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ C)))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])). 120.83/55.34 thf(1214,axiom,((! [A:$i]: (((A != zero_z891286103de_int) => ((((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) != zero_z891286103de_int) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (quickcheck_int_of @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int) = (quickcheck_int_of @ A))) & (((quickcheck_int_of @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (quickcheck_int_of @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) <= ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_z891286103de_int)))) & (((quickcheck_int_of @ A) = zero_zero_int) <= (zero_z891286103de_int = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4250_Quickcheck__Narrowing_Oint__of__code)). 120.83/55.34 thf(9098,plain,((! [A:$i]: (((~ (A = zero_z891286103de_int)) => (((~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_z891286103de_int)) => ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (quickcheck_int_of @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ one_one_int) = (quickcheck_int_of @ A))) & (((quickcheck_int_of @ A) = (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ (quickcheck_int_of @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ div_di1430059507de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) | ~ ((hAPP_Q1762011733de_int @ (div_mo231679042de_int @ A) @ (hAPP_i1732201573de_int @ number1226105091de_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) = zero_z891286103de_int)))) & (((quickcheck_int_of @ A) = zero_zero_int) | ~ (zero_z891286103de_int = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214])). 120.83/55.34 thf(3067,axiom,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2981_of__nat__power)). 120.83/55.34 thf(15629,plain,((! [A:$i,B:$i]: ((hAPP_nat_real @ semiri132038758t_real @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ (hAPP_nat_real @ semiri132038758t_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3067])). 120.83/55.34 thf(3245,axiom,((! [A:$i]: ((is_int @ A) => ((zero_zero_int = A) <=> (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1894_zero__reorient)). 120.83/55.34 thf(16250,plain,((! [A:$i]: ((is_int @ A) => (((zero_zero_int = A) => (A = zero_zero_int)) & ((A = zero_zero_int) => (zero_zero_int = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3245])). 120.83/55.34 thf(3296,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3346_real__sqrt__sum__squares__ge1)). 120.83/55.34 thf(16417,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ (hAPP_real_real @ sqrt @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_real @ (hAPP_r474017924t_real @ power_power_real @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3296])). 120.83/55.34 thf(2408,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A))) <= (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_zero__less__mult__pos2)). 120.83/55.34 thf(13306,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ B)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ A))) | ~ (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ ord_le1860547276de_int @ zero_z891286103de_int) @ (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2408])). 120.83/55.34 thf(2734,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_mult__nonneg__nonpos)). 120.83/55.34 thf(14450,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat) @ B)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ A) @ zero_zero_nat)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_eq_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ A)) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2734])). 120.83/55.34 thf(351,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B))) <=> (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4419_le__floor__eq)). 120.83/55.34 thf(6119,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B))) => (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B))) & ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ (hAPP_int_real @ real_int @ A)) @ B)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ A) @ (archim1246769320r_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 120.83/55.34 thf(2974,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3111_power__le__imp__le__base)). 120.83/55.34 thf(15272,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ A) @ (hAPP_nat_nat @ suc @ B))) @ (hAPP_n1108039445umeral @ (hAPP_C471253896umeral @ power_2100829034umeral @ C) @ (hAPP_nat_nat @ suc @ B)))) => ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ C)) => (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ A) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2974])). 120.83/55.34 thf(1680,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D = B) | (C = A)) <=> ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_crossproduct__eq)). 120.83/55.34 thf(10745,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((D = B) | (C = A)) => ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B)))) & (((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ B)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ D)) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ A) @ D)) @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ C) @ B))) => ((D = B) | (C = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680])). 120.83/55.34 thf(4189,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_add__number__of__left)). 120.83/55.34 thf(19592,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ A)) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ B)) @ C)) = (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ A) @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4189])). 120.83/55.34 thf(3908,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 120.83/55.34 thf(18523,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3908])). 120.83/55.34 thf(3119,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ (natfloor @ A))) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3690_real__natfloor__add__one__gt)). 120.83/55.34 thf(15801,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ (natfloor @ A))) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3119])). 120.83/55.34 thf(4825,axiom,((! [A:$i]: ((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)) <=> (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4050_neg__number__of__pred__iff__0)). 120.83/55.34 thf(22066,plain,((! [A:$i]: (((zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)) => (hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A))))) & ((hBOOL @ (hAPP_int_bool @ nat_neg @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ pred @ A)))) => (zero_zero_nat = (hAPP_int_nat @ number_number_of_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4825])). 120.83/55.34 thf(3152,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (C = A)) <= (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A))) <= ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3103_power__inject__base)). 120.83/55.34 thf(15906,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ C)) => (C = A)) | ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_eq_rat @ zero_zero_rat) @ A)) | ~ ((hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ C) @ (hAPP_nat_nat @ suc @ B)) = (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_nat_nat @ suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3152])). 120.83/55.34 thf(1526,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__sum__power2__lt__zero)). 120.83/55.34 thf(10192,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP_rat_bool @ (hAPP_r2115560837t_bool @ ord_less_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_nat_rat @ (hAPP_rat_fun_nat_rat @ power_power_rat @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526])). 120.83/55.34 thf(1520,axiom,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4079_complex__cnj__divide)). 120.83/55.34 thf(10161,plain,((! [A:$i,B:$i]: ((hAPP_complex_complex @ cnj @ (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ A) @ B)) = (hAPP_complex_complex @ (hAPP_c172932010omplex @ invers1025623611omplex @ (hAPP_complex_complex @ cnj @ A)) @ (hAPP_complex_complex @ cnj @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520])). 120.83/55.34 thf(3277,axiom,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3834_exp__gt__zero)). 120.83/55.34 thf(16358,plain,((! [A:$i]: (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ (hAPP_real_real @ exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3277])). 120.83/55.34 thf(2071,axiom,((! [A:$i,B:$i]: (((zero_z891286103de_int != (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) <= (zero_z891286103de_int != A)) <= (zero_z891286103de_int != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_no__zero__divisors)). 120.83/55.34 thf(12070,plain,((! [A:$i,B:$i]: (~ (zero_z891286103de_int = (hAPP_Q1762011733de_int @ (hAPP_Q1729056540de_int @ times_123202395de_int @ B) @ A)) | (zero_z891286103de_int = A) | (zero_z891286103de_int = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071])). 120.83/55.34 thf(1257,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ A) @ one_one_real) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3910_real__root__one)). 120.83/55.34 thf(9254,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ A)) => ((hAPP_real_real @ (hAPP_n546711566l_real @ root @ A) @ one_one_real) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257])). 120.83/55.34 thf(2000,axiom,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_dvd__0__right)). 120.83/55.34 thf(11858,plain,((! [A:$i]: (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ dvd_dv174992974umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000])). 120.83/55.34 thf(4158,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => ((((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => (! [C:$i]: (((hAPP_f957591787ol_nat @ finite_card_int @ C) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) <= (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ (setS @ A @ B)))))) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3302_SetS__elems__card)). 120.83/55.34 thf(19486,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_int_bool @ zprime @ B)) => (((~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ quadRes @ B) @ A))) => (! [C:$i]: (((hAPP_f957591787ol_nat @ finite_card_int @ C) = (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) | ~ (hBOOL @ (hAPP_f215623910l_bool @ (hAPP_f628503027l_bool @ member_fun_int_bool @ C) @ (setS @ A @ B)))))) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ zero_zero_int) @ B)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4158])). 120.83/55.34 thf(3668,axiom,((is_int @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_s____)). 120.83/55.34 thf(17658,plain,((is_int @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3668])). 120.83/55.34 thf(103,axiom,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 120.83/55.34 thf(5293,plain,((! [A:$i]: (zero_zero_real = (hAPP_real_real @ (hAPP_r1250527377l_real @ times_times_real @ zero_zero_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 120.83/55.34 thf(1127,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_dvd__power__same)). 120.83/55.34 thf(8818,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ B) @ C)) => (hBOOL @ (hAPP_Q2096512830t_bool @ (hAPP_Q1010094925t_bool @ dvd_dv1760642554de_int @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ B) @ A)) @ (hAPP_n522471361de_int @ (hAPP_Q125967240de_int @ power_881366806de_int @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127])). 120.83/55.34 thf(2619,axiom,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ uminus_uminus_int @ A)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3516_minus__numeral__code_I5_J)). 120.83/55.34 thf(14055,plain,((! [A:$i]: ((hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ uminus_uminus_int @ A)) = (hAPP_int_int @ uminus_uminus_int @ (hAPP_int_int @ number_number_of_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2619])). 120.83/55.34 thf(736,axiom,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ zero_z126310315umeral)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_mult__zero__right)). 120.83/55.34 thf(7424,plain,((! [A:$i]: (zero_z126310315umeral = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ A) @ zero_z126310315umeral)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])). 120.83/55.34 thf(4305,axiom,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1666_zdiff__power3)). 120.83/55.34 thf(20039,plain,((! [A:$i,B:$i]: ((hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) = (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ plus_plus_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls))))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) @ B))) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ (hAPP_int_fun_int_int @ times_times_int @ (hAPP_int_int @ number_number_of_int @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))) @ A)) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))) @ (hAPP_nat_int @ (hAPP_int_fun_nat_int @ power_power_int @ B) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit1 @ (hAPP_int_int @ bit1 @ pls)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4305])). 120.89/55.34 thf(1685,axiom,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3016_power__Suc)). 120.89/55.34 thf(10768,plain,((! [A:$i,B:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ A) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ B)) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ A) @ (hAPP_nat_nat @ suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685])). 120.89/55.34 thf(3548,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A))) <= (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_mult__nonneg__nonneg)). 120.89/55.34 thf(17224,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ times_1655362735umeral @ B) @ A))) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ A)) | ~ (hBOOL @ (hAPP_C24501650l_bool @ (hAPP_C10902773l_bool @ ord_le565307924umeral @ zero_z126310315umeral) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3548])). 120.89/55.34 thf(1168,axiom,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 120.89/55.34 thf(8961,plain,((! [A:$i]: ((hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ times_times_rat @ (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ one_one_rat) @ one_one_rat)) @ A) = (hAPP_rat_rat @ (hAPP_rat_fun_rat_rat @ plus_plus_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168])). 120.89/55.34 thf(885,axiom,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ (hAPP_nat_real @ real_nat @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3714_real__of__nat__div__aux)). 120.89/55.34 thf(7970,plain,((! [A:$i,B:$i]: (((hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ A)) @ (hAPP_nat_real @ real_nat @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ B))) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ inverse_divide_real @ (hAPP_nat_real @ real_nat @ (hAPP_nat_nat @ (div_mod_nat @ A) @ B))) @ (hAPP_nat_real @ real_nat @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[885])). 120.89/55.34 thf(962,axiom,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2841_of__nat__Suc)). 120.89/55.34 thf(8232,plain,((! [A:$i]: ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ one_on1645066479umeral) @ (hAPP_n1108039445umeral @ semiri1619134803umeral @ A)) = (hAPP_n1108039445umeral @ semiri1619134803umeral @ (hAPP_nat_nat @ suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])). 120.89/55.34 thf(4204,axiom,((! [A:$i,B:$i]: ((~ (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ zprime @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))))) <=> ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4522_zgcd1__iff__no__common__primedivisor)). 120.89/55.34 thf(19645,plain,((! [A:$i,B:$i]: (((~ (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ zprime @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))))) => ((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int)) & (((hAPP_int_int @ (legacy_zgcd @ A) @ B) = one_one_int) => (~ (? [C:$i]: ((is_int @ C) & (hBOOL @ (hAPP_int_bool @ zprime @ C)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ B)) & (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4204])). 120.89/55.34 thf(1600,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ A)) @ B)) <=> (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((zero_zero_nat = B) <= (~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3223_nat__dvd__iff)). 120.89/55.34 thf(10475,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ A)) @ B)) => (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((zero_zero_nat = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))))) & ((((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ A) @ (hAPP_nat_int @ semiri1621563631at_int @ B))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) & ((zero_zero_nat = B) | (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ (hAPP_int_nat @ nat @ A)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600])). 120.89/55.34 thf(586,axiom,((zero_zero_nat = (hAPP_nat_nat @ nat_size @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4061_nat_Osize_I1_J)). 120.89/55.34 thf(6879,plain,((zero_zero_nat = (hAPP_nat_nat @ nat_size @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])). 120.89/55.34 thf(4494,axiom,((! [A:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)) <=> (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3102_int__le__0__conv)). 120.89/55.34 thf(20759,plain,((! [A:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)) => (zero_zero_nat = A)) & ((zero_zero_nat = A) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ (hAPP_nat_int @ semiri1621563631at_int @ A)) @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4494])). 120.89/55.34 thf(2533,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) <=> (C = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1936_add__left__cancel)). 120.89/55.34 thf(13743,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)) => (C = B)) & ((C = B) => ((hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ C) = (hAPP_C498520661umeral @ (hAPP_C1594335432umeral @ plus_p1627245867umeral @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2533])). 120.89/55.34 thf(4382,axiom,((! [A:$i,B:$i]: (((((B = A) <=> ((hAPP_int_nat @ nat @ B) = (hAPP_int_nat @ nat @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A))) <= (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B))) <= ((is_int @ B) & (is_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2707_transfer__nat__int__relations_I1_J)). 120.89/55.34 thf(20324,plain,((! [A:$i,B:$i]: ((((B = A) => ((hAPP_int_nat @ nat @ B) = (hAPP_int_nat @ nat @ A))) & (((hAPP_int_nat @ nat @ B) = (hAPP_int_nat @ nat @ A)) => (B = A))) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ A)) | ~ (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ ord_less_eq_int @ zero_zero_int) @ B)) | ~ ((is_int @ B) & (is_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4382])). 120.89/55.34 thf(3467,axiom,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) <= (one_one_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3792_lemma__even__mod__4__div__2)). 120.89/55.34 thf(16960,plain,((! [A:$i]: ((hBOOL @ (hAPP_nat_bool @ even_odd_even_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ one_one_nat)) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls)))))) | ~ (one_one_nat = (hAPP_nat_nat @ (div_mod_nat @ A) @ (hAPP_int_nat @ number_number_of_nat @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit0 @ (hAPP_int_int @ bit1 @ pls))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3467])). 120.89/55.34 thf(3142,axiom,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ zero_zero_nat) @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5123_min__0L)). 120.89/55.34 thf(15872,plain,((! [A:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ ord_min_nat @ zero_zero_nat) @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3142])). 120.89/55.34 thf(2477,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ suc @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2878_Suc__diff__diff)). 120.89/55.34 thf(13537,plain,((! [A:$i,B:$i,C:$i]: ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ A) @ B)) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ minus_minus_nat @ (hAPP_nat_nat @ suc @ A)) @ B)) @ (hAPP_nat_nat @ suc @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2477])). 120.89/55.34 thf(2770,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) <=> (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1452_power__strict__increasing__iff)). 120.89/55.34 thf(14583,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B)))) & ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ A)) @ (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ power_power_nat @ C) @ B))) => (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ A) @ B)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ ord_less_nat @ one_one_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2770])). 120.89/55.34 thf(1329,axiom,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) @ (hAPP_int_real @ number267125858f_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_number__of__Bit1)). 120.89/55.34 thf(9519,plain,((! [A:$i]: ((hAPP_int_real @ number267125858f_real @ (hAPP_int_int @ bit1 @ A)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ one_one_real) @ (hAPP_int_real @ number267125858f_real @ A))) @ (hAPP_int_real @ number267125858f_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329])). 120.89/55.34 thf(2358,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D != zero_zero_nat) => ((C != zero_zero_nat) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ B)) => ((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ D)) <=> ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A))) <= (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2639_dvd__div__div__eq__mult)). 120.89/55.34 thf(13107,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (D = zero_zero_nat)) => ((~ (C = zero_zero_nat)) => ((hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ D) @ B)) => (((((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ D)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A))) & (((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ B) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ times_times_nat @ D) @ A)) => ((hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ A) @ C) = (hAPP_nat_nat @ (hAPP_nat_fun_nat_nat @ div_div_nat @ B) @ D)))) | ~ (hBOOL @ (hAPP_nat_bool @ (hAPP_n1699378549t_bool @ dvd_dvd_nat @ C) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358])). 120.89/55.34 thf(4366,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) <=> (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1559_zcong__def)). 120.89/55.34 thf(20263,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C))) & ((hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ (zcong @ A) @ B) @ C)) => (hBOOL @ (hAPP_int_bool @ (hAPP_i1948725293t_bool @ dvd_dvd_int @ C) @ (hAPP_int_int @ (hAPP_int_fun_int_int @ minus_minus_int @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4366])). 120.89/55.34 thf(3586,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B))) <= (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1872_add__strict__increasing)). 120.89/55.34 thf(17365,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ A) @ (hAPP_real_real @ (hAPP_r1250527377l_real @ plus_plus_real @ C) @ B))) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_eq_real @ A) @ B)) | ~ (hBOOL @ (hAPP_real_bool @ (hAPP_r1134773055l_bool @ ord_less_real @ zero_zero_real) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3586])). 120.89/55.34 thf(338,axiom,((! [A:$i,B:$i]: ((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4414_powr__minus)). 120.89/55.34 thf(6067,plain,((! [A:$i,B:$i]: ((hAPP_real_real @ inverse_inverse_real @ (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ B)) = (hAPP_real_real @ (hAPP_r1250527377l_real @ powr @ A) @ (hAPP_real_real @ uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 120.89/55.34 thf(22742,plain,($false),inference(cvc4,[status(thm)],[16466,10822,7375,19204,20194,11866,8536,15767,21624,14852,19370,10007,21729,15806,20256,19597,19904,7373,17959,11472,16662,6836,14782,7427,5116,10410,6405,19364,5561,18360,14343,17043,7272,20273,21175,20432,9273,13859,10259,22210,17358,10785,12564,17072,7854,21710,7973,7569,6231,15009,15418,11372,8663,8097,9648,11895,17684,18504,6544,19481,16243,22108,12526,16576,13643,21439,9516,11504,11922,16604,14404,9754,19971,21348,15472,19640,5320,6283,17226,16427,17903,7100,20464,10134,12753,16911,21450,14220,13933,16591,9685,19990,10743,12440,13410,15055,12148,17175,9076,20162,12344,19148,19543,10081,6819,15995,12383,20516,17214,18129,20332,11898,22012,9864,19755,14709,19494,10363,9411,6690,6042,11318,11620,18893,9965,14833,10976,21326,6566,6954,14932,20651,9305,19611,9222,10790,14944,16092,7903,12689,11659,10272,22257,11790,16950,14181,12738,18328,10507,11008,18691,12500,11175,10844,16898,13869,6142,19681,9342,12458,15361,11224,8855,8417,11352,12634,7888,12674,9621,12949,21353,10299,9573,10149,18646,15115,6177,12602,18020,15408,16708,17310,10198,14468,10446,7358,16086,10234,13520,22397,21114,10832,14235,21662,11043,11880,13120,9251,14750,6106,5696,9924,8797,13177,14117,20258,13234,8082,17437,17221,10542,6883,6744,5069,5644,17278,16765,18193,16619,10673,16830,21815,18101,10679,13255,21418,9383,15770,17014,10277,8402,20268,10780,10567,16566,18365,16698,18549,7322,8811,12089,9704,22384,14570,17143,19438,21984,8118,10711,13525,13035,5878,13672,18416,10705,16713,15293,10262,7726,16940,19391,13437,5793,20484,5173,8315,21961,17424,7253,10837,20534,16972,7198,17104,19533,6830,10017,9059,17495,16730,14377,18114,15981,18635,17046,11485,16353,7182,18052,17524,19550,13918,5237,17011,21697,8928,10125,9400,15780,10039,13811,15926,18837,8045,7341,11724,16581,16449,11881,9364,13020,9135,16229,18942,13212,6480,6732,14409,9268,14431,19501,16402,6214,14765,13202,14156,21538,20830,16027,20345,5501,12971,17665,8320,20198,20711,6522,5425,17253,14441,22030,20537,16645,20694,18184,6971,17907,17113,6278,5814,14617,19230,10775,9184,16481,6391,8182,9644,16424,19174,19477,6505,16982,14382,8551,19423,11848,16336,13219,7961,18316,9127,6939,19873,18781,21798,21688,13736,8150,16513,7695,10103,6675,13722,22175,15651,22448,10395,22434,14905,10358,13596,8622,5288,11058,12479,7873,11014,15632,7824,6127,13095,22347,11207,8747,18897,9428,10864,15299,8519,13270,11917,17211,18161,11288,16071,5316,18001,7484,16817,6416,22076,21766,7949,21627,12921,9855,19468,12865,22225,6851,21454,15175,21383,9218,16587,12725,13115,15034,17556,15885,21016,21999,5713,5163,17609,5674,14959,11239,14818,20862,12421,21403,5161,15331,19919,9509,6996,7068,11994,13640,8838,16762,15611,5636,12585,16236,16520,11055,12077,16965,19863,9278,9433,14301,13901,21343,7980,21096,16915,10737,11549,6877,14591,19932,11816,13056,5192,21781,10341,13488,20011,9481,15735,9672,21482,22101,14292,17924,21224,20031,12026,17766,17158,11449,7168,16668,20034,21467,6236,16994,10336,11645,13452,10427,9476,14089,14168,5740,7944,9064,12929,16733,17549,6909,15863,16039,9292,13965,8086,15335,6268,11834,5486,20662,19575,12141,21948,10022,13098,10599,7079,17710,12225,16720,15032,8539,22197,18834,7499,6381,17081,8816,18321,10545,5745,16877,11146,20926,19410,19732,9096,6583,15730,7729,18925,21253,18728,13552,19518,11588,20107,5056,8866,13378,14396,14553,15870,11024,16319,14488,18955,18496,16268,20941,9708,16488,22429,12356,20845,21560,12009,16530,12388,17739,8165,12770,9396,16211,20643,20409,21203,19387,14023,8699,19318,14644,8779,21503,19209,14188,12785,5269,21239,21752,14871,11831,13003,6291,13923,14245,9394,13346,8224,18015,12062,15119,12661,21274,20078,11250,10501,15605,18717,7311,17197,17534,21856,10248,20209,15178,15104,5024,10584,5352,14213,5342,21079,20679,7390,17132,19968,14630,9960,18437,21143,18539,20665,13191,18754,11426,5765,10619,17036,9056,10903,13313,18920,13664,7620,16552,5585,15922,21916,17381,14474,8500,12475,20594,11976,19443,22353,7701,19473,19145,6039,13803,6538,4956,15990,14825,21307,11798,10089,8996,5883,21101,9597,12832,10997,8089,15231,6547,10999,6274,18750,17824,14260,13821,19693,9561,17857,10053,20583,9988,11913,5759,13030,11652,14351,22207,7822,7683,20281,20511,21825,7294,16022,16609,8806,17983,14722,8647,6723,17598,13619,14173,7349,17234,6749,13651,20881,16890,13151,21861,10719,12407,11458,16176,8214,17481,6968,17270,8522,11111,16985,12394,6315,12901,13776,22229,5130,7867,16789,11812,9909,8208,18385,14923,18030,15680,22287,17149,12589,22321,10174,12606,6662,18187,5989,12161,6332,6519,21530,13067,15441,13275,11628,5108,6643,20508,12713,21268,7665,22304,5461,18688,14830,11040,12745,9877,8770,8849,17154,7835,16809,7997,9629,7156,22268,21220,8121,20445,16523,6240,7754,21367,17694,15819,17852,6253,11232,16716,12682,22144,17894,5355,20719,9800,11981,5256,11463,5214,18617,5605,17097,18190,9612,20098,8389,8902,15028,19658,20276,10850,11911,14205,11285,20364,21820,10516,11609,11512,21447,17049,8310,7803,9155,13942,11564,18624,18094,16495,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120.89/55.34 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 120.89/55.34 % [INFO] Killing All external provers ... 120.89/55.37 EOF