TSTP Solution File: NUM924_4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924_4 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:48:56 EDT 2023
% Result : Theorem 8.35s 8.58s
% Output : Proof 8.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.36/1.38 % Problem : NUM924_4 : TPTP v8.1.2. Released v5.3.0.
% 1.36/1.39 % Command : do_cvc5 %s %d
% 1.42/1.60 % Computer : n025.cluster.edu
% 1.42/1.60 % Model : x86_64 x86_64
% 1.42/1.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.42/1.60 % Memory : 8042.1875MB
% 1.42/1.60 % OS : Linux 3.10.0-693.el7.x86_64
% 1.42/1.60 % CPULimit : 300
% 1.42/1.60 % WCLimit : 300
% 1.42/1.60 % DateTime : Fri Aug 25 17:18:08 EDT 2023
% 1.42/1.60 % CPUTime :
% 2.60/3.01 %----Proving TF0_NAR, FOF, or CNF
% 8.35/8.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.1PkPvtaLBl/cvc5---1.0.5_29207.p...
% 8.35/8.58 ------- get file name : TPTP file name is NUM924_4
% 8.35/8.58 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29207.smt2...
% 8.35/8.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.35/8.58 % SZS status Theorem for NUM924_4
% 8.35/8.58 % SZS output start Proof for NUM924_4
% 8.35/8.58 (
% 8.35/8.58 (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 _let_1))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.s) _let_3))) (let ((_let_5 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_4) tptp.one_one_int))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_5) tptp.zero_zero_int)))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.hAPP_int_int tptp.number_number_of_int _let_2))) (let ((_let_9 (tptp.hAPP_int_int tptp.bit1 _let_1))) (let ((_let_10 (tptp.hAPP_int_int tptp.number_number_of_int _let_9))) (let ((_let_11 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat))) (let ((_let_12 (tptp.hAPP_int_real tptp.number267125858f_real _let_2))) (let ((_let_13 (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi))) (let ((_let_14 (tptp.hAPP_real_real _let_13 _let_12))) (let ((_let_15 (tptp.hAPP_f1352333353l_real (tptp.hAPP_f318350629l_real tptp.cOMBB_1946221070al_int tptp.inverse_divide_real) tptp.real_int))) (let ((_let_16 (tptp.hAPP_f1925507189l_bool tptp.cOMBB_1121934354l_real tptp.fEx_int))) (let ((_let_17 (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat))) (let ((_let_18 (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_8))) (let ((_let_19 (tptp.hAPP_f735247205t_bool tptp.cOMBC_983868720t_bool (tptp.hAPP_f1251097615t_bool (tptp.hAPP_f1475822739t_bool tptp.cOMBB_2027861294ol_int tptp.cOMBB_int_bool_int) tptp.fequal_int)))) (let ((_let_20 (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int tptp.fEx_int))) (let ((_let_21 (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj))) (let ((_let_22 (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.plus_plus_int))) (let ((_let_23 (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj))) (let ((_let_24 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_25 (tptp.the_real (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_23 _let_24)) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_23 (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool tptp.ord_less_eq_real) _let_12))) (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) tptp.cos)) tptp.zero_zero_real)))))) (let ((_let_26 (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_12))) (let ((_let_27 (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real))) (let ((_let_28 (tptp.hAPP_real_real _let_27 _let_12))) (let ((_let_29 (tptp.hAPP_f1855025978nt_int (tptp.hAPP_f1038672605nt_int tptp.cOMBB_1506897658nt_int tptp.times_times_int) tptp.product_fst_int_int))) (let ((_let_30 (tptp.hAPP_f214467655t_bool tptp.cOMBB_182850971nt_int tptp.fequal_int))) (let ((_let_31 (tptp.hAPP_f365317245l_bool (tptp.hAPP_f1961001761l_bool tptp.cOMBB_1550063917nt_int tptp.fconj) (tptp.hAPP_f237669397t_bool (tptp.hAPP_f513299955t_bool tptp.cOMBB_1344650379nt_int tptp.fNot) (tptp.hAPP_i119638232t_bool (tptp.hAPP_f2018027565t_bool tptp.cOMBC_33652895t_bool (tptp.hAPP_f291087797t_bool _let_30 tptp.product_snd_int_int)) tptp.zero_zero_int))))) (let ((_let_32 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_33 (tptp.hAPP_nat_fun_int_int (tptp.hAPP_f2105620693nt_int tptp.cOMBC_int_nat_int tptp.power_power_int) _let_3))) (let ((_let_34 (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (let ((_let_35 (tptp.hAPP_int_int tptp.bit0 _let_2))) (let ((_let_36 (tptp.hAPP_int_real tptp.number267125858f_real _let_35))) (let ((_let_37 (tptp.hAPP_real_real _let_13 _let_36))) (let ((_let_38 (tptp.ratreal tptp.one_one_rat))) (let ((_let_39 (tptp.ratreal tptp.zero_zero_rat))) (let ((_let_40 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract tptp.one_one_int) tptp.one_one_int))) (let ((_let_41 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_42 (= tptp.real_int tptp.ring_1_of_int_real))) (let ((_let_43 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_44 (tptp.hAPP_complex_complex tptp.uminus473333897omplex tptp.ii))) (let ((_let_45 (tptp.hAPP_int_complex tptp.number528085621omplex _let_2))) (let ((_let_46 (tptp.hAPP_complex_complex tptp.uminus473333897omplex tptp.one_one_complex))) (let ((_let_47 (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_48 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.ii) tptp.ii))) (let ((_let_49 (tptp.hAPP_int_complex tptp.number528085621omplex tptp.min))) (let ((_let_50 (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real))) (let ((_let_51 (tptp.hAPP_int_real tptp.number267125858f_real _let_9))) (let ((_let_52 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_51) _let_12)) tptp.pi))) (let ((_let_53 (tptp.hAPP_real_real tptp.sqrt _let_12))) (let ((_let_54 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_53) _let_12))) (let ((_let_55 (tptp.hAPP_real_real tptp.sqrt _let_51))) (let ((_let_56 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_55) _let_12))) (let ((_let_57 (tptp.hAPP_real_real _let_13 _let_51))) (let ((_let_58 (tptp.hAPP_real_real _let_13 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 _let_9))))) (let ((_let_59 (tptp.hAPP_real_real _let_26 tptp.pi))) (let ((_let_60 (= tptp.real_nat tptp.semiri132038758t_real))) (let ((_let_61 (tptp.hAPP_real_real tptp.cos _let_12))) (let ((_let_62 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_63 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.pi))) (let ((_let_64 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_65 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (let ((_let_66 (tptp.hAPP_int_int tptp.number_number_of_int tptp.pls))) (let ((_let_67 (tptp.hAPP_nat_nat tptp.suc _let_43))) (let ((_let_68 (tptp.hAPP_int_nat tptp.nat_1 _let_8))) (let ((_let_69 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (let ((_let_70 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_9))) (let ((_let_71 (tptp.hAPP_int_nat tptp.nat_1 tptp.one_one_int))) (let ((_let_72 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_73 (= _let_72 tptp.one_one_int))) (let ((_let_74 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_75 (= _let_74 tptp.zero_zero_int))) (let ((_let_76 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_77 (tptp.hAPP_int_nat tptp.nat_1 tptp.zero_zero_int))) (let ((_let_78 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_35)) tptp.m)) tptp.one_one_int))) (let ((_let_79 (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_78))) (let ((_let_80 (tptp.hAPP_int_int _let_79 tptp.t))) (let ((_let_81 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_82 (= (tptp.hAPP_int_int (tptp.legendre _let_65) _let_78) tptp.one_one_int))) (let ((_let_83 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes _let_78) _let_65)))) (let ((_let_84 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_4) _let_65))) (let ((_let_85 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_78))) (let ((_let_86 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_87 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_88 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (let ((_let_89 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (let ((_let_90 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_91 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))) (let ((_let_92 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_93 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_94 (tptp.hBOOL (tptp.hAPP_int_bool _let_32 tptp.one_one_int)))) (let ((_let_95 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_96 (tptp.hBOOL (tptp.hAPP_int_bool _let_76 tptp.one_one_int)))) (let ((_let_97 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_98 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (let ((_let_99 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (let ((_let_100 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (let ((_let_101 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (let ((_let_102 (tptp.zcong _let_4))) (let ((_let_103 (forall ((A_221 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_221) tptp.zero_zero_int) tptp.zero_zero_int)))) (let ((_let_104 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.s1) _let_3))) (let ((_let_105 (= _let_86 (tptp.hAPP_int_rat tptp.number_number_of_rat _let_2)))) (let ((_let_106 (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) _let_45))) (let ((_let_107 (= _let_90 _let_12))) (let ((_let_108 (= _let_93 _let_8))) (let ((_let_109 (= _let_91 _let_3))) (let ((_let_110 (tptp.hAPP_int_rat tptp.number_number_of_rat _let_1))) (let ((_let_111 (tptp.hAPP_int_complex tptp.number528085621omplex _let_1))) (let ((_let_112 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (let ((_let_113 (tptp.hAPP_int_int tptp.number_number_of_int _let_1))) (let ((_let_114 (= tptp.one_one_int _let_113))) (let ((_let_115 (= _let_110 tptp.one_one_rat))) (let ((_let_116 (= _let_111 tptp.one_one_complex))) (let ((_let_117 (= _let_112 tptp.one_one_real))) (let ((_let_118 (= _let_113 tptp.one_one_int))) (let ((_let_119 (= _let_69 tptp.one_one_nat))) (let ((_let_120 (tptp.hAPP_int_rat tptp.number_number_of_rat tptp.pls))) (let ((_let_121 (tptp.hAPP_int_complex tptp.number528085621omplex tptp.pls))) (let ((_let_122 (tptp.hAPP_int_real tptp.number267125858f_real tptp.pls))) (let ((_let_123 (= tptp.zero_zero_int _let_66))) (let ((_let_124 (= _let_120 tptp.zero_zero_rat))) (let ((_let_125 (= _let_121 tptp.zero_zero_complex))) (let ((_let_126 (= _let_122 tptp.zero_zero_real))) (let ((_let_127 (= _let_66 tptp.zero_zero_int))) (let ((_let_128 (tptp.hAPP_int_nat tptp.number_number_of_nat tptp.pls))) (let ((_let_129 (= _let_128 tptp.zero_zero_nat))) (let ((_let_130 (forall ((T tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.s) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) tptp.one_one_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T))))))) (let ((_let_131 (not _let_130))) (let ((_let_132 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.t))) (let ((_let_133 (= _let_5 _let_80))) (let ((_let_134 (tptp.hAPP_int_int _let_79 tptp.zero_zero_int))) (let ((_let_135 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_80) _let_134)))) (let ((_let_136 (= _let_80 _let_5))) (let ((_let_137 (= _let_5 (tptp.hAPP_int_int _let_79 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_138 (= tptp.zero_zero_int _let_134))) (let ((_let_139 (ASSUME :args (_let_135)))) (let ((_let_140 (SYMM (ASSUME :args (_let_133))))) (let ((_let_141 (ASSUME :args (_let_7)))) (let ((_let_142 (_let_131))) (let ((_let_143 (ASSUME :args _let_142))) (let ((_let_144 (or))) (let ((_let_145 (_let_137))) (let ((_let_146 (not _let_137))) (let ((_let_147 (forall ((A_221 tptp.int)) (= tptp.zero_zero_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_221) tptp.zero_zero_int))))) (let ((_let_148 (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO :args (_let_103 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (not _let_138))) (let ((_let_150 (not _let_136))) (let ((_let_151 (not _let_135))) (let ((_let_152 (APPLY_UF tptp.hBOOL))) (let ((_let_153 (APPLY_UF tptp.hAPP_int_bool))) (let ((_let_154 (ASSUME :args (_let_138)))) (let ((_let_155 (APPLY_UF tptp.hAPP_i1948725293t_bool))) (let ((_let_156 (SYMM _let_140))) (let ((_let_157 (REFL :args (tptp.ord_less_int)))) (let ((_let_158 (ASSUME :args _let_145))) (let ((_let_159 (CONG _let_157 (TRANS (SYMM _let_158) _let_156) :args _let_155))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_141 _let_140 _let_158 _let_154 _let_139) :args (_let_135 _let_7 _let_136 _let_137 _let_138)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_139)) (CONG (CONG (SYMM _let_159) (REFL :args (_let_134)) :args _let_153) :args _let_152) (CONG (CONG (TRANS _let_159 (CONG _let_157 (SYMM _let_156) :args _let_155)) (SYMM _let_154) :args _let_153) :args _let_152) (FALSE_INTRO _let_141))) :args (_let_7 _let_136 _let_137 _let_138 _let_135)) :args ((not (and _let_135 _let_7 _let_136 _let_137 _let_138)) SB_LITERAL))) (CONG (REFL :args (_let_151)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args (_let_150)) (REFL :args (_let_146)) (REFL :args (_let_149)) :args _let_144)) :args ((or _let_6 _let_151 _let_150 _let_146 _let_149))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_148 :args (_let_78 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_int_fun_int_int tptp.times_times_int A_221)))) :args (_let_147))) _let_148 :args (_let_138 false _let_147)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_143) :args _let_142) (REWRITE :args ((=> _let_131 (not _let_146)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_131) _let_130))) (REFL :args _let_145) :args _let_144)) _let_143 :args (_let_137 true _let_130)) _let_141 _let_140 _let_139 :args (false false _let_138 false _let_137 true _let_6 false _let_136 false _let_135)) :args ((tptp.hBOOL (tptp.hAPP_int_bool _let_132 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_132 tptp.one_one_int)) _let_135 _let_133 (=> (= tptp.t tptp.zero_zero_int) (= _let_5 tptp.zero_zero_int)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_95 tptp.t))) (tptp.hBOOL (tptp.hAPP_int_bool _let_32 _let_78)) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_2) _let_1)))) (or (not (= X_1 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int)))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_2) _let_1)))) (or (not (= X_1 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real)))))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_1) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_2) _let_1)))) (or (not (= X_1 tptp.zero_zero_rat)) (not (= Y_2 tptp.zero_zero_rat)))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_2) _let_1)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_2) _let_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_1) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_2) _let_1)) tptp.zero_zero_rat) (and (= X_1 tptp.zero_zero_rat) (= Y_2 tptp.zero_zero_rat))))) (forall ((A_240 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_240) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.zero_zero_int)))) (forall ((A_240 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_240) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.zero_zero_real)))) (forall ((A_240 tptp.rat)) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_240) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (not (= A tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (not (= A tptp.zero_zero_rat)))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.one_one_int) _let_3) tptp.one_one_int) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) _let_3) tptp.one_one_nat) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.one_one_real) _let_3) tptp.one_one_real) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.one_on1645066479umeral) _let_3) tptp.one_on1645066479umeral) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.one_one_complex) _let_3) tptp.one_one_complex) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.one_on1684967323de_int) _let_3) tptp.one_on1684967323de_int) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.one_one_rat) _let_3) tptp.one_one_rat) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) _let_3) tptp.zero_zero_int) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) _let_3) tptp.zero_zero_nat) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) _let_3) tptp.zero_zero_real) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.zero_z126310315umeral) _let_3) tptp.zero_z126310315umeral) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.zero_zero_complex) _let_3) tptp.zero_zero_complex) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.zero_z891286103de_int) _let_3) tptp.zero_z891286103de_int) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.zero_zero_rat) _let_3) tptp.zero_zero_rat) (forall ((A tptp.int)) (= (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.complex)) (= (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.rat)) (= (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((W_17 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int W_17)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) W_17)))) (forall ((W_17 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real W_17)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) W_17)))) (forall ((W_17 tptp.int)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) (tptp.hAPP_int_complex tptp.number528085621omplex W_17)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) W_17)))) (forall ((W_17 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat W_17)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) W_17)))) (forall ((V_23 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_23)) tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_23) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((V_23 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_23)) tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_23) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((V_23 tptp.int)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_23)) tptp.one_one_complex) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_23) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((V_23 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_23)) tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_23) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_132 _let_78)) _let_131 (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_78)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu1425020248sum2sq _let_80)) (forall ((W tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) W))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.number_number_of_int K_2) K_2)) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int W) Z_1))) (forall ((Z_1 tptp.int) (W tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)))) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_int tptp.number_number_of_int W)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_2) W)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int K_1)) (tptp.hAPP_int_int tptp.number_number_of_int L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_2)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_2)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_2)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) Z3))))) (forall ((K_2 tptp.int) (I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_2) K_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2)))))) (forall ((Z_1 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)) (= Z_1 W)))) (forall ((X tptp.int) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 Y)) (tptp.hAPP_nat_int _let_1 Z_1))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K1)) (tptp.hAPP_int_int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K_1)) (tptp.hAPP_int_int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_98 tptp.pls)) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K1)) (tptp.hAPP_int_int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K_1)) (tptp.hAPP_int_int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)))) (forall ((Z_2 tptp.int) (W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) W_1)) (not (= Z_2 W_1))))) (forall ((K_2 tptp.int) (I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) J_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J_2)))))) (forall ((V tptp.int)) (= (= (tptp.hAPP_int_nat tptp.number_number_of_nat V) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V) tptp.pls)))) (forall ((V tptp.int)) (= (= tptp.zero_zero_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V) tptp.pls)))) (forall ((V_22 tptp.int) (V_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_22)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_21)) (tptp.hAPP_int_int tptp.number_number_of_int V_22)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_21) V_22))))))) (forall ((V_22 tptp.int) (V_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_22)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_21)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_22)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_21) V_22))))))) (forall ((V_22 tptp.int) (V_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_22)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_21)) (tptp.hAPP_int_real tptp.number267125858f_real V_22)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_21) V_22))))))) (forall ((V_22 tptp.int) (V_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_22)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_21)) (tptp.hAPP_int_complex tptp.number528085621omplex V_22)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_21) V_22))))))) (forall ((V_22 tptp.int) (V_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_22)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_21)) (tptp.hAPP_int_rat tptp.number_number_of_rat V_22)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_21) V_22))))))) (forall ((V_20 tptp.int) (W_16 tptp.int) (Z_15 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_20)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int W_16)) Z_15)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_20) W_16))) Z_15))) (forall ((V_20 tptp.int) (W_16 tptp.int) (Z_15 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_20)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real W_16)) Z_15)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_20) W_16))) Z_15))) (forall ((V_20 tptp.int) (W_16 tptp.int) (Z_15 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_20)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex W_16)) Z_15)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_20) W_16))) Z_15))) (forall ((V_20 tptp.int) (W_16 tptp.int) (Z_15 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_20)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat W_16)) Z_15)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_20) W_16))) Z_15))) (forall ((V_19 tptp.int) (W_15 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_19)) (tptp.hAPP_int_int tptp.number_number_of_int W_15)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_19) W_15)))) (forall ((V_19 tptp.int) (W_15 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_19)) (tptp.hAPP_int_real tptp.number267125858f_real W_15)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_19) W_15)))) (forall ((V_19 tptp.int) (W_15 tptp.int)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_19)) (tptp.hAPP_int_complex tptp.number528085621omplex W_15)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_19) W_15)))) (forall ((V_19 tptp.int) (W_15 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_19)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_15)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_19) W_15)))) (forall ((V_18 tptp.int) (W_14 tptp.int)) (= (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_18) W_14)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_18)) (tptp.hAPP_int_int tptp.number_number_of_int W_14)))) (forall ((V_18 tptp.int) (W_14 tptp.int)) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_18) W_14)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_18)) (tptp.hAPP_int_real tptp.number267125858f_real W_14)))) (forall ((V_18 tptp.int) (W_14 tptp.int)) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_18) W_14)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_18)) (tptp.hAPP_int_complex tptp.number528085621omplex W_14)))) (forall ((V_18 tptp.int) (W_14 tptp.int)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_18) W_14)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_18)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_14)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) X_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_2) Y_2))) tptp.zero_zero_int)) (and (= X_1 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) X_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Y_2))) tptp.zero_zero_real)) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_1) X_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_2) Y_2))) tptp.zero_zero_rat)) (and (= X_1 tptp.zero_zero_rat) (= Y_2 tptp.zero_zero_rat)))) (forall ((X_47 tptp.int) (Y_35 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_47) X_47)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_35) Y_35))))) (forall ((X_47 tptp.real) (Y_35 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_47) X_47)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_35) Y_35))))) (forall ((X_47 tptp.rat) (Y_35 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_47) X_47)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_35) Y_35))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) tptp.pls)))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) tptp.pls)))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) tptp.pls)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) Y_2)))) (forall ((V tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat V))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V)))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral V))) (let ((_let_2 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral W_1))) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral _let_2) _let_1))))))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) _let_1))))))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_2) _let_1))))))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real V))) (let ((_let_2 (tptp.hAPP_int_real tptp.number267125858f_real W_1))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) _let_1))))))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int V))) (let ((_let_2 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int W_1))) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int _let_2) _let_1))))))) (forall ((V tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat V))) (let ((_let_2 (tptp.hAPP_int_rat tptp.number_number_of_rat W_1))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat _let_2) _let_1))))))) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit1 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K1)) (tptp.hAPP_int_int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K_1)) (tptp.hAPP_int_int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K_1)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) tptp.pls)))) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit0 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (forall ((Z_4 tptp.int) (Z_1 tptp.int) (W_13 tptp.int) (W tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_13) W)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_4) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_13) Z_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) Z_1)))))) _let_129 (= tptp.zero_zero_nat _let_128) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) _let_109 (forall ((W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.pls) W) tptp.pls)) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.bit0 K_2)) L_2) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) L_2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int K_1)) (tptp.hAPP_int_int tptp.number_number_of_int L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)))) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) tptp.one_one_int) Z_1)) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) Z_1) Z_1)) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_int tptp.number_number_of_int W)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_2) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K_1)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.pls)))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) (tptp.hAPP_int_int tptp.bit1 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls) K_1)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K1)) (tptp.hAPP_int_int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K_1)) (tptp.hAPP_int_int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K1)) (tptp.hAPP_int_int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K1) K2)))) (forall ((X_1 tptp.int) (A_1 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool A_1 X_1)))) (forall ((X_1 tptp.produc1322466333at_nat) (A_1 tptp.fun_Pr587612383t_bool)) (= (tptp.hBOOL (tptp.hAPP_f115998247l_bool (tptp.hAPP_P1876494581l_bool tptp.member180897546at_nat X_1) A_1)) (tptp.hBOOL (tptp.hAPP_P1463840893t_bool A_1 X_1)))) (forall ((X_1 tptp.fun_int_bool) (A_1 tptp.fun_fu819804446l_bool)) (= (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool A_1 X_1)))) (forall ((X_1 tptp.nat) (A_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool A_1 X_1)))) (forall ((X_1 tptp.real) (A_1 tptp.fun_real_bool)) (= (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) A_1)) (tptp.hBOOL (tptp.hAPP_real_bool A_1 X_1)))) (forall ((X_1 tptp.produc1137372701nt_int) (A_1 tptp.fun_Pr1333588703t_bool)) (= (tptp.hBOOL (tptp.hAPP_f526364711l_bool (tptp.hAPP_P1062890741l_bool tptp.member2143287562nt_int X_1) A_1)) (tptp.hBOOL (tptp.hAPP_P62333565t_bool A_1 X_1)))) (forall ((X_1 tptp.produc1450482951t_bool) (A_1 tptp.fun_Pr4007113l_bool)) (= (tptp.hBOOL (tptp.hAPP_f1469637905l_bool (tptp.hAPP_P1681069257l_bool tptp.member308914164t_bool X_1) A_1)) (tptp.hBOOL (tptp.hAPP_P880235623l_bool A_1 X_1)))) (forall ((P_1 tptp.fun_int_bool)) (= (tptp.collect_int P_1) P_1)) (forall ((P_1 tptp.fun_nat_bool)) (= (tptp.collect_nat P_1) P_1)) (forall ((P_1 tptp.fun_Pr1333588703t_bool)) (= (tptp.collec50511176nt_int P_1) P_1)) (forall ((P_1 tptp.fun_Pr974702441t_bool)) (= (tptp.collec1347809874nt_int P_1) P_1)) (forall ((P_1 tptp.fun_real_bool)) (= (tptp.collect_real P_1) P_1)) (forall ((P_1 tptp.fun_Pr1927655017t_bool)) (= (tptp.collec1979865426at_nat P_1) P_1)) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K_1)) (tptp.hAPP_int_int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)))) (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V) V_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_1))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_1))) _let_1)))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_2)))) _let_119 (= tptp.one_one_nat _let_69) (forall ((W tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z_1)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) tptp.one_one_int)) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_2) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_2)))) (forall ((V_17 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_17)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_16)) (tptp.hAPP_int_int tptp.number_number_of_int V_17)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_16) V_17))))))) (forall ((V_17 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_17)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_16)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_17)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_16) V_17))))))) (forall ((V_17 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_17)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_16)) (tptp.hAPP_int_real tptp.number267125858f_real V_17)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_16) V_17))))))) (forall ((V_17 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_17)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_16)) (tptp.hAPP_int_complex tptp.number528085621omplex V_17)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_16) V_17))))))) (forall ((V_17 tptp.int) (V_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_17)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_16)) (tptp.hAPP_int_rat tptp.number_number_of_rat V_17)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_16) V_17))))))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V_3))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat V_2))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_3) tptp.pls)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_2) V_3))))))))))))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z_1))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_int tptp.number_number_of_int X_1) (tptp.hAPP_int_int tptp.number_number_of_int Y_2)) (= X_1 Y_2))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_real tptp.number267125858f_real X_1) (tptp.hAPP_int_real tptp.number267125858f_real Y_2)) (= X_1 Y_2))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_complex tptp.number528085621omplex X_1) (tptp.hAPP_int_complex tptp.number528085621omplex Y_2)) (= X_1 Y_2))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_rat tptp.number_number_of_rat X_1) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2)) (= X_1 Y_2))) (forall ((W_1 tptp.int) (X_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.complex)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((W_1 tptp.int) (X_1 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat W_1))) (= (= _let_1 X_1) (= X_1 _let_1)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (= (tptp.hAPP_int_int tptp.bit1 K_1) (tptp.hAPP_int_int tptp.bit1 L)) (= K_1 L))) (forall ((K_1 tptp.int) (L tptp.int)) (= (= (tptp.hAPP_int_int tptp.bit0 K_1) (tptp.hAPP_int_int tptp.bit0 L)) (= K_1 L))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) X_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_2) Y_2)) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) X_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Y_2)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_1) X_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_2) Y_2)) tptp.zero_zero_rat) (and (= X_1 tptp.zero_zero_rat) (= Y_2 tptp.zero_zero_rat)))) (forall ((A_239 tptp.code_code_numeral) (B_167 tptp.code_code_numeral) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral V_15))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_239) B_167)) _let_1) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_239) _let_1)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_167) _let_1))))) (forall ((A_239 tptp.int) (B_167 tptp.int) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_15))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_239) B_167)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_239) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_167) _let_1))))) (forall ((A_239 tptp.nat) (B_167 tptp.nat) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V_15))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_239) B_167)) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_239) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_167) _let_1))))) (forall ((A_239 tptp.real) (B_167 tptp.real) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real V_15))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_239) B_167)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_239) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_167) _let_1))))) (forall ((A_239 tptp.complex) (B_167 tptp.complex) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex V_15))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_239) B_167)) _let_1) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_239) _let_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_167) _let_1))))) (forall ((A_239 tptp.quickcheck_code_int) (B_167 tptp.quickcheck_code_int) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int V_15))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_239) B_167)) _let_1) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_239) _let_1)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_167) _let_1))))) (forall ((A_239 tptp.rat) (B_167 tptp.rat) (V_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat V_15))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_239) B_167)) _let_1) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_239) _let_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_167) _let_1))))) (forall ((V_14 tptp.int) (B_166 tptp.code_code_numeral) (C_97 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_i769753017umeral tptp.number1443263063umeral V_14)))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_166) C_97)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 B_166)) (tptp.hAPP_C498520661umeral _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.int) (C_97 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_14)))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_166) C_97)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_166)) (tptp.hAPP_int_int _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.nat) (C_97 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_14)))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_166) C_97)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_166)) (tptp.hAPP_nat_nat _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.real) (C_97 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_14)))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_166) C_97)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_166)) (tptp.hAPP_real_real _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.complex) (C_97 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_14)))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_166) C_97)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_166)) (tptp.hAPP_complex_complex _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.quickcheck_code_int) (C_97 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int V_14)))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_166) C_97)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 B_166)) (tptp.hAPP_Q1762011733de_int _let_1 C_97))))) (forall ((V_14 tptp.int) (B_166 tptp.rat) (C_97 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_14)))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_166) C_97)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 B_166)) (tptp.hAPP_rat_rat _let_1 C_97))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z_1)))))) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) Z_1))) _let_123 (forall ((K_2 tptp.int) (I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J_2))))))) (forall ((X_46 tptp.int) (Y_34 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_46) _let_2) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_46 tptp.nat) (Y_34 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_46) _let_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_46 tptp.real) (Y_34 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_46) _let_2) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_46 tptp.code_code_numeral) (Y_34 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_46) _let_2) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_46 tptp.quickcheck_code_int) (Y_34 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_46) _let_2) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_46 tptp.rat) (Y_34 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_46) _let_2) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_34) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 X_46)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Y_34)) (= X_46 Y_34))))))) (forall ((X_45 tptp.int) (Y_33 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_45) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_33)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_45) Y_33)))))) (forall ((X_45 tptp.nat) (Y_33 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_45) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_33)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_45) Y_33)))))) (forall ((X_45 tptp.real) (Y_33 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_45) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_33)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_45) Y_33)))))) (forall ((X_45 tptp.code_code_numeral) (Y_33 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_45) _let_1)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) Y_33)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral X_45) Y_33)))))) (forall ((X_45 tptp.quickcheck_code_int) (Y_33 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_45) _let_1)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) Y_33)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int X_45) Y_33)))))) (forall ((X_45 tptp.rat) (Y_33 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_45) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_33) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y_33)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat X_45) Y_33)))))) (forall ((A_238 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_238) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (forall ((A_238 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_238) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (forall ((A_238 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_238) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (forall ((X_44 tptp.int) (Y_32 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_44) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_32)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_44) Y_32)))))) (forall ((X_44 tptp.nat) (Y_32 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_44) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_32)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_44) Y_32)))))) (forall ((X_44 tptp.real) (Y_32 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_44) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_32)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_44) Y_32)))))) (forall ((X_44 tptp.code_code_numeral) (Y_32 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_44) _let_1)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) Y_32)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral X_44) Y_32)))))) (forall ((X_44 tptp.quickcheck_code_int) (Y_32 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_44) _let_1)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) Y_32)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int X_44) Y_32)))))) (forall ((X_44 tptp.rat) (Y_32 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_44) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_32) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y_32)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_44) Y_32)))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_2) _let_1))) tptp.zero_zero_int)) (and (= X_1 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_2) _let_1))) tptp.zero_zero_real)) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_1) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_2) _let_1))) tptp.zero_zero_rat)) (and (= X_1 tptp.zero_zero_rat) (= Y_2 tptp.zero_zero_rat))))) (forall ((X_43 tptp.int) (Y_31 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_43) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_31) _let_1)))))) (forall ((X_43 tptp.real) (Y_31 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_43) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_31) _let_1)))))) (forall ((X_43 tptp.rat) (Y_31 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_43) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_31) _let_1)))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) X_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_2) Y_2)))) (or (not (= X_1 tptp.zero_zero_int)) (not (= Y_2 tptp.zero_zero_int))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) X_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Y_2)))) (or (not (= X_1 tptp.zero_zero_real)) (not (= Y_2 tptp.zero_zero_real))))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_1) X_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_2) Y_2)))) (or (not (= X_1 tptp.zero_zero_rat)) (not (= Y_2 tptp.zero_zero_rat))))) (forall ((X_42 tptp.int) (Y_30 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_42) X_42)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_30) Y_30))) tptp.zero_zero_int)))) (forall ((X_42 tptp.real) (Y_30 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_42) X_42)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_30) Y_30))) tptp.zero_zero_real)))) (forall ((X_42 tptp.rat) (Y_30 tptp.rat)) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_42) X_42)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_30) Y_30))) tptp.zero_zero_rat)))) (forall ((A_237 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_237) A_237)) (forall ((A_237 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_237) A_237)) (forall ((A_237 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_237) A_237)) (forall ((A_237 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_237) A_237)) (forall ((A_236 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_236) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_236)) (forall ((A_236 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_236) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_236)) (forall ((A_236 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_236) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_236)) (forall ((A_236 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_236) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit1 tptp.pls))) A_236)) _let_114 (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.bit1 K_2)) L_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) L_2))) L_2))) (forall ((N_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ma) N_1) tptp.one_one_int) (and (= Ma tptp.one_one_int) (= N_1 tptp.one_one_int))))) (forall ((A tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((K_2 tptp.int)) (not (= (tptp.hAPP_int_int tptp.bit1 K_2) tptp.pls))) (forall ((L_2 tptp.int)) (not (= tptp.pls (tptp.hAPP_int_int tptp.bit1 L_2)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (not (= (tptp.hAPP_int_int tptp.bit1 K_2) (tptp.hAPP_int_int tptp.bit0 L_2)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (not (= (tptp.hAPP_int_int tptp.bit0 K_2) (tptp.hAPP_int_int tptp.bit1 L_2)))) (forall ((K_1 tptp.int)) (= (= (tptp.hAPP_int_int tptp.bit0 K_1) tptp.pls) (= K_1 tptp.pls))) (forall ((L tptp.int)) (= (= tptp.pls (tptp.hAPP_int_int tptp.bit0 L)) (= tptp.pls L))) (= (tptp.hAPP_int_int tptp.bit0 tptp.pls) tptp.pls) (= tptp.pls tptp.zero_zero_int) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K1)) (tptp.hAPP_int_int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K_1)) (tptp.hAPP_int_int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_101 tptp.pls))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K1)) (tptp.hAPP_int_int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K_1)) (tptp.hAPP_int_int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)))) _let_97 (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) tptp.pls) K_2)) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.pls) K_2) K_2)) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) L_2)))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.bit0 K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) K_2))) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) tptp.zero_zero_int) Z_1)) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) Z_1) Z_1)) (forall ((K_2 tptp.int) (I tptp.int) (J_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I) K_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int J_2) K_2))))) (forall ((W_12 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (tptp.hAPP_int_int tptp.number_number_of_int W_12)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W_12)))) (forall ((W_12 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) (tptp.hAPP_int_real tptp.number267125858f_real W_12)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 W_12)))) (forall ((W_12 tptp.int)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex)) (tptp.hAPP_int_complex tptp.number528085621omplex W_12)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 W_12)))) (forall ((W_12 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_12)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 W_12)))) (forall ((A_235 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_235) A_235)) A_235))) (forall ((A_235 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_235) A_235)) A_235))) (forall ((A_235 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_235) A_235)) A_235))) (forall ((A_235 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_235) A_235)) A_235))) (forall ((A_235 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_235) A_235)) A_235))) (forall ((A_235 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_235) A_235)) A_235))) (forall ((A_235 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_235) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_235) A_235)) A_235))) (forall ((Z_14 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_14) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_14) Z_14))) (forall ((Z_14 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_14) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Z_14) Z_14))) (forall ((Z_14 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_14) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z_14) Z_14))) (forall ((Z_14 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_14) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Z_14) Z_14))) (forall ((Z_14 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_14) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Z_14) Z_14))) (forall ((Z_13 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_13) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_13) Z_13))) (forall ((Z_13 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_13) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z_13) Z_13))) (forall ((Z_13 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_13) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Z_13) Z_13))) (forall ((Z_13 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_13) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Z_13) Z_13))) (forall ((Z_12 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_12) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_12) Z_12))) (forall ((Z_12 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Z_12) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Z_12) Z_12))) (forall ((Z_12 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z_12) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z_12) Z_12))) (forall ((Z_12 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_12) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Z_12) Z_12))) (forall ((Z_12 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Z_12) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Z_12) Z_12))) (forall ((Z_11 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_11) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_11) Z_11))) (forall ((Z_11 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z_11) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z_11) Z_11))) (forall ((Z_11 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_11) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Z_11) Z_11))) (forall ((Z_11 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Z_11) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Z_11) Z_11))) (forall ((A_234 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_234) A_234))) (forall ((A_234 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_234) A_234))) (forall ((A_234 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_234) A_234))) (forall ((A_234 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_234) A_234))) (forall ((A_234 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_234) A_234))) (forall ((A_234 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_234) A_234))) (forall ((A_234 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_234) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_234) A_234))) (forall ((A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) _let_127 _let_129 _let_126 _let_125 _let_124 _let_127 _let_126 _let_125 _let_124 _let_123 (= tptp.zero_zero_real _let_122) (= tptp.zero_zero_complex _let_121) (= tptp.zero_zero_rat _let_120) (forall ((A_233 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.pls)) A_233) A_233)) (forall ((A_233 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.pls)) A_233) A_233)) (forall ((A_233 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex tptp.pls)) A_233) A_233)) (forall ((A_233 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat tptp.pls)) A_233) A_233)) (forall ((A_232 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_232) (tptp.hAPP_int_int tptp.number_number_of_int tptp.pls)) A_232)) (forall ((A_232 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_232) (tptp.hAPP_int_real tptp.number267125858f_real tptp.pls)) A_232)) (forall ((A_232 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_232) (tptp.hAPP_int_complex tptp.number528085621omplex tptp.pls)) A_232)) (forall ((A_232 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_232) (tptp.hAPP_int_rat tptp.number_number_of_rat tptp.pls)) A_232)) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2)))) (forall ((V_13 tptp.int) (W_11 tptp.int) (Z_10 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_13)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int W_11)) Z_10)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_13) W_11))) Z_10))) (forall ((V_13 tptp.int) (W_11 tptp.int) (Z_10 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_13)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real W_11)) Z_10)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_13) W_11))) Z_10))) (forall ((V_13 tptp.int) (W_11 tptp.int) (Z_10 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_13)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex W_11)) Z_10)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_13) W_11))) Z_10))) (forall ((V_13 tptp.int) (W_11 tptp.int) (Z_10 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_13)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat W_11)) Z_10)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_13) W_11))) Z_10))) (forall ((V_12 tptp.int) (W_10 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_12)) (tptp.hAPP_int_int tptp.number_number_of_int W_10)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_12) W_10)))) (forall ((V_12 tptp.int) (W_10 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_12)) (tptp.hAPP_int_real tptp.number267125858f_real W_10)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_12) W_10)))) (forall ((V_12 tptp.int) (W_10 tptp.int)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_12)) (tptp.hAPP_int_complex tptp.number528085621omplex W_10)) (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_12) W_10)))) (forall ((V_12 tptp.int) (W_10 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_12)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_10)) (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_12) W_10)))) (forall ((V_11 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_11) W_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_11)) (tptp.hAPP_int_int tptp.number_number_of_int W_9)))) (forall ((V_11 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_11) W_9)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_11)) (tptp.hAPP_int_real tptp.number267125858f_real W_9)))) (forall ((V_11 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_11) W_9)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_11)) (tptp.hAPP_int_complex tptp.number528085621omplex W_9)))) (forall ((V_11 tptp.int) (W_9 tptp.int)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_11) W_9)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_11)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_9)))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K_1)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.pls)))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K1)) (tptp.hAPP_int_int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K1) K2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K_1)) (tptp.hAPP_int_int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K_1)) tptp.pls)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.pls)))) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit0 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_101 tptp.zero_zero_int))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 W_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) tptp.zero_zero_int)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) L_2)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) L_2)))) _let_94 (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.bit1 K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) K_2)) K_2))) (forall ((Z_1 tptp.int)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z_1)) Z_1) tptp.zero_zero_int))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_2) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_2)) (= W_1 Z_2))))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral W_8))) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int W_8))) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat W_8))) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W_8))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_8))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real W_8))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_1) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex W_8))) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex _let_1) _let_1)))) (forall ((X_41 tptp.int) (Y_29 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_41) Y_29)) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_41) _let_2)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_29) _let_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) X_41)) Y_29)))))) (forall ((X_41 tptp.nat) (Y_29 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_41) Y_29)) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_41) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_29) _let_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) X_41)) Y_29))))) (forall ((X_41 tptp.real) (Y_29 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_41) Y_29)) _let_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_41) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_29) _let_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) X_41)) Y_29)))))) (forall ((X_41 tptp.complex) (Y_29 tptp.complex)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_41) Y_29)) _let_2) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_41) _let_2)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_29) _let_2))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex _let_1)) X_41)) Y_29)))))) (forall ((X_41 tptp.rat) (Y_29 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_41) Y_29)) _let_2) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_41) _let_2)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_29) _let_2))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat _let_1)) X_41)) Y_29)))))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W_7))) (= (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W_7)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real W_7))) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 W_7)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex W_7))) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit0 W_7)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.zero_zero_complex) _let_1)) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat W_7))) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 W_7)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) _let_1)) _let_1)))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W_6))) (= (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 W_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real W_6))) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit1 W_6)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex W_6))) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int tptp.bit1 W_6)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) _let_1)) _let_1)))) (forall ((W_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat W_6))) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit1 W_6)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) _let_1)) _let_1)))) _let_118 _let_119 _let_117 _let_116 _let_115 _let_118 _let_117 _let_116 _let_115 _let_114 (= tptp.one_one_real _let_112) (= tptp.one_one_complex _let_111) (= tptp.one_one_rat _let_110) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z_2)) Z_2)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_2) tptp.zero_zero_int)))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) tptp.pls)))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) tptp.pls)))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) tptp.pls)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) Y_2)))) _let_108 _let_109 _let_107 _let_106 _let_105 _let_108 _let_107 _let_106 _let_105 (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int X_1)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat tptp.number_number_of_rat X_1)) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) (forall ((Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 tptp.pls)) Y_2)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_85 _let_5)) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit1 _let_1))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2))) (let ((_let_5 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1)))) (let ((_let_6 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2)) _let_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_6 A_3)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2)) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) _let_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) A_3)) B_2))) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) _let_2)))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (or (= X tptp.zero_zero_int) (= X tptp.one_one_int))))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_76 tptp.s)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.s) _let_78)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.s1) tptp.s) _let_78))) (forall ((A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_nat_int _let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1)))) (tptp.hAPP_nat_int _let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 _let_1))))))) (forall ((X tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (forall ((R_3 tptp.int) (Q_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int R_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) Q_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) A_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) Q_2)))))) (forall ((R_3 tptp.int) (Q_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int R_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) Q_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_76 _let_8)) (forall ((X_40 tptp.code_code_numeral) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_40))) (let ((_let_2 (tptp.hAPP_n1108039445umeral _let_1 N_69))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral _let_2) _let_2))))) (forall ((X_40 tptp.quickcheck_code_int) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_40))) (let ((_let_2 (tptp.hAPP_n522471361de_int _let_1 N_69))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int _let_2) _let_2))))) (forall ((X_40 tptp.rat) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_40))) (let ((_let_2 (tptp.hAPP_nat_rat _let_1 N_69))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_2))))) (forall ((X_40 tptp.int) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_40))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 N_69))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_2) _let_2))))) (forall ((X_40 tptp.nat) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_40))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 N_69))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_2))))) (forall ((X_40 tptp.real) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_40))) (let ((_let_2 (tptp.hAPP_nat_real _let_1 N_69))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) _let_2))))) (forall ((X_40 tptp.complex) (N_69 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_40))) (let ((_let_2 (tptp.hAPP_nat_complex _let_1 N_69))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_69)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex _let_2) _let_2))))) (forall ((X_39 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_39) X_39) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_39) X_39) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_39) X_39) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_39) X_39) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_39) X_39) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_39) X_39) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X_39 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_39) X_39) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_39) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_102 _let_104) _let_78)) (exists ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.s1) X_2) _let_1)) (forall ((Y_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.s1) Y_1) _let_1))) (= Y_1 X_2))))))) (not (forall ((S_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) S_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int S_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.s1) S_2) _let_1))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong _let_104) _let_65) _let_78)) (forall ((X_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) N_1))) (or (= N_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)))))) (forall ((A_3 tptp.int) (N tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)))))) (forall ((X_38 tptp.quickcheck_code_int) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_38))) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_n522471361de_int _let_1 P_8)) Q_12) (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.code_code_numeral) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_38))) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_n1108039445umeral _let_1 P_8)) Q_12) (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.rat) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_38))) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_nat_rat _let_1 P_8)) Q_12) (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.int) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_38))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_1 P_8)) Q_12) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.nat) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_38))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 P_8)) Q_12) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.real) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_38))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real _let_1 P_8)) Q_12) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((X_38 tptp.complex) (P_8 tptp.nat) (Q_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_38))) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_nat_complex _let_1 P_8)) Q_12) (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_8) Q_12))))) (forall ((N tptp.nat) (A_3 tptp.int) (B_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int P_3) N)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3))))))) (forall ((N tptp.nat) (B_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int P_3) N)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2))))))) (forall ((X tptp.int) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y)) Z_1) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Y) Z_1))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) N)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)))))) (forall ((N tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)) (= M N))))))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N))) (=> (not (= K_2 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) N)))))) (forall ((K_1 tptp.int) (N_1 tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) Ma)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1))))) (forall ((C tptp.int) (X_1 tptp.int) (Ta tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_1))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 D)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int _let_1 Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C) D))) Ta)))))))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_8)) (forall ((Z_1 tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_1) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) N))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu1425020248sum2sq X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu1425020248sum2sq Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu1425020248sum2sq (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)))))) (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.pls)))))) (forall ((Lx_6 tptp.code_code_numeral) (Ly_4 tptp.code_code_numeral) (Rx_6 tptp.code_code_numeral) (Ry_4 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_6))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Ly_4)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Rx_6) Ry_4)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Rx_6)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Ly_4) Ry_4))))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_6))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_6) Ry_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly_4) Ry_4))))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_6))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_6) Ry_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly_4) Ry_4))))) (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_6))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_4)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Rx_6) Ry_4)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_6)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Ly_4) Ry_4))))) (forall ((Lx_6 tptp.complex) (Ly_4 tptp.complex) (Rx_6 tptp.complex) (Ry_4 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_6))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Ly_4)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Rx_6) Ry_4)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Rx_6)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Ly_4) Ry_4))))) (forall ((Lx_6 tptp.quickcheck_code_int) (Ly_4 tptp.quickcheck_code_int) (Rx_6 tptp.quickcheck_code_int) (Ry_4 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_6))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Ly_4)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Rx_6) Ry_4)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Rx_6)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Ly_4) Ry_4))))) (forall ((Lx_6 tptp.rat) (Ly_4 tptp.rat) (Rx_6 tptp.rat) (Ry_4 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_6))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Ly_4)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Rx_6) Ry_4)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Rx_6)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Ly_4) Ry_4))))) (forall ((Lx_5 tptp.code_code_numeral) (Ly_3 tptp.code_code_numeral) (Rx_5 tptp.code_code_numeral) (Ry_3 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Rx_5))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral _let_2 Ry_3)) (tptp.hAPP_C498520661umeral _let_2 (tptp.hAPP_C498520661umeral _let_1 Ry_3)))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_5))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry_3)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry_3)))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_5))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry_3)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry_3)))))) (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real Rx_5))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry_3)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry_3)))))) (forall ((Lx_5 tptp.complex) (Ly_3 tptp.complex) (Rx_5 tptp.complex) (Ry_3 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex Rx_5))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex _let_2 Ry_3)) (tptp.hAPP_complex_complex _let_2 (tptp.hAPP_complex_complex _let_1 Ry_3)))))) (forall ((Lx_5 tptp.quickcheck_code_int) (Ly_3 tptp.quickcheck_code_int) (Rx_5 tptp.quickcheck_code_int) (Ry_3 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Rx_5))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int _let_2 Ry_3)) (tptp.hAPP_Q1762011733de_int _let_2 (tptp.hAPP_Q1762011733de_int _let_1 Ry_3)))))) (forall ((Lx_5 tptp.rat) (Ly_3 tptp.rat) (Rx_5 tptp.rat) (Ry_3 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Rx_5))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat _let_2 Ry_3)) (tptp.hAPP_rat_rat _let_2 (tptp.hAPP_rat_rat _let_1 Ry_3)))))) (forall ((Lx_4 tptp.code_code_numeral) (Ly_2 tptp.code_code_numeral) (Rx_4 tptp.code_code_numeral) (Ry_2 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_4))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_2 Ly_2)) _let_1) (tptp.hAPP_C498520661umeral _let_2 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Ly_2) _let_1)))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_4))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_2 Ly_2)) _let_1) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_4))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_2 Ly_2)) _let_1) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_4))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_2 Ly_2)) _let_1) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Ly_2) _let_1)))))) (forall ((Lx_4 tptp.complex) (Ly_2 tptp.complex) (Rx_4 tptp.complex) (Ry_2 tptp.complex)) (let ((_let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_4))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_2 Ly_2)) _let_1) (tptp.hAPP_complex_complex _let_2 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Ly_2) _let_1)))))) (forall ((Lx_4 tptp.quickcheck_code_int) (Ly_2 tptp.quickcheck_code_int) (Rx_4 tptp.quickcheck_code_int) (Ry_2 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_4))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_2 Ly_2)) _let_1) (tptp.hAPP_Q1762011733de_int _let_2 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Ly_2) _let_1)))))) (forall ((Lx_4 tptp.rat) (Ly_2 tptp.rat) (Rx_4 tptp.rat) (Ry_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_4))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_2 Ly_2)) _let_1) (tptp.hAPP_rat_rat _let_2 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Ly_2) _let_1)))))) (forall ((Lx_3 tptp.code_code_numeral) (Ly_1 tptp.code_code_numeral) (Rx_3 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_3))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Ly_1)) Rx_3) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_1)) Rx_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_1)) Rx_3) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_3))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly_1)) Rx_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.complex) (Ly_1 tptp.complex) (Rx_3 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_3))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Ly_1)) Rx_3) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.quickcheck_code_int) (Ly_1 tptp.quickcheck_code_int) (Rx_3 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_3))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Ly_1)) Rx_3) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.rat) (Ly_1 tptp.rat) (Rx_3 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_3))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Ly_1)) Rx_3) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_2 tptp.code_code_numeral) (Ly tptp.code_code_numeral) (Rx_2 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_2))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Ly)) Rx_2) (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Ly) Rx_2))))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_2))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly)) Rx_2) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly) Rx_2))))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly)) Rx_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_2))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Ly)) Rx_2) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Ly) Rx_2))))) (forall ((Lx_2 tptp.complex) (Ly tptp.complex) (Rx_2 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_2))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Ly)) Rx_2) (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Ly) Rx_2))))) (forall ((Lx_2 tptp.quickcheck_code_int) (Ly tptp.quickcheck_code_int) (Rx_2 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_2))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Ly)) Rx_2) (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Ly) Rx_2))))) (forall ((Lx_2 tptp.rat) (Ly tptp.rat) (Rx_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_2))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Ly)) Rx_2) (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Ly) Rx_2))))) (forall ((Lx_1 tptp.code_code_numeral) (Rx_1 tptp.code_code_numeral) (Ry_1 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx_1))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Rx_1) Ry_1)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_1) Ry_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_1) Ry_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx_1))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Rx_1) Ry_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.complex) (Rx_1 tptp.complex) (Ry_1 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx_1))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Rx_1) Ry_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.quickcheck_code_int) (Rx_1 tptp.quickcheck_code_int) (Ry_1 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx_1))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Rx_1) Ry_1)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.rat) (Rx_1 tptp.rat) (Ry_1 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx_1))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Rx_1) Ry_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 Rx_1)) Ry_1)))) (forall ((Lx tptp.code_code_numeral) (Rx tptp.code_code_numeral) (Ry tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Lx))) (let ((_let_2 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Rx))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral _let_2 Ry)) (tptp.hAPP_C498520661umeral _let_2 (tptp.hAPP_C498520661umeral _let_1 Ry)))))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry)))))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry)))))) (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Lx))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real Rx))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Ry)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 Ry)))))) (forall ((Lx tptp.complex) (Rx tptp.complex) (Ry tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Lx))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex Rx))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex _let_2 Ry)) (tptp.hAPP_complex_complex _let_2 (tptp.hAPP_complex_complex _let_1 Ry)))))) (forall ((Lx tptp.quickcheck_code_int) (Rx tptp.quickcheck_code_int) (Ry tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Lx))) (let ((_let_2 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Rx))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int _let_2 Ry)) (tptp.hAPP_Q1762011733de_int _let_2 (tptp.hAPP_Q1762011733de_int _let_1 Ry)))))) (forall ((Lx tptp.rat) (Rx tptp.rat) (Ry tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Lx))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Rx))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat _let_2 Ry)) (tptp.hAPP_rat_rat _let_2 (tptp.hAPP_rat_rat _let_1 Ry)))))) (forall ((A_231 tptp.code_code_numeral) (B_165 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_231) B_165) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_165) A_231))) (forall ((A_231 tptp.int) (B_165 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_231) B_165) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_165) A_231))) (forall ((A_231 tptp.nat) (B_165 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_231) B_165) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_165) A_231))) (forall ((A_231 tptp.real) (B_165 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_231) B_165) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_165) A_231))) (forall ((A_231 tptp.complex) (B_165 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_231) B_165) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_165) A_231))) (forall ((A_231 tptp.quickcheck_code_int) (B_165 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_231) B_165) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_165) A_231))) (forall ((A_231 tptp.rat) (B_165 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_231) B_165) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_165) A_231))) (forall ((A_230 tptp.code_code_numeral) (C_96 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_230) C_96) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_96) A_230))) (forall ((A_230 tptp.int) (C_96 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_230) C_96) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_96) A_230))) (forall ((A_230 tptp.nat) (C_96 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_230) C_96) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_96) A_230))) (forall ((A_230 tptp.real) (C_96 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_230) C_96) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_96) A_230))) (forall ((A_230 tptp.complex) (C_96 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_230) C_96) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C_96) A_230))) (forall ((A_230 tptp.quickcheck_code_int) (C_96 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_230) C_96) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_96) A_230))) (forall ((A_230 tptp.rat) (C_96 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_230) C_96) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_96) A_230))) (forall ((A_229 tptp.code_code_numeral) (C_95 tptp.code_code_numeral) (D_20 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_229))) (let ((_let_2 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_95))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral _let_2 D_20)) (tptp.hAPP_C498520661umeral _let_2 (tptp.hAPP_C498520661umeral _let_1 D_20)))))) (forall ((A_229 tptp.int) (C_95 tptp.int) (D_20 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_229))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_95))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 D_20)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 D_20)))))) (forall ((A_229 tptp.nat) (C_95 tptp.nat) (D_20 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_229))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_95))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_20)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_20)))))) (forall ((A_229 tptp.real) (C_95 tptp.real) (D_20 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_229))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_95))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 D_20)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 D_20)))))) (forall ((A_229 tptp.complex) (C_95 tptp.complex) (D_20 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_229))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C_95))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex _let_2 D_20)) (tptp.hAPP_complex_complex _let_2 (tptp.hAPP_complex_complex _let_1 D_20)))))) (forall ((A_229 tptp.quickcheck_code_int) (C_95 tptp.quickcheck_code_int) (D_20 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_229))) (let ((_let_2 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_95))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int _let_2 D_20)) (tptp.hAPP_Q1762011733de_int _let_2 (tptp.hAPP_Q1762011733de_int _let_1 D_20)))))) (forall ((A_229 tptp.rat) (C_95 tptp.rat) (D_20 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_229))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_95))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat _let_2 D_20)) (tptp.hAPP_rat_rat _let_2 (tptp.hAPP_rat_rat _let_1 D_20)))))) (forall ((A_228 tptp.code_code_numeral) (C_94 tptp.code_code_numeral) (D_19 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_228))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_94) D_19)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 C_94)) D_19)))) (forall ((A_228 tptp.int) (C_94 tptp.int) (D_19 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_228))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_94) D_19)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_94)) D_19)))) (forall ((A_228 tptp.nat) (C_94 tptp.nat) (D_19 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_228))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_94) D_19)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_94)) D_19)))) (forall ((A_228 tptp.real) (C_94 tptp.real) (D_19 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_228))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_94) D_19)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_94)) D_19)))) (forall ((A_228 tptp.complex) (C_94 tptp.complex) (D_19 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_228))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C_94) D_19)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 C_94)) D_19)))) (forall ((A_228 tptp.quickcheck_code_int) (C_94 tptp.quickcheck_code_int) (D_19 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_228))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_94) D_19)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 C_94)) D_19)))) (forall ((A_228 tptp.rat) (C_94 tptp.rat) (D_19 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_228))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_94) D_19)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 C_94)) D_19)))) (forall ((A_227 tptp.code_code_numeral) (B_164 tptp.code_code_numeral) (C_93 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_227))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 B_164)) C_93) (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_164) C_93))))) (forall ((A_227 tptp.int) (B_164 tptp.int) (C_93 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_227))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_164)) C_93) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_164) C_93))))) (forall ((A_227 tptp.nat) (B_164 tptp.nat) (C_93 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_227))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_164)) C_93) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_164) C_93))))) (forall ((A_227 tptp.real) (B_164 tptp.real) (C_93 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_227))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_164)) C_93) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_164) C_93))))) (forall ((A_227 tptp.complex) (B_164 tptp.complex) (C_93 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_227))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_164)) C_93) (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_164) C_93))))) (forall ((A_227 tptp.quickcheck_code_int) (B_164 tptp.quickcheck_code_int) (C_93 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_227))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 B_164)) C_93) (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_164) C_93))))) (forall ((A_227 tptp.rat) (B_164 tptp.rat) (C_93 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_227))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 B_164)) C_93) (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_164) C_93))))) (forall ((A_226 tptp.code_code_numeral) (B_163 tptp.code_code_numeral) (C_92 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_226))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 B_163)) C_92) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 C_92)) B_163)))) (forall ((A_226 tptp.int) (B_163 tptp.int) (C_92 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_226))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_163)) C_92) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_92)) B_163)))) (forall ((A_226 tptp.nat) (B_163 tptp.nat) (C_92 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_226))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_163)) C_92) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_92)) B_163)))) (forall ((A_226 tptp.real) (B_163 tptp.real) (C_92 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_226))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_163)) C_92) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_92)) B_163)))) (forall ((A_226 tptp.complex) (B_163 tptp.complex) (C_92 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_226))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_163)) C_92) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 C_92)) B_163)))) (forall ((A_226 tptp.quickcheck_code_int) (B_163 tptp.quickcheck_code_int) (C_92 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_226))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 B_163)) C_92) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 C_92)) B_163)))) (forall ((A_226 tptp.rat) (B_163 tptp.rat) (C_92 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_226))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 B_163)) C_92) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 C_92)) B_163)))) (forall ((A_225 tptp.code_code_numeral) (B_162 tptp.code_code_numeral) (C_91 tptp.code_code_numeral) (D_18 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_225))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 B_162)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_91) D_18)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 C_91)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_162) D_18))))) (forall ((A_225 tptp.int) (B_162 tptp.int) (C_91 tptp.int) (D_18 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_225))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_162)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_91) D_18)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_91)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_162) D_18))))) (forall ((A_225 tptp.nat) (B_162 tptp.nat) (C_91 tptp.nat) (D_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_225))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_162)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_91) D_18)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_91)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_162) D_18))))) (forall ((A_225 tptp.real) (B_162 tptp.real) (C_91 tptp.real) (D_18 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_225))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_162)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_91) D_18)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 C_91)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_162) D_18))))) (forall ((A_225 tptp.complex) (B_162 tptp.complex) (C_91 tptp.complex) (D_18 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_225))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_162)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C_91) D_18)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 C_91)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_162) D_18))))) (forall ((A_225 tptp.quickcheck_code_int) (B_162 tptp.quickcheck_code_int) (C_91 tptp.quickcheck_code_int) (D_18 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_225))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 B_162)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_91) D_18)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 C_91)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_162) D_18))))) (forall ((A_225 tptp.rat) (B_162 tptp.rat) (C_91 tptp.rat) (D_18 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_225))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 B_162)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_91) D_18)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 C_91)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_162) D_18))))) (forall ((X_37 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_37) tptp.one_one_nat) X_37)) (forall ((X_37 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_37) tptp.one_one_nat) X_37)) (forall ((X_1 tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1))))))) (forall ((Z_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Z_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Z_1) Z_1))) (forall ((Z_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Z_1) Z_1))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_2) V_3)))))))) (forall ((V_3 tptp.int) (K_2 tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)) K_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_2) V_3))) K_2))))))) (forall ((A_224 tptp.quickcheck_code_int) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_224))) (= (tptp.hAPP_n522471361de_int _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_n522471361de_int _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.code_code_numeral) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_224))) (= (tptp.hAPP_n1108039445umeral _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_n1108039445umeral _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.rat) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_224))) (= (tptp.hAPP_nat_rat _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_nat_rat _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.int) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_224))) (= (tptp.hAPP_nat_int _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.nat) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_224))) (= (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.real) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_r474017924t_real tptp.power_power_real A_224))) (= (tptp.hAPP_nat_real _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real _let_2 N_68)) _let_1))))) (forall ((A_224 tptp.complex) (N_68 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_224))) (= (tptp.hAPP_nat_complex _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_68)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_nat_complex _let_2 N_68)) _let_1))))) (forall ((A_223 tptp.int) (K_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_223) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K_8))) tptp.zero_zero_int)) (= A_223 tptp.zero_zero_int))) (forall ((A_223 tptp.real) (K_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_223) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K_8))) tptp.zero_zero_real)) (= A_223 tptp.zero_zero_real))) (forall ((A_223 tptp.rat) (K_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_223) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K_8))) tptp.zero_zero_rat)) (= A_223 tptp.zero_zero_rat))) (forall ((A_222 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) A_222) tptp.zero_zero_int)) (forall ((A_222 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) A_222) tptp.zero_zero_nat)) (forall ((A_222 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.zero_zero_real) A_222) tptp.zero_zero_real)) (forall ((A_222 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral tptp.zero_z126310315umeral) A_222) tptp.zero_z126310315umeral)) (forall ((A_222 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.zero_zero_complex) A_222) tptp.zero_zero_complex)) (forall ((A_222 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int tptp.zero_z891286103de_int) A_222) tptp.zero_z891286103de_int)) (forall ((A_222 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat) A_222) tptp.zero_zero_rat)) _let_103 (forall ((A_221 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_221) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_221 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_221) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_221 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_221) tptp.zero_z126310315umeral) tptp.zero_z126310315umeral)) (forall ((A_221 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_221) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A_221 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_221) tptp.zero_z891286103de_int) tptp.zero_z891286103de_int)) (forall ((A_221 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_221) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A_220 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.zero_z126310315umeral) A_220) A_220)) (forall ((A_220 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A_220) A_220)) (forall ((A_220 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A_220) A_220)) (forall ((A_220 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.zero_zero_real) A_220) A_220)) (forall ((A_220 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.zero_zero_complex) A_220) A_220)) (forall ((A_220 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.zero_z891286103de_int) A_220) A_220)) (forall ((A_220 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A_220) A_220)) (forall ((A_219 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_219) tptp.zero_z126310315umeral) A_219)) (forall ((A_219 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_219) tptp.zero_zero_int) A_219)) (forall ((A_219 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_219) tptp.zero_zero_nat) A_219)) (forall ((A_219 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_219) tptp.zero_zero_real) A_219)) (forall ((A_219 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_219) tptp.zero_zero_complex) A_219)) (forall ((A_219 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_219) tptp.zero_z891286103de_int) A_219)) (forall ((A_219 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_219) tptp.zero_zero_rat) A_219)) (forall ((B tptp.int) (A tptp.int)) (= (= B (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))) (forall ((B tptp.nat) (A tptp.nat)) (= (= B (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))) (forall ((B tptp.real) (A tptp.real)) (= (= B (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))) (forall ((B tptp.complex) (A tptp.complex)) (= (= B (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))) (forall ((B tptp.rat) (A tptp.rat)) (= (= B (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))) (forall ((X_36 tptp.code_code_numeral) (Y_28 tptp.code_code_numeral) (Z_9 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_36))) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral Y_28) Z_9)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 Y_28)) (tptp.hAPP_C498520661umeral _let_1 Z_9))))) (forall ((X_36 tptp.int) (Y_28 tptp.int) (Z_9 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int X_36))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y_28) Z_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Y_28)) (tptp.hAPP_int_int _let_1 Z_9))))) (forall ((X_36 tptp.nat) (Y_28 tptp.nat) (Z_9 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_36))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_28) Z_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Y_28)) (tptp.hAPP_nat_nat _let_1 Z_9))))) (forall ((X_36 tptp.real) (Y_28 tptp.real) (Z_9 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real X_36))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Y_28) Z_9)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 Y_28)) (tptp.hAPP_real_real _let_1 Z_9))))) (forall ((X_36 tptp.complex) (Y_28 tptp.complex) (Z_9 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex X_36))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Y_28) Z_9)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 Y_28)) (tptp.hAPP_complex_complex _let_1 Z_9))))) (forall ((X_36 tptp.quickcheck_code_int) (Y_28 tptp.quickcheck_code_int) (Z_9 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_36))) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int Y_28) Z_9)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 Y_28)) (tptp.hAPP_Q1762011733de_int _let_1 Z_9))))) (forall ((X_36 tptp.rat) (Y_28 tptp.rat) (Z_9 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_36))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Y_28) Z_9)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 Y_28)) (tptp.hAPP_rat_rat _let_1 Z_9))))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 C)) (tptp.hAPP_int_int _let_1 D)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 D)) (tptp.hAPP_int_int _let_1 C)))))))) (forall ((C tptp.nat) (D tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 C)) (tptp.hAPP_nat_nat _let_1 D)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 D)) (tptp.hAPP_nat_nat _let_1 C)))))))) (forall ((C tptp.real) (D tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real B))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_2 C)) (tptp.hAPP_real_real _let_1 D)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_2 D)) (tptp.hAPP_real_real _let_1 C)))))))) (forall ((C tptp.complex) (D tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex B))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_2 C)) (tptp.hAPP_complex_complex _let_1 D)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_2 D)) (tptp.hAPP_complex_complex _let_1 C)))))))) (forall ((C tptp.rat) (D tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_2 C)) (tptp.hAPP_rat_rat _let_1 D)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_2 D)) (tptp.hAPP_rat_rat _let_1 C)))))))) (forall ((A_218 tptp.code_code_numeral) (B_161 tptp.code_code_numeral) (C_90 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_218) B_161)) C_90) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_218) C_90)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_161) C_90)))) (forall ((A_218 tptp.int) (B_161 tptp.int) (C_90 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_218) B_161)) C_90) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_218) C_90)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_161) C_90)))) (forall ((A_218 tptp.nat) (B_161 tptp.nat) (C_90 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_218) B_161)) C_90) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_218) C_90)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_161) C_90)))) (forall ((A_218 tptp.real) (B_161 tptp.real) (C_90 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_218) B_161)) C_90) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_218) C_90)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_161) C_90)))) (forall ((A_218 tptp.complex) (B_161 tptp.complex) (C_90 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_218) B_161)) C_90) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_218) C_90)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_161) C_90)))) (forall ((A_218 tptp.quickcheck_code_int) (B_161 tptp.quickcheck_code_int) (C_90 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_218) B_161)) C_90) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_218) C_90)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_161) C_90)))) (forall ((A_218 tptp.rat) (B_161 tptp.rat) (C_90 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_218) B_161)) C_90) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_218) C_90)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_161) C_90)))) (forall ((A_217 tptp.code_code_numeral) (M_29 tptp.code_code_numeral) (B_160 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_217) M_29)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_160) M_29)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_217) B_160)) M_29))) (forall ((A_217 tptp.int) (M_29 tptp.int) (B_160 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_217) M_29)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_160) M_29)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_217) B_160)) M_29))) (forall ((A_217 tptp.nat) (M_29 tptp.nat) (B_160 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_217) M_29)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_160) M_29)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_217) B_160)) M_29))) (forall ((A_217 tptp.real) (M_29 tptp.real) (B_160 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_217) M_29)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_160) M_29)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_217) B_160)) M_29))) (forall ((A_217 tptp.complex) (M_29 tptp.complex) (B_160 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_217) M_29)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_160) M_29)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_217) B_160)) M_29))) (forall ((A_217 tptp.quickcheck_code_int) (M_29 tptp.quickcheck_code_int) (B_160 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_217) M_29)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_160) M_29)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_217) B_160)) M_29))) (forall ((A_217 tptp.rat) (M_29 tptp.rat) (B_160 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_217) M_29)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_160) M_29)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_217) B_160)) M_29))) (forall ((W_1 tptp.int) (Y_2 tptp.int) (X_1 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1))) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Y_2)) (tptp.hAPP_int_int _let_1 Z_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Z_2)) (tptp.hAPP_int_int _let_1 Y_2))) (or (= W_1 X_1) (= Y_2 Z_2)))))) (forall ((W_1 tptp.nat) (Y_2 tptp.nat) (X_1 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Y_2)) (tptp.hAPP_nat_nat _let_1 Z_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Z_2)) (tptp.hAPP_nat_nat _let_1 Y_2))) (or (= W_1 X_1) (= Y_2 Z_2)))))) (forall ((W_1 tptp.real) (Y_2 tptp.real) (X_1 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real W_1))) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Y_2)) (tptp.hAPP_real_real _let_1 Z_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_2 Z_2)) (tptp.hAPP_real_real _let_1 Y_2))) (or (= W_1 X_1) (= Y_2 Z_2)))))) (forall ((W_1 tptp.complex) (Y_2 tptp.complex) (X_1 tptp.complex) (Z_2 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex X_1))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex W_1))) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_2 Y_2)) (tptp.hAPP_complex_complex _let_1 Z_2)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_2 Z_2)) (tptp.hAPP_complex_complex _let_1 Y_2))) (or (= W_1 X_1) (= Y_2 Z_2)))))) (forall ((W_1 tptp.rat) (Y_2 tptp.rat) (X_1 tptp.rat) (Z_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_1))) (let ((_let_2 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat W_1))) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_2 Y_2)) (tptp.hAPP_rat_rat _let_1 Z_2)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_2 Z_2)) (tptp.hAPP_rat_rat _let_1 Y_2))) (or (= W_1 X_1) (= Y_2 Z_2)))))) (forall ((A_216 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) A_216) A_216)) (forall ((A_216 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A_216) A_216)) (forall ((A_216 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.one_one_real) A_216) A_216)) (forall ((A_216 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral tptp.one_on1645066479umeral) A_216) A_216)) (forall ((A_216 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.one_one_complex) A_216) A_216)) (forall ((A_216 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int tptp.one_on1684967323de_int) A_216) A_216)) (forall ((A_216 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A_216) A_216)) (forall ((A_215 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_215) tptp.one_one_int) A_215)) (forall ((A_215 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_215) tptp.one_one_nat) A_215)) (forall ((A_215 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_215) tptp.one_one_real) A_215)) (forall ((A_215 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_215) tptp.one_on1645066479umeral) A_215)) (forall ((A_215 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_215) tptp.one_one_complex) A_215)) (forall ((A_215 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_215) tptp.one_on1684967323de_int) A_215)) (forall ((A_215 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_215) tptp.one_one_rat) A_215)) (forall ((X_35 tptp.code_code_numeral) (Y_27 tptp.code_code_numeral) (Q_11 tptp.nat)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_35) Y_27)) Q_11) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_35) Q_11)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_27) Q_11)))) (forall ((X_35 tptp.quickcheck_code_int) (Y_27 tptp.quickcheck_code_int) (Q_11 tptp.nat)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_35) Y_27)) Q_11) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_35) Q_11)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_27) Q_11)))) (forall ((X_35 tptp.rat) (Y_27 tptp.rat) (Q_11 tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_35) Y_27)) Q_11) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_35) Q_11)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_27) Q_11)))) (forall ((X_35 tptp.int) (Y_27 tptp.int) (Q_11 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_35) Y_27)) Q_11) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_35) Q_11)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_27) Q_11)))) (forall ((X_35 tptp.nat) (Y_27 tptp.nat) (Q_11 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_35) Y_27)) Q_11) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_35) Q_11)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_27) Q_11)))) (forall ((X_35 tptp.real) (Y_27 tptp.real) (Q_11 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_35) Y_27)) Q_11) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_35) Q_11)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_27) Q_11)))) (forall ((X_35 tptp.complex) (Y_27 tptp.complex) (Q_11 tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_35) Y_27)) Q_11) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_35) Q_11)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_27) Q_11)))) (forall ((X_34 tptp.code_code_numeral) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_34))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 P_7)) (tptp.hAPP_n1108039445umeral _let_1 Q_10)) (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.quickcheck_code_int) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_34))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 P_7)) (tptp.hAPP_n522471361de_int _let_1 Q_10)) (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.rat) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_34))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 P_7)) (tptp.hAPP_nat_rat _let_1 Q_10)) (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.int) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_34))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 P_7)) (tptp.hAPP_nat_int _let_1 Q_10)) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.nat) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_34))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 P_7)) (tptp.hAPP_nat_nat _let_1 Q_10)) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.real) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_34))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 P_7)) (tptp.hAPP_nat_real _let_1 Q_10)) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_34 tptp.complex) (P_7 tptp.nat) (Q_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_34))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 P_7)) (tptp.hAPP_nat_complex _let_1 Q_10)) (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat P_7) Q_10))))) (forall ((X_33 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_33) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X_33 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_33) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_33 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_33) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_33 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_33) tptp.zero_zero_nat) tptp.one_on1645066479umeral)) (forall ((X_33 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_33) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((X_33 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_33) tptp.zero_zero_nat) tptp.one_on1684967323de_int)) (forall ((X_33 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_33) tptp.zero_zero_nat) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_int_bool _let_76 tptp.zero_zero_int)) (forall ((A_214 tptp.int) (N_67 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_214) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_67))))) (forall ((A_214 tptp.real) (N_67 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_214) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_67))))) (forall ((A_214 tptp.rat) (N_67 tptp.nat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_214) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_67))))) (forall ((C_89 tptp.int) (D_17 tptp.int) (A_213 tptp.int) (B_159 tptp.int) (R_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int R_8))) (=> (not (= R_8 tptp.zero_zero_int)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_213) (tptp.hAPP_int_int _let_1 C_89)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_159) (tptp.hAPP_int_int _let_1 D_17)))))))) (forall ((C_89 tptp.nat) (D_17 tptp.nat) (A_213 tptp.nat) (B_159 tptp.nat) (R_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_8))) (=> (not (= R_8 tptp.zero_zero_nat)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_213) (tptp.hAPP_nat_nat _let_1 C_89)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_159) (tptp.hAPP_nat_nat _let_1 D_17)))))))) (forall ((C_89 tptp.real) (D_17 tptp.real) (A_213 tptp.real) (B_159 tptp.real) (R_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_8))) (=> (not (= R_8 tptp.zero_zero_real)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_213) (tptp.hAPP_real_real _let_1 C_89)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_159) (tptp.hAPP_real_real _let_1 D_17)))))))) (forall ((C_89 tptp.complex) (D_17 tptp.complex) (A_213 tptp.complex) (B_159 tptp.complex) (R_8 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex R_8))) (=> (not (= R_8 tptp.zero_zero_complex)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_213) (tptp.hAPP_complex_complex _let_1 C_89)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_159) (tptp.hAPP_complex_complex _let_1 D_17)))))))) (forall ((C_89 tptp.rat) (D_17 tptp.rat) (A_213 tptp.rat) (B_159 tptp.rat) (R_8 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat R_8))) (=> (not (= R_8 tptp.zero_zero_rat)) (=> (and (= A_213 B_159) (not (= C_89 D_17))) (not (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_213) (tptp.hAPP_rat_rat _let_1 C_89)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_159) (tptp.hAPP_rat_rat _let_1 D_17)))))))) (forall ((M_28 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M_28) M_28) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) M_28))) (forall ((M_28 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_28) M_28) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) M_28))) (forall ((M_28 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real M_28) M_28) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) M_28))) (forall ((M_28 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral M_28) M_28) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.one_on1645066479umeral) tptp.one_on1645066479umeral)) M_28))) (forall ((M_28 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex M_28) M_28) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex)) M_28))) (forall ((M_28 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int M_28) M_28) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.one_on1684967323de_int) tptp.one_on1684967323de_int)) M_28))) (forall ((M_28 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat M_28) M_28) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)) M_28))) (forall ((M_27 tptp.int) (A_212 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M_27) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_212) M_27)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_212) tptp.one_one_int)) M_27))) (forall ((M_27 tptp.nat) (A_212 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_27) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_212) M_27)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_212) tptp.one_one_nat)) M_27))) (forall ((M_27 tptp.real) (A_212 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real M_27) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_212) M_27)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_212) tptp.one_one_real)) M_27))) (forall ((M_27 tptp.code_code_numeral) (A_212 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral M_27) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_212) M_27)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_212) tptp.one_on1645066479umeral)) M_27))) (forall ((M_27 tptp.complex) (A_212 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex M_27) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_212) M_27)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_212) tptp.one_one_complex)) M_27))) (forall ((M_27 tptp.quickcheck_code_int) (A_212 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int M_27) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_212) M_27)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_212) tptp.one_on1684967323de_int)) M_27))) (forall ((M_27 tptp.rat) (A_212 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat M_27) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_212) M_27)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_212) tptp.one_one_rat)) M_27))) (forall ((A_211 tptp.int) (M_26 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_211) M_26)) M_26) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_211) tptp.one_one_int)) M_26))) (forall ((A_211 tptp.nat) (M_26 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_211) M_26)) M_26) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_211) tptp.one_one_nat)) M_26))) (forall ((A_211 tptp.real) (M_26 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_211) M_26)) M_26) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_211) tptp.one_one_real)) M_26))) (forall ((A_211 tptp.code_code_numeral) (M_26 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_211) M_26)) M_26) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_211) tptp.one_on1645066479umeral)) M_26))) (forall ((A_211 tptp.complex) (M_26 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_211) M_26)) M_26) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_211) tptp.one_one_complex)) M_26))) (forall ((A_211 tptp.quickcheck_code_int) (M_26 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_211) M_26)) M_26) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_211) tptp.one_on1684967323de_int)) M_26))) (forall ((A_211 tptp.rat) (M_26 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_211) M_26)) M_26) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_211) tptp.one_one_rat)) M_26))) (forall ((A tptp.int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) _let_1) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A) _let_1) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.real) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A) _let_1) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.code_code_numeral) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A) _let_1) tptp.zero_z126310315umeral) (and (= A tptp.zero_z126310315umeral) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.complex) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A) _let_1) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.quickcheck_code_int) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A) _let_1) tptp.zero_z891286103de_int) (and (= A tptp.zero_z891286103de_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A tptp.rat) (W_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_1))) (= (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A) _let_1) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2)))))) _let_96 (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 tptp.zero_zero_int))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_nat))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.zero_z126310315umeral) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_on1645066479umeral)) (=> (not _let_3) (= _let_2 tptp.zero_z126310315umeral))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.zero_zero_complex) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 tptp.zero_zero_complex))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.zero_z891286103de_int) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_on1684967323de_int)) (=> (not _let_3) (= _let_2 tptp.zero_z891286103de_int))))))) (forall ((W_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W_5))) (let ((_let_2 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.zero_zero_rat) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_rat))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_76 _let_10)) (forall ((B_5 tptp.int) (Q_8 tptp.int) (R_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_5) Q_8)) R_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Q_8))))))) (forall ((B_5 tptp.int) (Q_8 tptp.int) (R_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_5) Q_8)) R_5)) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_8) tptp.zero_zero_int)))))) (forall ((B_2 tptp.int) (Q_8 tptp.int) (R_5 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_8)) R_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_2)) R_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_5) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_8) Q_2)))))))) (forall ((B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int) (B_5 tptp.int) (Q_8 tptp.int) (R_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_5) Q_8)) R_5))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) Q_2)) R_3) _let_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) Q_8))))))))))) (forall ((B_2 tptp.int) (Q_8 tptp.int) (R_5 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_8)) R_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Q_2)) R_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_2) Q_8))))))))) (forall ((B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int) (B_5 tptp.int) (Q_8 tptp.int) (R_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_5) Q_8)) R_5))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) Q_2)) R_3) _let_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Q_8) Q_2)))))))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_2 _let_3)) _let_3) (tptp.hAPP_nat_int _let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1)))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_102 _let_65) _let_78)) (forall ((Y tptp.int) (X tptp.int) (P_3 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X) P_3)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) Y)))))) (forall ((P_5 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) P_5)) (forall ((M_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M_1) P_5))) (or (= M_1 tptp.one_one_int) (= M_1 P_5))))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (= P_3 (tptp.hAPP_int_int tptp.number_number_of_int _let_2))) (=> (not (= P_3 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 _let_1)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 _let_2))) P_3)))))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_92 _let_3)) (forall ((N_66 tptp.nat) (A_210 tptp.int) (B_158 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_210) N_66)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_158) N_66))))))) (forall ((N_66 tptp.nat) (A_210 tptp.nat) (B_158 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_210) N_66)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_158) N_66))))))) (forall ((N_66 tptp.nat) (A_210 tptp.real) (B_158 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_210) N_66)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_158) N_66))))))) (forall ((N_66 tptp.nat) (A_210 tptp.code_code_numeral) (B_158 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_210) N_66)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_158) N_66))))))) (forall ((N_66 tptp.nat) (A_210 tptp.quickcheck_code_int) (B_158 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_210) N_66)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_158) N_66))))))) (forall ((N_66 tptp.nat) (A_210 tptp.rat) (B_158 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_210) B_158)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_210)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_66)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_210) N_66)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_158) N_66))))))) (forall ((V_10 tptp.int) (U_3 tptp.int) (Y_26 tptp.int) (X_32 tptp.int) (A_209 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_32) A_209)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_26) A_209)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_10)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int U_3) V_10) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int U_3) X_32)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_10) Y_26))) A_209))))))))) (forall ((V_10 tptp.real) (U_3 tptp.real) (Y_26 tptp.real) (X_32 tptp.real) (A_209 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_32) A_209)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_26) A_209)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_10)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real U_3) V_10) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real U_3) X_32)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real V_10) Y_26))) A_209))))))))) (forall ((V_10 tptp.rat) (U_3 tptp.rat) (Y_26 tptp.rat) (X_32 tptp.rat) (A_209 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_32) A_209)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Y_26) A_209)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 U_3)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 V_10)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat U_3) V_10) tptp.one_one_rat) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat U_3) X_32)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat V_10) Y_26))) A_209))))))))) (forall ((Y tptp.int) (N tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y))))))) (forall ((N tptp.int) (P_3 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (and (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong B_2) tptp.zero_zero_int) P_3)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) tptp.zero_zero_int) P_3))))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) tptp.zero_zero_int) P_3)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong B_2) tptp.zero_zero_int) P_3))))))) (forall ((A_208 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_208) tptp.zero_zero_real))) (forall ((A_208 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_208) tptp.zero_z126310315umeral))) (forall ((A_208 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_208) tptp.zero_zero_complex))) (forall ((A_208 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_208) tptp.zero_z891286103de_int))) (forall ((A_208 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_208) tptp.zero_zero_rat))) (forall ((A_208 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_208) tptp.zero_zero_int))) (forall ((A_208 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_208) tptp.zero_zero_nat))) (not (forall ((S1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int S1) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int))))))) _let_82 (forall ((K_1 tptp.int)) (= (= (tptp.hAPP_int_int tptp.bit1 K_1) tptp.min) (= K_1 tptp.min))) (forall ((L tptp.int)) (= (= tptp.min (tptp.hAPP_int_int tptp.bit1 L)) (= tptp.min L))) (= (tptp.hAPP_int_int tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K_2 tptp.int)) (not (= (tptp.hAPP_int_int tptp.bit0 K_2) tptp.min))) (forall ((L_2 tptp.int)) (not (= tptp.min (tptp.hAPP_int_int tptp.bit0 L_2)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_100 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_99 tptp.min)) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit1 K_1)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.min)))) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit1 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_101 tptp.min))) (tptp.hBOOL (tptp.hAPP_int_bool _let_100 tptp.pls)) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit0 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_100 tptp.zero_zero_int)) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.bit1 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1))))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit1 K_1)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) tptp.min)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_99 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_98 tptp.min))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.bit0 K_1)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) tptp.min)))) (not (= _let_66 _let_65)) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.bit0 K_1)) tptp.min)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) tptp.min)))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.min) (tptp.hAPP_int_int tptp.bit0 K_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.min) K_1)))) (forall ((Ma tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ma) N_1) tptp.one_one_int) (or (and (= Ma tptp.one_one_int) (= N_1 tptp.one_one_int)) (and (= Ma _let_1) (= N_1 _let_1)))))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))))) (forall ((X_31 tptp.int) (Y_25 tptp.int)) (=> (not (= X_31 Y_25)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_31) Y_25))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_25) X_31))))) (forall ((X_31 tptp.real) (Y_25 tptp.real)) (=> (not (= X_31 Y_25)) (=> (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_31) Y_25))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_25) X_31))))) (forall ((X_31 tptp.rat) (Y_25 tptp.rat)) (=> (not (= X_31 Y_25)) (=> (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_31) Y_25))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Y_25) X_31))))) (forall ((A_207 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_207) A_207))) (forall ((A_207 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_207) A_207))) (forall ((A_207 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_207) A_207))) (forall ((A_207 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_207) A_207))) (forall ((A_207 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_207) A_207))) (forall ((A_207 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_207) A_207))) (forall ((A_207 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_207) A_207))) (forall ((C_88 tptp.quickcheck_code_int) (A_206 tptp.quickcheck_code_int) (B_157 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_206))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int B_157) C_88)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_88)))))) (forall ((C_88 tptp.code_code_numeral) (A_206 tptp.code_code_numeral) (B_157 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_206))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral B_157) C_88)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_88)))))) (forall ((C_88 tptp.rat) (A_206 tptp.rat) (B_157 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_206))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat B_157) C_88)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_88)))))) (forall ((C_88 tptp.real) (A_206 tptp.real) (B_157 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_206))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_157) C_88)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_88)))))) (forall ((C_88 tptp.complex) (A_206 tptp.complex) (B_157 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_206))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex B_157) C_88)) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 C_88)))))) (forall ((C_88 tptp.int) (A_206 tptp.int) (B_157 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_206))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_157) C_88)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_88)))))) (forall ((C_88 tptp.nat) (A_206 tptp.nat) (B_157 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_206))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_157)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_157) C_88)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_88)))))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong B) A) Ma)))) (forall ((K_2 tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong K_2) K_2) M))) (forall ((D_3 tptp.int) (C_1 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.zcong A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 B_2) M)) (=> (= B_2 C_1) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong C_1) D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 D_3) M))))))) (forall ((C_1 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.zcong A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 B_2) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong B_2) C_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 C_1) M)))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) P_3)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 tptp.one_one_int) P_3))))))) (forall ((X_30 tptp.code_code_numeral) (Y_24 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral X_30) Y_24))))) (forall ((X_30 tptp.int) (Y_24 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_30) Y_24))))) (forall ((X_30 tptp.nat) (Y_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_30) Y_24))))) (forall ((X_30 tptp.real) (Y_24 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_30) Y_24))))) (forall ((X_30 tptp.quickcheck_code_int) (Y_24 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int X_30) Y_24))))) (forall ((X_1 tptp.fun_nat_bool) (Y_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_2)) (=> (not (= X_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool X_1) Y_2))))) (forall ((X_1 tptp.fun_int_bool) (Y_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_2)) (=> (not (= X_1 Y_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool X_1) Y_2))))) (forall ((X_30 tptp.rat) (Y_24 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat X_30) Y_24)) (=> (not (= X_30 Y_24)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_30) Y_24))))) (forall ((A_205 tptp.int) (B_156 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_205) B_156) tptp.zero_zero_int) (or (= A_205 tptp.zero_zero_int) (= B_156 tptp.zero_zero_int)))) (forall ((A_205 tptp.nat) (B_156 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_205) B_156) tptp.zero_zero_nat) (or (= A_205 tptp.zero_zero_nat) (= B_156 tptp.zero_zero_nat)))) (forall ((A_205 tptp.real) (B_156 tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_205) B_156) tptp.zero_zero_real) (or (= A_205 tptp.zero_zero_real) (= B_156 tptp.zero_zero_real)))) (forall ((A_205 tptp.code_code_numeral) (B_156 tptp.code_code_numeral)) (=> (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_205) B_156) tptp.zero_z126310315umeral) (or (= A_205 tptp.zero_z126310315umeral) (= B_156 tptp.zero_z126310315umeral)))) (forall ((A_205 tptp.complex) (B_156 tptp.complex)) (=> (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_205) B_156) tptp.zero_zero_complex) (or (= A_205 tptp.zero_zero_complex) (= B_156 tptp.zero_zero_complex)))) (forall ((A_205 tptp.quickcheck_code_int) (B_156 tptp.quickcheck_code_int)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_205) B_156) tptp.zero_z891286103de_int) (or (= A_205 tptp.zero_z891286103de_int) (= B_156 tptp.zero_z891286103de_int)))) (forall ((A_205 tptp.rat) (B_156 tptp.rat)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_205) B_156) tptp.zero_zero_rat) (or (= A_205 tptp.zero_zero_rat) (= B_156 tptp.zero_zero_rat)))) (forall ((B_155 tptp.int) (A_204 tptp.int)) (=> (not (= A_204 tptp.zero_zero_int)) (=> (not (= B_155 tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_204) B_155) tptp.zero_zero_int))))) (forall ((B_155 tptp.nat) (A_204 tptp.nat)) (=> (not (= A_204 tptp.zero_zero_nat)) (=> (not (= B_155 tptp.zero_zero_nat)) (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_204) B_155) tptp.zero_zero_nat))))) (forall ((B_155 tptp.real) (A_204 tptp.real)) (=> (not (= A_204 tptp.zero_zero_real)) (=> (not (= B_155 tptp.zero_zero_real)) (not (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_204) B_155) tptp.zero_zero_real))))) (forall ((B_155 tptp.code_code_numeral) (A_204 tptp.code_code_numeral)) (=> (not (= A_204 tptp.zero_z126310315umeral)) (=> (not (= B_155 tptp.zero_z126310315umeral)) (not (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_204) B_155) tptp.zero_z126310315umeral))))) (forall ((B_155 tptp.complex) (A_204 tptp.complex)) (=> (not (= A_204 tptp.zero_zero_complex)) (=> (not (= B_155 tptp.zero_zero_complex)) (not (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_204) B_155) tptp.zero_zero_complex))))) (forall ((B_155 tptp.quickcheck_code_int) (A_204 tptp.quickcheck_code_int)) (=> (not (= A_204 tptp.zero_z891286103de_int)) (=> (not (= B_155 tptp.zero_z891286103de_int)) (not (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_204) B_155) tptp.zero_z891286103de_int))))) (forall ((B_155 tptp.rat) (A_204 tptp.rat)) (=> (not (= A_204 tptp.zero_zero_rat)) (=> (not (= B_155 tptp.zero_zero_rat)) (not (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_204) B_155) tptp.zero_zero_rat))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A_203 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_203) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_203 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_203) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_203 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_203) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_203 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_203) tptp.zero_z126310315umeral) tptp.zero_z126310315umeral)) (forall ((A_203 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_203) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A_203 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_203) tptp.zero_z891286103de_int) tptp.zero_z891286103de_int)) (forall ((A_203 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_203) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A_202 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) A_202) tptp.zero_zero_int)) (forall ((A_202 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) A_202) tptp.zero_zero_nat)) (forall ((A_202 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.zero_zero_real) A_202) tptp.zero_zero_real)) (forall ((A_202 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral tptp.zero_z126310315umeral) A_202) tptp.zero_z126310315umeral)) (forall ((A_202 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.zero_zero_complex) A_202) tptp.zero_zero_complex)) (forall ((A_202 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int tptp.zero_z891286103de_int) A_202) tptp.zero_z891286103de_int)) (forall ((A_202 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat) A_202) tptp.zero_zero_rat)) _let_97 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_81 (not (= tptp.zero_z126310315umeral tptp.one_on1645066479umeral)) (not (= tptp.zero_zero_complex tptp.one_one_complex)) (not (= tptp.zero_z891286103de_int tptp.one_on1684967323de_int)) (not (= tptp.zero_zero_rat tptp.one_one_rat)) (not (= tptp.one_one_int tptp.zero_zero_int)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_real tptp.zero_zero_real)) (not (= tptp.one_on1645066479umeral tptp.zero_z126310315umeral)) (not (= tptp.one_one_complex tptp.zero_zero_complex)) (not (= tptp.one_on1684967323de_int tptp.zero_z891286103de_int)) (not (= tptp.one_one_rat tptp.zero_zero_rat)) (forall ((A_201 tptp.code_code_numeral) (E_3 tptp.code_code_numeral) (B_154 tptp.code_code_numeral) (C_87 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_201) E_3)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_154) E_3)) C_87)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.int) (E_3 tptp.int) (B_154 tptp.int) (C_87 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_201) E_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_154) E_3)) C_87)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.nat) (E_3 tptp.nat) (B_154 tptp.nat) (C_87 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_201) E_3)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_154) E_3)) C_87)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.real) (E_3 tptp.real) (B_154 tptp.real) (C_87 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_201) E_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_154) E_3)) C_87)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.complex) (E_3 tptp.complex) (B_154 tptp.complex) (C_87 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_201) E_3)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_154) E_3)) C_87)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.quickcheck_code_int) (E_3 tptp.quickcheck_code_int) (B_154 tptp.quickcheck_code_int) (C_87 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_201) E_3)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_154) E_3)) C_87)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_201) B_154)) E_3)) C_87))) (forall ((A_201 tptp.rat) (E_3 tptp.rat) (B_154 tptp.rat) (C_87 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_201) E_3)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_154) E_3)) C_87)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_201) B_154)) E_3)) C_87))) (forall ((A_200 tptp.code_code_numeral) (B_153 tptp.code_code_numeral) (C_86 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_200) B_153)) C_86) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_200) C_86)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_153) C_86)))) (forall ((A_200 tptp.int) (B_153 tptp.int) (C_86 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_200) B_153)) C_86) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_200) C_86)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_153) C_86)))) (forall ((A_200 tptp.nat) (B_153 tptp.nat) (C_86 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_200) B_153)) C_86) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_200) C_86)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_153) C_86)))) (forall ((A_200 tptp.real) (B_153 tptp.real) (C_86 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_200) B_153)) C_86) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_200) C_86)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_153) C_86)))) (forall ((A_200 tptp.complex) (B_153 tptp.complex) (C_86 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_200) B_153)) C_86) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_200) C_86)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_153) C_86)))) (forall ((A_200 tptp.quickcheck_code_int) (B_153 tptp.quickcheck_code_int) (C_86 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_200) B_153)) C_86) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_200) C_86)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_153) C_86)))) (forall ((A_200 tptp.rat) (B_153 tptp.rat) (C_86 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_200) B_153)) C_86) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_200) C_86)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_153) C_86)))) (forall ((N_65 tptp.nat) (A_199 tptp.int)) (=> (not (= A_199 tptp.zero_zero_int)) (not (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_199) N_65) tptp.zero_zero_int)))) (forall ((N_65 tptp.nat) (A_199 tptp.real)) (=> (not (= A_199 tptp.zero_zero_real)) (not (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_199) N_65) tptp.zero_zero_real)))) (forall ((N_65 tptp.nat) (A_199 tptp.complex)) (=> (not (= A_199 tptp.zero_zero_complex)) (not (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_199) N_65) tptp.zero_zero_complex)))) (forall ((N_65 tptp.nat) (A_199 tptp.rat)) (=> (not (= A_199 tptp.zero_zero_rat)) (not (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_199) N_65) tptp.zero_zero_rat)))) (forall ((A_198 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A_198)) (= A_198 tptp.zero_zero_real))) (forall ((A_198 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral tptp.zero_z126310315umeral) A_198)) (= A_198 tptp.zero_z126310315umeral))) (forall ((A_198 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex tptp.zero_zero_complex) A_198)) (= A_198 tptp.zero_zero_complex))) (forall ((A_198 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int tptp.zero_z891286103de_int) A_198)) (= A_198 tptp.zero_z891286103de_int))) (forall ((A_198 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat tptp.zero_zero_rat) A_198)) (= A_198 tptp.zero_zero_rat))) (forall ((A_198 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.zero_zero_int) A_198)) (= A_198 tptp.zero_zero_int))) (forall ((A_198 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_198)) (= A_198 tptp.zero_zero_nat))) (forall ((A_197 tptp.code_code_numeral) (B_152 tptp.code_code_numeral) (N_64 tptp.nat)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_197) B_152)) N_64) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_197) N_64)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_152) N_64)))) (forall ((A_197 tptp.quickcheck_code_int) (B_152 tptp.quickcheck_code_int) (N_64 tptp.nat)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_197) B_152)) N_64) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_197) N_64)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_152) N_64)))) (forall ((A_197 tptp.rat) (B_152 tptp.rat) (N_64 tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_197) B_152)) N_64) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_197) N_64)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_152) N_64)))) (forall ((A_197 tptp.int) (B_152 tptp.int) (N_64 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_197) B_152)) N_64) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_197) N_64)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_152) N_64)))) (forall ((A_197 tptp.nat) (B_152 tptp.nat) (N_64 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_197) B_152)) N_64) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_197) N_64)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_152) N_64)))) (forall ((A_197 tptp.real) (B_152 tptp.real) (N_64 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_197) B_152)) N_64) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_197) N_64)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_152) N_64)))) (forall ((A_197 tptp.complex) (B_152 tptp.complex) (N_64 tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_197) B_152)) N_64) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_197) N_64)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex B_152) N_64)))) (forall ((A_196 tptp.code_code_numeral) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_196) N_63))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral _let_1) A_196) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_196) _let_1)))) (forall ((A_196 tptp.quickcheck_code_int) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_196) N_63))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int _let_1) A_196) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_196) _let_1)))) (forall ((A_196 tptp.rat) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_196) N_63))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat _let_1) A_196) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_196) _let_1)))) (forall ((A_196 tptp.int) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_196) N_63))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) A_196) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_196) _let_1)))) (forall ((A_196 tptp.nat) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_196) N_63))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) A_196) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_196) _let_1)))) (forall ((A_196 tptp.real) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_196) N_63))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_1) A_196) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_196) _let_1)))) (forall ((A_196 tptp.complex) (N_63 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_196) N_63))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex _let_1) A_196) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_196) _let_1)))) (forall ((A_195 tptp.code_code_numeral) (B_151 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_195) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_195) B_151)))) (forall ((A_195 tptp.real) (B_151 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_195) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_195) B_151)))) (forall ((A_195 tptp.complex) (B_151 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_195) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_195) B_151)))) (forall ((A_195 tptp.quickcheck_code_int) (B_151 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_195) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_195) B_151)))) (forall ((A_195 tptp.rat) (B_151 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_195) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_195) B_151)))) (forall ((A_195 tptp.int) (B_151 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_195) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_195) B_151)))) (forall ((A_195 tptp.nat) (B_151 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_195) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_195) B_151)))) (forall ((A_194 tptp.code_code_numeral) (B_150 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_194) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_150) A_194)))) (forall ((A_194 tptp.real) (B_150 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_194) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_150) A_194)))) (forall ((A_194 tptp.complex) (B_150 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_194) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_150) A_194)))) (forall ((A_194 tptp.quickcheck_code_int) (B_150 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_194) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_150) A_194)))) (forall ((A_194 tptp.rat) (B_150 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_194) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_150) A_194)))) (forall ((A_194 tptp.int) (B_150 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_194) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_150) A_194)))) (forall ((A_194 tptp.nat) (B_150 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_194) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_150) A_194)))) (forall ((C_85 tptp.code_code_numeral) (A_193 tptp.code_code_numeral) (B_149 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_193))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_149) C_85)))))) (forall ((C_85 tptp.real) (A_193 tptp.real) (B_149 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_193))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_149) C_85)))))) (forall ((C_85 tptp.complex) (A_193 tptp.complex) (B_149 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_193))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_149) C_85)))))) (forall ((C_85 tptp.quickcheck_code_int) (A_193 tptp.quickcheck_code_int) (B_149 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_193))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_149) C_85)))))) (forall ((C_85 tptp.rat) (A_193 tptp.rat) (B_149 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_193))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_149) C_85)))))) (forall ((C_85 tptp.int) (A_193 tptp.int) (B_149 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_193))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_149) C_85)))))) (forall ((C_85 tptp.nat) (A_193 tptp.nat) (B_149 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_193))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_149)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_149) C_85)))))) (forall ((B_148 tptp.code_code_numeral) (A_192 tptp.code_code_numeral) (C_84 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_192))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_148) C_84)))))) (forall ((B_148 tptp.real) (A_192 tptp.real) (C_84 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_192))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_148) C_84)))))) (forall ((B_148 tptp.complex) (A_192 tptp.complex) (C_84 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_192))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_148) C_84)))))) (forall ((B_148 tptp.quickcheck_code_int) (A_192 tptp.quickcheck_code_int) (C_84 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_192))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_148) C_84)))))) (forall ((B_148 tptp.rat) (A_192 tptp.rat) (C_84 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_192))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_148) C_84)))))) (forall ((B_148 tptp.int) (A_192 tptp.int) (C_84 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_192))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_148) C_84)))))) (forall ((B_148 tptp.nat) (A_192 tptp.nat) (C_84 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_192))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_84)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_148) C_84)))))) (forall ((C_83 tptp.code_code_numeral) (D_16 tptp.code_code_numeral) (A_191 tptp.code_code_numeral) (B_147 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral C_83) D_16)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_191) C_83)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_147) D_16)))))) (forall ((C_83 tptp.real) (D_16 tptp.real) (A_191 tptp.real) (B_147 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real C_83) D_16)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_191) C_83)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_147) D_16)))))) (forall ((C_83 tptp.complex) (D_16 tptp.complex) (A_191 tptp.complex) (B_147 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex C_83) D_16)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_191) C_83)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_147) D_16)))))) (forall ((C_83 tptp.quickcheck_code_int) (D_16 tptp.quickcheck_code_int) (A_191 tptp.quickcheck_code_int) (B_147 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int C_83) D_16)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_191) C_83)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_147) D_16)))))) (forall ((C_83 tptp.rat) (D_16 tptp.rat) (A_191 tptp.rat) (B_147 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat C_83) D_16)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_191) C_83)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_147) D_16)))))) (forall ((C_83 tptp.int) (D_16 tptp.int) (A_191 tptp.int) (B_147 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C_83) D_16)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_191) C_83)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_147) D_16)))))) (forall ((C_83 tptp.nat) (D_16 tptp.nat) (A_191 tptp.nat) (B_147 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_191) B_147)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_83) D_16)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_191) C_83)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_147) D_16)))))) (forall ((A_190 tptp.code_code_numeral) (B_146 tptp.code_code_numeral) (K_7 tptp.code_code_numeral)) (=> (= A_190 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_146) K_7)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral B_146) A_190)))) (forall ((A_190 tptp.real) (B_146 tptp.real) (K_7 tptp.real)) (=> (= A_190 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_146) K_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_146) A_190)))) (forall ((A_190 tptp.complex) (B_146 tptp.complex) (K_7 tptp.complex)) (=> (= A_190 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_146) K_7)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex B_146) A_190)))) (forall ((A_190 tptp.quickcheck_code_int) (B_146 tptp.quickcheck_code_int) (K_7 tptp.quickcheck_code_int)) (=> (= A_190 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_146) K_7)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int B_146) A_190)))) (forall ((A_190 tptp.rat) (B_146 tptp.rat) (K_7 tptp.rat)) (=> (= A_190 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_146) K_7)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat B_146) A_190)))) (forall ((A_190 tptp.int) (B_146 tptp.int) (K_7 tptp.int)) (=> (= A_190 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_146) K_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_146) A_190)))) (forall ((A_190 tptp.nat) (B_146 tptp.nat) (K_7 tptp.nat)) (=> (= A_190 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_146) K_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_146) A_190)))) (forall ((A_189 tptp.code_code_numeral) (B_145 tptp.code_code_numeral) (C_82 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_189) C_82)))) (forall ((A_189 tptp.real) (B_145 tptp.real) (C_82 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_189) C_82)))) (forall ((A_189 tptp.complex) (B_145 tptp.complex) (C_82 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_189) C_82)))) (forall ((A_189 tptp.quickcheck_code_int) (B_145 tptp.quickcheck_code_int) (C_82 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_189) C_82)))) (forall ((A_189 tptp.rat) (B_145 tptp.rat) (C_82 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_189) C_82)))) (forall ((A_189 tptp.int) (B_145 tptp.int) (C_82 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_189) C_82)))) (forall ((A_189 tptp.nat) (B_145 tptp.nat) (C_82 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_189) B_145)) C_82)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_189) C_82)))) (forall ((A_188 tptp.code_code_numeral) (B_144 tptp.code_code_numeral) (C_81 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral B_144) C_81)))) (forall ((A_188 tptp.real) (B_144 tptp.real) (C_81 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real B_144) C_81)))) (forall ((A_188 tptp.complex) (B_144 tptp.complex) (C_81 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex B_144) C_81)))) (forall ((A_188 tptp.quickcheck_code_int) (B_144 tptp.quickcheck_code_int) (C_81 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int B_144) C_81)))) (forall ((A_188 tptp.rat) (B_144 tptp.rat) (C_81 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat B_144) C_81)))) (forall ((A_188 tptp.int) (B_144 tptp.int) (C_81 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_144) C_81)))) (forall ((A_188 tptp.nat) (B_144 tptp.nat) (C_81 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_188) B_144)) C_81)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_144) C_81)))) (forall ((C_80 tptp.code_code_numeral) (A_187 tptp.code_code_numeral) (B_143 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_187))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_143) C_80))))))) (forall ((C_80 tptp.real) (A_187 tptp.real) (B_143 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A_187))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_143) C_80))))))) (forall ((C_80 tptp.complex) (A_187 tptp.complex) (B_143 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A_187))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_143) C_80))))))) (forall ((C_80 tptp.quickcheck_code_int) (A_187 tptp.quickcheck_code_int) (B_143 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_187))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_143) C_80))))))) (forall ((C_80 tptp.rat) (A_187 tptp.rat) (B_143 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A_187))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_143) C_80))))))) (forall ((C_80 tptp.int) (A_187 tptp.int) (B_143 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_187))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_143) C_80))))))) (forall ((C_80 tptp.nat) (A_187 tptp.nat) (B_143 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_187))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_143)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_80)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_143) C_80))))))) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.one_one_int) N_62) tptp.one_one_int)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) N_62) tptp.one_one_nat)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.one_one_real) N_62) tptp.one_one_real)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.one_on1645066479umeral) N_62) tptp.one_on1645066479umeral)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.one_one_complex) N_62) tptp.one_one_complex)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.one_on1684967323de_int) N_62) tptp.one_on1684967323de_int)) (forall ((N_62 tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.one_one_rat) N_62) tptp.one_one_rat)) (forall ((A_186 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real tptp.one_one_real) A_186))) (forall ((A_186 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral tptp.one_on1645066479umeral) A_186))) (forall ((A_186 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex tptp.one_one_complex) A_186))) (forall ((A_186 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int tptp.one_on1684967323de_int) A_186))) (forall ((A_186 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat tptp.one_one_rat) A_186))) (forall ((A_186 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int tptp.one_one_int) A_186))) (forall ((A_186 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_186))) (forall ((N_61 tptp.nat) (X_29 tptp.quickcheck_code_int) (Y_23 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_29) N_61)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.code_code_numeral) (Y_23 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_29) N_61)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.rat) (Y_23 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_29) N_61)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.real) (Y_23 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_29) N_61)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.complex) (Y_23 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_29) N_61)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.int) (Y_23 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_29) N_61)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_23) N_61))))) (forall ((N_61 tptp.nat) (X_29 tptp.nat) (Y_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_29) Y_23)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_29) N_61)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_23) N_61))))) (forall ((M_25 tptp.nat) (A_185 tptp.quickcheck_code_int) (N_60 tptp.nat) (B_142 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_185))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_n522471361de_int _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_n522471361de_int _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.code_code_numeral) (N_60 tptp.nat) (B_142 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_185))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_n1108039445umeral _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_n1108039445umeral _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.rat) (N_60 tptp.nat) (B_142 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_185))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_nat_rat _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_nat_rat _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.real) (N_60 tptp.nat) (B_142 tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_185))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.complex) (N_60 tptp.nat) (B_142 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_185))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_nat_complex _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_nat_complex _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.int) (N_60 tptp.nat) (B_142 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_185))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_25)) B_142)))))) (forall ((M_25 tptp.nat) (A_185 tptp.nat) (N_60 tptp.nat) (B_142 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_185))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 N_60)) B_142)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_25) N_60)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_25)) B_142)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.quickcheck_code_int) (Y_22 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_28) N_59)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.code_code_numeral) (Y_22 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_28) N_59)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.rat) (Y_22 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_28) N_59)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.real) (Y_22 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_28) N_59)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.complex) (Y_22 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_28) N_59)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.int) (Y_22 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_28) N_59)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_22) M_24)))))) (forall ((N_59 tptp.nat) (M_24 tptp.nat) (X_28 tptp.nat) (Y_22 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_28) Y_22)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_59) M_24)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_28) N_59)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_22) M_24)))))) (forall ((A_184 tptp.quickcheck_code_int) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_n522471361de_int _let_1 M_23)) (tptp.hAPP_n522471361de_int _let_1 N_58)))))) (forall ((A_184 tptp.code_code_numeral) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_n1108039445umeral _let_1 M_23)) (tptp.hAPP_n1108039445umeral _let_1 N_58)))))) (forall ((A_184 tptp.rat) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_nat_rat _let_1 M_23)) (tptp.hAPP_nat_rat _let_1 N_58)))))) (forall ((A_184 tptp.real) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_nat_real _let_1 M_23)) (tptp.hAPP_nat_real _let_1 N_58)))))) (forall ((A_184 tptp.complex) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_nat_complex _let_1 M_23)) (tptp.hAPP_nat_complex _let_1 N_58)))))) (forall ((A_184 tptp.int) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int _let_1 M_23)) (tptp.hAPP_nat_int _let_1 N_58)))))) (forall ((A_184 tptp.nat) (M_23 tptp.nat) (N_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_184))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_23) N_58)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M_23)) (tptp.hAPP_nat_nat _let_1 N_58)))))) (forall ((M tptp.nat) (N tptp.nat) (I tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) I)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))))) (forall ((X_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) N_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (= N_1 tptp.zero_zero_nat))))) (forall ((A_183 tptp.quickcheck_code_int) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_183))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_n522471361de_int _let_1 M_22)) N_57)))) (forall ((A_183 tptp.code_code_numeral) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_183))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_n1108039445umeral _let_1 M_22)) N_57)))) (forall ((A_183 tptp.rat) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_183))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_nat_rat _let_1 M_22)) N_57)))) (forall ((A_183 tptp.int) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_183))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_1 M_22)) N_57)))) (forall ((A_183 tptp.nat) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_183))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat _let_1 M_22)) N_57)))) (forall ((A_183 tptp.real) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_183))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real _let_1 M_22)) N_57)))) (forall ((A_183 tptp.complex) (M_22 tptp.nat) (N_57 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_183))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_22) N_57)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_nat_complex _let_1 M_22)) N_57)))) (forall ((B_2 tptp.int) (A_3 tptp.int) (C_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) C_1)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) A_3)))))) (forall ((A_182 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_182) tptp.one_one_nat) A_182)) (forall ((A_182 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_182) tptp.one_one_nat) A_182)) (forall ((M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong M) tptp.zero_zero_int) M))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) tptp.zero_zero_int)) (= A B))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) tptp.one_one_int))) (forall ((A_3 tptp.int) (M tptp.int) (B_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) M)) M))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.zcong C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) D)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) D)) Ma)))))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int D))) (let ((_let_2 (tptp.zcong C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_2 (tptp.hAPP_int_int _let_1 A)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_2 (tptp.hAPP_int_int _let_1 B)) Ma))))))) (forall ((K_2 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) K_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) K_2)) M)))) (forall ((K_2 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int _let_1 B_2)) M))))) (forall ((C_1 tptp.int) (D_3 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong C_1) D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) D_3)) M))))) (forall ((C_1 tptp.int) (D_3 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong C_1) D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_2) D_3)) M))))) (forall ((C_1 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_2) C_1)) M)))) (forall ((Z_1 tptp.nat) (X tptp.int) (Y tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) Z_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y) Z_1)) M)))) (forall ((N_56 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_56)) tptp.one_one_int)) (forall ((N_56 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_56)) tptp.one_one_real)) (forall ((N_56 tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_int_complex tptp.number528085621omplex tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_56)) tptp.one_one_complex)) (forall ((N_56 tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_int_rat tptp.number_number_of_rat tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_56)) tptp.one_one_rat)) (forall ((B_141 tptp.int) (A_181 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_141) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_181) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_181) B_141)) tptp.zero_zero_int))))) (forall ((B_141 tptp.nat) (A_181 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_141) tptp.zero_zero_nat))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_181) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_181) B_141)) tptp.zero_zero_nat))))) (forall ((B_141 tptp.real) (A_181 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_141) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_181) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_181) B_141)) tptp.zero_zero_real))))) (forall ((B_141 tptp.code_code_numeral) (A_181 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (or (and (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_141) tptp.zero_z126310315umeral))) (and (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_181) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_181) B_141)) tptp.zero_z126310315umeral))))) (forall ((B_141 tptp.quickcheck_code_int) (A_181 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_141) tptp.zero_z891286103de_int))) (and (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_181) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_181) B_141)) tptp.zero_z891286103de_int))))) (forall ((B_141 tptp.rat) (A_181 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_181)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_141) tptp.zero_zero_rat))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_181) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_141)))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_181) B_141)) tptp.zero_zero_rat))))) (forall ((B_140 tptp.int) (A_180 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_180)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_140))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_180) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_140) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_180) B_140)))))) (forall ((B_140 tptp.real) (A_180 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_180)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_140))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_180) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_140) tptp.zero_zero_real)))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_180) B_140)))))) (forall ((B_140 tptp.rat) (A_180 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_180)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_140))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_180) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_140) tptp.zero_zero_rat)))) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_180) B_140)))))) (forall ((C_79 tptp.int) (D_15 tptp.int) (A_179 tptp.int) (B_139 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_179) C_79)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_139) D_15))))))))) (forall ((C_79 tptp.nat) (D_15 tptp.nat) (A_179 tptp.nat) (B_139 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_179) C_79)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_139) D_15))))))))) (forall ((C_79 tptp.real) (D_15 tptp.real) (A_179 tptp.real) (B_139 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_179) C_79)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_139) D_15))))))))) (forall ((C_79 tptp.code_code_numeral) (D_15 tptp.code_code_numeral) (A_179 tptp.code_code_numeral) (B_139 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_179) C_79)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_139) D_15))))))))) (forall ((C_79 tptp.quickcheck_code_int) (D_15 tptp.quickcheck_code_int) (A_179 tptp.quickcheck_code_int) (B_139 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_179) C_79)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_139) D_15))))))))) (forall ((C_79 tptp.rat) (D_15 tptp.rat) (A_179 tptp.rat) (B_139 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_179) B_139)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_79) D_15)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_139)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_79)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_179) C_79)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_139) D_15))))))))) (forall ((C_78 tptp.int) (D_14 tptp.int) (A_178 tptp.int) (B_138 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_178) C_78)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_138) D_14))))))))) (forall ((C_78 tptp.nat) (D_14 tptp.nat) (A_178 tptp.nat) (B_138 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_178) C_78)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_138) D_14))))))))) (forall ((C_78 tptp.real) (D_14 tptp.real) (A_178 tptp.real) (B_138 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_178) C_78)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_138) D_14))))))))) (forall ((C_78 tptp.code_code_numeral) (D_14 tptp.code_code_numeral) (A_178 tptp.code_code_numeral) (B_138 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_178) C_78)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_138) D_14))))))))) (forall ((C_78 tptp.quickcheck_code_int) (D_14 tptp.quickcheck_code_int) (A_178 tptp.quickcheck_code_int) (B_138 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_178) C_78)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_138) D_14))))))))) (forall ((C_78 tptp.rat) (D_14 tptp.rat) (A_178 tptp.rat) (B_138 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_178) B_138)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_78) D_14)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_178)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_78)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_178) C_78)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_138) D_14))))))))) (forall ((C_77 tptp.int) (B_137 tptp.int) (A_177 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_77))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_137) A_177)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_77) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_177)) (tptp.hAPP_int_int _let_1 B_137))))))) (forall ((C_77 tptp.real) (B_137 tptp.real) (A_177 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_77))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_137) A_177)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_77) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_177)) (tptp.hAPP_real_real _let_1 B_137))))))) (forall ((C_77 tptp.rat) (B_137 tptp.rat) (A_177 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_77))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_137) A_177)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_77) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_177)) (tptp.hAPP_rat_rat _let_1 B_137))))))) (forall ((C_76 tptp.int) (B_136 tptp.int) (A_176 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_136) A_176)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_76) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_176) C_76)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_136) C_76)))))) (forall ((C_76 tptp.real) (B_136 tptp.real) (A_176 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_136) A_176)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_76) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_176) C_76)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_136) C_76)))))) (forall ((C_76 tptp.rat) (B_136 tptp.rat) (A_176 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_136) A_176)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_76) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_176) C_76)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_136) C_76)))))) (forall ((C_75 tptp.int) (A_175 tptp.int) (B_135 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_75))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_75)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_175)) (tptp.hAPP_int_int _let_1 B_135))))))) (forall ((C_75 tptp.nat) (A_175 tptp.nat) (B_135 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_75))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_75)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_175)) (tptp.hAPP_nat_nat _let_1 B_135))))))) (forall ((C_75 tptp.real) (A_175 tptp.real) (B_135 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_75))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_75)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_175)) (tptp.hAPP_real_real _let_1 B_135))))))) (forall ((C_75 tptp.code_code_numeral) (A_175 tptp.code_code_numeral) (B_135 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_75))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_75)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A_175)) (tptp.hAPP_C498520661umeral _let_1 B_135))))))) (forall ((C_75 tptp.quickcheck_code_int) (A_175 tptp.quickcheck_code_int) (B_135 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_75))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_75)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A_175)) (tptp.hAPP_Q1762011733de_int _let_1 B_135))))))) (forall ((C_75 tptp.rat) (A_175 tptp.rat) (B_135 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_75))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_175) B_135)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_75)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_175)) (tptp.hAPP_rat_rat _let_1 B_135))))))) (forall ((C_74 tptp.int) (A_174 tptp.int) (B_134 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_74))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_74)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_174)) (tptp.hAPP_int_int _let_1 B_134))))))) (forall ((C_74 tptp.nat) (A_174 tptp.nat) (B_134 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_74))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_74)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_174)) (tptp.hAPP_nat_nat _let_1 B_134))))))) (forall ((C_74 tptp.real) (A_174 tptp.real) (B_134 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_74))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_74)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_174)) (tptp.hAPP_real_real _let_1 B_134))))))) (forall ((C_74 tptp.code_code_numeral) (A_174 tptp.code_code_numeral) (B_134 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_74))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_74)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A_174)) (tptp.hAPP_C498520661umeral _let_1 B_134))))))) (forall ((C_74 tptp.quickcheck_code_int) (A_174 tptp.quickcheck_code_int) (B_134 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_74))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_74)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A_174)) (tptp.hAPP_Q1762011733de_int _let_1 B_134))))))) (forall ((C_74 tptp.rat) (A_174 tptp.rat) (B_134 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_74))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_174) B_134)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_74)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_174)) (tptp.hAPP_rat_rat _let_1 B_134))))))) (forall ((C_73 tptp.int) (A_173 tptp.int) (B_133 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_73)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_173) C_73)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_133) C_73)))))) (forall ((C_73 tptp.nat) (A_173 tptp.nat) (B_133 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_73)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_173) C_73)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_133) C_73)))))) (forall ((C_73 tptp.real) (A_173 tptp.real) (B_133 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_73)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_173) C_73)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_133) C_73)))))) (forall ((C_73 tptp.code_code_numeral) (A_173 tptp.code_code_numeral) (B_133 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_73)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_173) C_73)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_133) C_73)))))) (forall ((C_73 tptp.quickcheck_code_int) (A_173 tptp.quickcheck_code_int) (B_133 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_73)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_173) C_73)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_133) C_73)))))) (forall ((C_73 tptp.rat) (A_173 tptp.rat) (B_133 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_173) B_133)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_73)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_173) C_73)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_133) C_73)))))) (forall ((B_132 tptp.int) (A_172 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_172) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_132) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_172) B_132)))))) (forall ((B_132 tptp.real) (A_172 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_172) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_132) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_172) B_132)))))) (forall ((B_132 tptp.rat) (A_172 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_172) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_132) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_172) B_132)))))) (forall ((B_131 tptp.int) (A_171 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_171) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_131)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_171) B_131)) tptp.zero_zero_int))))) (forall ((B_131 tptp.nat) (A_171 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_171) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_131)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_171) B_131)) tptp.zero_zero_nat))))) (forall ((B_131 tptp.real) (A_171 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_171) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_131)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_171) B_131)) tptp.zero_zero_real))))) (forall ((B_131 tptp.code_code_numeral) (A_171 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_171) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) B_131)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_171) B_131)) tptp.zero_z126310315umeral))))) (forall ((B_131 tptp.quickcheck_code_int) (A_171 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_171) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) B_131)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_171) B_131)) tptp.zero_z891286103de_int))))) (forall ((B_131 tptp.rat) (A_171 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_171) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B_131)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_171) B_131)) tptp.zero_zero_rat))))) (forall ((B_130 tptp.int) (A_170 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_170)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_130) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_130) A_170)) tptp.zero_zero_int))))) (forall ((B_130 tptp.nat) (A_170 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_170)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_130) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_130) A_170)) tptp.zero_zero_nat))))) (forall ((B_130 tptp.real) (A_170 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_170)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_130) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_130) A_170)) tptp.zero_zero_real))))) (forall ((B_130 tptp.code_code_numeral) (A_170 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_170)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_130) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_130) A_170)) tptp.zero_z126310315umeral))))) (forall ((B_130 tptp.quickcheck_code_int) (A_170 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_170)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_130) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_130) A_170)) tptp.zero_z891286103de_int))))) (forall ((B_130 tptp.rat) (A_170 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_170)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_130) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_130) A_170)) tptp.zero_zero_rat))))) (forall ((B_129 tptp.int) (A_169 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_169)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_129) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_169) B_129)) tptp.zero_zero_int))))) (forall ((B_129 tptp.nat) (A_169 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_169)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_129) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_169) B_129)) tptp.zero_zero_nat))))) (forall ((B_129 tptp.real) (A_169 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_169)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_129) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_169) B_129)) tptp.zero_zero_real))))) (forall ((B_129 tptp.code_code_numeral) (A_169 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_169)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_129) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_169) B_129)) tptp.zero_z126310315umeral))))) (forall ((B_129 tptp.quickcheck_code_int) (A_169 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_169)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_129) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_169) B_129)) tptp.zero_z891286103de_int))))) (forall ((B_129 tptp.rat) (A_169 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_169)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_129) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_169) B_129)) tptp.zero_zero_rat))))) (forall ((B_128 tptp.int) (A_168 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_168) B_128))))))) (forall ((B_128 tptp.nat) (A_168 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_168) B_128))))))) (forall ((B_128 tptp.real) (A_168 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_168) B_128))))))) (forall ((B_128 tptp.code_code_numeral) (A_168 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_168) B_128))))))) (forall ((B_128 tptp.quickcheck_code_int) (A_168 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_168) B_128))))))) (forall ((B_128 tptp.rat) (A_168 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_168)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_128)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_168) B_128))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int)) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) B)) tptp.zero_zero_real)) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) tptp.zero_zero_real))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) B))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) B))) (or (and (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))))))) (forall ((A_167 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_167) A_167)))) (forall ((A_167 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_167) A_167)))) (forall ((A_167 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_167) A_167)))) (forall ((C_72 tptp.int) (B_127 tptp.int) (A_166 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_72))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_127) A_166)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_72) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_166)) (tptp.hAPP_int_int _let_1 B_127))))))) (forall ((C_72 tptp.real) (B_127 tptp.real) (A_166 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_72))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_127) A_166)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_72) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_166)) (tptp.hAPP_real_real _let_1 B_127))))))) (forall ((C_72 tptp.rat) (B_127 tptp.rat) (A_166 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_72))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_127) A_166)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_72) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_166)) (tptp.hAPP_rat_rat _let_1 B_127))))))) (forall ((C_71 tptp.int) (B_126 tptp.int) (A_165 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_126) A_165)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_71) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_165) C_71)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_126) C_71)))))) (forall ((C_71 tptp.real) (B_126 tptp.real) (A_165 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_126) A_165)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_71) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_165) C_71)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_126) C_71)))))) (forall ((C_71 tptp.rat) (B_126 tptp.rat) (A_165 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_126) A_165)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_71) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_165) C_71)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_126) C_71)))))) (forall ((C_70 tptp.int) (A_164 tptp.int) (B_125 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_70))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_70)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_164)) (tptp.hAPP_int_int _let_1 B_125))))))) (forall ((C_70 tptp.nat) (A_164 tptp.nat) (B_125 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_70))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_70)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_164)) (tptp.hAPP_nat_nat _let_1 B_125))))))) (forall ((C_70 tptp.real) (A_164 tptp.real) (B_125 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_70))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_70)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_164)) (tptp.hAPP_real_real _let_1 B_125))))))) (forall ((C_70 tptp.code_code_numeral) (A_164 tptp.code_code_numeral) (B_125 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_70))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_70)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_164)) (tptp.hAPP_C498520661umeral _let_1 B_125))))))) (forall ((C_70 tptp.quickcheck_code_int) (A_164 tptp.quickcheck_code_int) (B_125 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_70))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_70)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_164)) (tptp.hAPP_Q1762011733de_int _let_1 B_125))))))) (forall ((C_70 tptp.rat) (A_164 tptp.rat) (B_125 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_70))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_164) B_125)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_70)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_164)) (tptp.hAPP_rat_rat _let_1 B_125))))))) (forall ((C_69 tptp.int) (A_163 tptp.int) (B_124 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_69))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_69)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_163)) (tptp.hAPP_int_int _let_1 B_124))))))) (forall ((C_69 tptp.nat) (A_163 tptp.nat) (B_124 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_69))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_69)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_163)) (tptp.hAPP_nat_nat _let_1 B_124))))))) (forall ((C_69 tptp.real) (A_163 tptp.real) (B_124 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_69))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_69)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_163)) (tptp.hAPP_real_real _let_1 B_124))))))) (forall ((C_69 tptp.code_code_numeral) (A_163 tptp.code_code_numeral) (B_124 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_69))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_69)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_163)) (tptp.hAPP_C498520661umeral _let_1 B_124))))))) (forall ((C_69 tptp.quickcheck_code_int) (A_163 tptp.quickcheck_code_int) (B_124 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_69))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_69)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_163)) (tptp.hAPP_Q1762011733de_int _let_1 B_124))))))) (forall ((C_69 tptp.rat) (A_163 tptp.rat) (B_124 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_69))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_163) B_124)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_69)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_163)) (tptp.hAPP_rat_rat _let_1 B_124))))))) (forall ((C_68 tptp.int) (A_162 tptp.int) (B_123 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_68)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_162) C_68)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_123) C_68)))))) (forall ((C_68 tptp.nat) (A_162 tptp.nat) (B_123 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_68)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_162) C_68)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_123) C_68)))))) (forall ((C_68 tptp.real) (A_162 tptp.real) (B_123 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_68)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_162) C_68)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_123) C_68)))))) (forall ((C_68 tptp.code_code_numeral) (A_162 tptp.code_code_numeral) (B_123 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_68)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_162) C_68)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_123) C_68)))))) (forall ((C_68 tptp.quickcheck_code_int) (A_162 tptp.quickcheck_code_int) (B_123 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_68)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_162) C_68)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_123) C_68)))))) (forall ((C_68 tptp.rat) (A_162 tptp.rat) (B_123 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_162) B_123)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_68)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_162) C_68)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_123) C_68)))))) (forall ((B_122 tptp.int) (A_161 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_161) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_122) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_161) B_122)))))) (forall ((B_122 tptp.real) (A_161 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_161) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_122) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_161) B_122)))))) (forall ((B_122 tptp.rat) (A_161 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_161) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_122) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_161) B_122)))))) (forall ((B_121 tptp.int) (A_160 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_160) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_121)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_160) B_121)) tptp.zero_zero_int))))) (forall ((B_121 tptp.nat) (A_160 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_160) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_121)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_160) B_121)) tptp.zero_zero_nat))))) (forall ((B_121 tptp.real) (A_160 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_160) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_121)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_160) B_121)) tptp.zero_zero_real))))) (forall ((B_121 tptp.code_code_numeral) (A_160 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_160) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) B_121)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_160) B_121)) tptp.zero_z126310315umeral))))) (forall ((B_121 tptp.quickcheck_code_int) (A_160 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_160) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) B_121)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_160) B_121)) tptp.zero_z891286103de_int))))) (forall ((B_121 tptp.rat) (A_160 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_160) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) B_121)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_160) B_121)) tptp.zero_zero_rat))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B) A)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B) A)))))) (forall ((B_120 tptp.int) (A_159 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_120)))))) (forall ((B_120 tptp.nat) (A_159 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_120)))))) (forall ((B_120 tptp.real) (A_159 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_120)))))) (forall ((B_120 tptp.code_code_numeral) (A_159 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_120)))))) (forall ((B_120 tptp.quickcheck_code_int) (A_159 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_120)))))) (forall ((B_120 tptp.rat) (A_159 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_120) A_159))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_159)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_120)))))) (forall ((A_158 tptp.int) (B_119 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_119)))))) (forall ((A_158 tptp.nat) (B_119 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_119)))))) (forall ((A_158 tptp.real) (B_119 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_119)))))) (forall ((A_158 tptp.code_code_numeral) (B_119 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_119)))))) (forall ((A_158 tptp.quickcheck_code_int) (B_119 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_119)))))) (forall ((A_158 tptp.rat) (B_119 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_158) B_119))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_158)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_119)))))) (forall ((B_118 tptp.int) (A_157 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_157)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_118) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_118) A_157)) tptp.zero_zero_int))))) (forall ((B_118 tptp.nat) (A_157 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_157)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_118) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_118) A_157)) tptp.zero_zero_nat))))) (forall ((B_118 tptp.real) (A_157 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_157)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_118) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_118) A_157)) tptp.zero_zero_real))))) (forall ((B_118 tptp.code_code_numeral) (A_157 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_157)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_118) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_118) A_157)) tptp.zero_z126310315umeral))))) (forall ((B_118 tptp.quickcheck_code_int) (A_157 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_157)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_118) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_118) A_157)) tptp.zero_z891286103de_int))))) (forall ((B_118 tptp.rat) (A_157 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_157)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_118) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_118) A_157)) tptp.zero_zero_rat))))) (forall ((B_117 tptp.int) (A_156 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_156)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_117) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_156) B_117)) tptp.zero_zero_int))))) (forall ((B_117 tptp.nat) (A_156 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_156)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_117) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_156) B_117)) tptp.zero_zero_nat))))) (forall ((B_117 tptp.real) (A_156 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_156)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_117) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_156) B_117)) tptp.zero_zero_real))))) (forall ((B_117 tptp.code_code_numeral) (A_156 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_156)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_117) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_156) B_117)) tptp.zero_z126310315umeral))))) (forall ((B_117 tptp.quickcheck_code_int) (A_156 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_156)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_117) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_156) B_117)) tptp.zero_z891286103de_int))))) (forall ((B_117 tptp.rat) (A_156 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_156)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_117) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_156) B_117)) tptp.zero_zero_rat))))) (forall ((B_116 tptp.int) (A_155 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_155) B_116))))))) (forall ((B_116 tptp.nat) (A_155 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_155) B_116))))))) (forall ((B_116 tptp.real) (A_155 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_155) B_116))))))) (forall ((B_116 tptp.code_code_numeral) (A_155 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_155) B_116))))))) (forall ((B_116 tptp.quickcheck_code_int) (A_155 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_155) B_116))))))) (forall ((B_116 tptp.rat) (A_155 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_155)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_116)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_155) B_116))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A))))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (or (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B) A))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) C))) (or (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A)))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) C))) (or (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) C))) (or (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B) A)))))) (forall ((A_154 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_154) A_154)) tptp.zero_zero_int)))) (forall ((A_154 tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_154) A_154)) tptp.zero_zero_real)))) (forall ((A_154 tptp.rat)) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_154) A_154)) tptp.zero_zero_rat)))) (forall ((B_115 tptp.code_code_numeral) (C_67 tptp.code_code_numeral) (A_153 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_115))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_153)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_153) C_67))))))) (forall ((B_115 tptp.int) (C_67 tptp.int) (A_153 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_115))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_153)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_153) C_67))))))) (forall ((B_115 tptp.nat) (C_67 tptp.nat) (A_153 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_115))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_153)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_153) C_67))))))) (forall ((B_115 tptp.real) (C_67 tptp.real) (A_153 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_115))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_153)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_153) C_67))))))) (forall ((B_115 tptp.quickcheck_code_int) (C_67 tptp.quickcheck_code_int) (A_153 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_115))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_153)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_153) C_67))))))) (forall ((B_115 tptp.rat) (C_67 tptp.rat) (A_153 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_115))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_153)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_67)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_153) C_67))))))) _let_96 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_95 tptp.zero_zero_int))) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat))) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real))) (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.one_on1645066479umeral) tptp.zero_z126310315umeral))) (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.one_on1684967323de_int) tptp.zero_z891286103de_int))) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat))) _let_94 (tptp.hBOOL (tptp.hAPP_nat_bool _let_92 tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_real_bool _let_62 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_89 tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_88 tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_87 tptp.one_one_rat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int))) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat))) (not (tptp.hBOOL (tptp.hAPP_real_bool _let_64 tptp.zero_zero_real))) (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) tptp.zero_z126310315umeral))) (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) tptp.zero_z891286103de_int))) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat))) (forall ((N_55 tptp.nat) (A_152 tptp.int) (B_114 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_152)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_152) N_55)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_114) N_55)))))) (forall ((N_55 tptp.nat) (A_152 tptp.nat) (B_114 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_152)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_152) N_55)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_114) N_55)))))) (forall ((N_55 tptp.nat) (A_152 tptp.real) (B_114 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_152)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_152) N_55)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_114) N_55)))))) (forall ((N_55 tptp.nat) (A_152 tptp.code_code_numeral) (B_114 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_152)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_152) N_55)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_114) N_55)))))) (forall ((N_55 tptp.nat) (A_152 tptp.quickcheck_code_int) (B_114 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_152)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_152) N_55)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_114) N_55)))))) (forall ((N_55 tptp.nat) (A_152 tptp.rat) (B_114 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_152) B_114)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_152)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_152) N_55)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_114) N_55)))))) (forall ((N_54 tptp.nat) (A_151 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_151) N_54)))))) (forall ((N_54 tptp.nat) (A_151 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_151) N_54)))))) (forall ((N_54 tptp.nat) (A_151 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_151) N_54)))))) (forall ((N_54 tptp.nat) (A_151 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_151) N_54)))))) (forall ((N_54 tptp.nat) (A_151 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_151) N_54)))))) (forall ((N_54 tptp.nat) (A_151 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_151)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_151) N_54)))))) (forall ((N_53 tptp.int) (M_21 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M_21) N_53))))))) (forall ((N_53 tptp.nat) (M_21 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_21) N_53))))))) (forall ((N_53 tptp.real) (M_21 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real M_21) N_53))))))) (forall ((N_53 tptp.code_code_numeral) (M_21 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral M_21) N_53))))))) (forall ((N_53 tptp.quickcheck_code_int) (M_21 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int M_21) N_53))))))) (forall ((N_53 tptp.rat) (M_21 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 M_21)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 N_53)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat M_21) N_53))))))) (forall ((N_52 tptp.nat) (A_150 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_150) N_52)))))) (forall ((N_52 tptp.nat) (A_150 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_150) N_52)))))) (forall ((N_52 tptp.nat) (A_150 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_150) N_52)))))) (forall ((N_52 tptp.nat) (A_150 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_150) N_52)))))) (forall ((N_52 tptp.nat) (A_150 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_150) N_52)))))) (forall ((N_52 tptp.nat) (A_150 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_150)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_150) N_52)))))) (forall ((A_149 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_149) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_149) tptp.one_one_int)))) (forall ((A_149 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_149) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_149) tptp.one_one_nat)))) (forall ((A_149 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_149) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_149) tptp.one_one_real)))) (forall ((A_149 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_149) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_149) tptp.one_on1645066479umeral)))) (forall ((A_149 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_149) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_149) tptp.one_on1684967323de_int)))) (forall ((A_149 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_149) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_149) tptp.one_one_rat)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (or (= C tptp.zero_zero_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A) B)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex C))) (= (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_complex_complex _let_1 A)) (tptp.hAPP_complex_complex _let_1 B))) (or (= C tptp.zero_zero_complex) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (or (= C tptp.zero_zero_rat) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (or (= C tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B)))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) C))) (or (= C tptp.zero_zero_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real A) B))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A) C)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B) C))) (or (= C tptp.zero_zero_complex) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) C))) (or (= C tptp.zero_zero_rat) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat A) B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) C))) (or (= C tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B))))) (forall ((A_148 tptp.int) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) A_148)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_51)) (tptp.hAPP_nat_int _let_1 N_50))))))) (forall ((A_148 tptp.nat) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) A_148)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_51)) (tptp.hAPP_nat_nat _let_1 N_50))))))) (forall ((A_148 tptp.real) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) A_148)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_51)) (tptp.hAPP_nat_real _let_1 N_50))))))) (forall ((A_148 tptp.code_code_numeral) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.one_on1645066479umeral) A_148)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral _let_1 N_51)) (tptp.hAPP_n1108039445umeral _let_1 N_50))))))) (forall ((A_148 tptp.quickcheck_code_int) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.one_on1684967323de_int) A_148)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int _let_1 N_51)) (tptp.hAPP_n522471361de_int _let_1 N_50))))))) (forall ((A_148 tptp.rat) (N_51 tptp.nat) (N_50 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_148))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_51) N_50)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.one_one_rat) A_148)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat _let_1 N_51)) (tptp.hAPP_nat_rat _let_1 N_50))))))) (forall ((N_49 tptp.nat) (A_147 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_147) N_49)))))) (forall ((N_49 tptp.nat) (A_147 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_147) N_49)))))) (forall ((N_49 tptp.nat) (A_147 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_147) N_49)))))) (forall ((N_49 tptp.nat) (A_147 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.one_on1645066479umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_147) N_49)))))) (forall ((N_49 tptp.nat) (A_147 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.one_on1684967323de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_147) N_49)))))) (forall ((N_49 tptp.nat) (A_147 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_147)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_147) N_49)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (= (= (tptp.hAPP_nat_int _let_1 Ma) (tptp.hAPP_nat_int _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A)) (= (= (tptp.hAPP_nat_real _let_1 Ma) (tptp.hAPP_nat_real _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) A)) (= (= (tptp.hAPP_n1108039445umeral _let_1 Ma) (tptp.hAPP_n1108039445umeral _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) A)) (= (= (tptp.hAPP_n522471361de_int _let_1 Ma) (tptp.hAPP_n522471361de_int _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) A)) (= (= (tptp.hAPP_nat_rat _let_1 Ma) (tptp.hAPP_nat_rat _let_1 N_1)) (= Ma N_1))))) (forall ((A tptp.int) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) N_1) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A) N_1) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.real) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A) N_1) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.code_code_numeral) (N_1 tptp.nat)) (= (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A) N_1) tptp.zero_z126310315umeral) (and (= A tptp.zero_z126310315umeral) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.complex) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A) N_1) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.quickcheck_code_int) (N_1 tptp.nat)) (= (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A) N_1) tptp.zero_z891286103de_int) (and (= A tptp.zero_z891286103de_int) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A tptp.rat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A) N_1) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (not (= N_1 tptp.zero_zero_nat))))) (forall ((A_146 tptp.int)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_146) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_146 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_146) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_146 tptp.real)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_146) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_146 tptp.code_code_numeral)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_146) tptp.zero_zero_nat) tptp.one_on1645066479umeral)) (forall ((A_146 tptp.complex)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_146) tptp.zero_zero_nat) tptp.one_one_complex)) (forall ((A_146 tptp.quickcheck_code_int)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_146) tptp.zero_zero_nat) tptp.one_on1684967323de_int)) (forall ((A_146 tptp.rat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_146) tptp.zero_zero_nat) tptp.one_one_rat)) (forall ((A_145 tptp.code_code_numeral) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_145))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 M_20)) (tptp.hAPP_n1108039445umeral _let_1 N_48))))) (forall ((A_145 tptp.quickcheck_code_int) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_145))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 M_20)) (tptp.hAPP_n522471361de_int _let_1 N_48))))) (forall ((A_145 tptp.rat) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_145))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 M_20)) (tptp.hAPP_nat_rat _let_1 N_48))))) (forall ((A_145 tptp.int) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_145))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 M_20)) (tptp.hAPP_nat_int _let_1 N_48))))) (forall ((A_145 tptp.nat) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_145))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 M_20)) (tptp.hAPP_nat_nat _let_1 N_48))))) (forall ((A_145 tptp.real) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_145))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 M_20)) (tptp.hAPP_nat_real _let_1 N_48))))) (forall ((A_145 tptp.complex) (M_20 tptp.nat) (N_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_145))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_20) N_48)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 M_20)) (tptp.hAPP_nat_complex _let_1 N_48))))) (forall ((B_2 tptp.int) (M tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_3)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) M)))))) (forall ((M tptp.int) (Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) Y) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) M)) (= X Y))))))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N) M))))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (exists ((K tptp.int)) (= B (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ma) K)))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_1) tptp.zero_zero_int) P_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_5) X_1)))) (forall ((A tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) A)))) (forall ((M tptp.int) (N tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N))))))) (forall ((C_66 tptp.int) (A_144 tptp.int) (B_113 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_66))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_144)) (tptp.hAPP_int_int _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_66)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_144) B_113)))))) (forall ((C_66 tptp.nat) (A_144 tptp.nat) (B_113 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_66))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_144)) (tptp.hAPP_nat_nat _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_66)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_144) B_113)))))) (forall ((C_66 tptp.real) (A_144 tptp.real) (B_113 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_66))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_144)) (tptp.hAPP_real_real _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_66)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_144) B_113)))))) (forall ((C_66 tptp.code_code_numeral) (A_144 tptp.code_code_numeral) (B_113 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_66))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A_144)) (tptp.hAPP_C498520661umeral _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_66)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_144) B_113)))))) (forall ((C_66 tptp.quickcheck_code_int) (A_144 tptp.quickcheck_code_int) (B_113 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_66))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A_144)) (tptp.hAPP_Q1762011733de_int _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_66)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_144) B_113)))))) (forall ((C_66 tptp.rat) (A_144 tptp.rat) (B_113 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_66))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_144)) (tptp.hAPP_rat_rat _let_1 B_113))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_66)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_144) B_113)))))) (forall ((A_143 tptp.int) (C_65 tptp.int) (B_112 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_143) C_65)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_65)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_143) B_112))))) (forall ((A_143 tptp.nat) (C_65 tptp.nat) (B_112 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_143) C_65)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_65)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_143) B_112))))) (forall ((A_143 tptp.real) (C_65 tptp.real) (B_112 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_143) C_65)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_65)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_143) B_112))))) (forall ((A_143 tptp.code_code_numeral) (C_65 tptp.code_code_numeral) (B_112 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_143) C_65)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_65)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_143) B_112))))) (forall ((A_143 tptp.quickcheck_code_int) (C_65 tptp.quickcheck_code_int) (B_112 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_143) C_65)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_65)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_143) B_112))))) (forall ((A_143 tptp.rat) (C_65 tptp.rat) (B_112 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_143) C_65)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_112) C_65))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_65)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_143) B_112))))) (forall ((C_64 tptp.int) (A_142 tptp.int) (B_111 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_64))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_142)) (tptp.hAPP_int_int _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_64)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_142) B_111)))))) (forall ((C_64 tptp.nat) (A_142 tptp.nat) (B_111 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_64))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_142)) (tptp.hAPP_nat_nat _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_64)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_142) B_111)))))) (forall ((C_64 tptp.real) (A_142 tptp.real) (B_111 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_64))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_142)) (tptp.hAPP_real_real _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_64)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_142) B_111)))))) (forall ((C_64 tptp.code_code_numeral) (A_142 tptp.code_code_numeral) (B_111 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_64))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_142)) (tptp.hAPP_C498520661umeral _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_64)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_142) B_111)))))) (forall ((C_64 tptp.quickcheck_code_int) (A_142 tptp.quickcheck_code_int) (B_111 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_64))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_142)) (tptp.hAPP_Q1762011733de_int _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_64)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_142) B_111)))))) (forall ((C_64 tptp.rat) (A_142 tptp.rat) (B_111 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_64))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_142)) (tptp.hAPP_rat_rat _let_1 B_111))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_64)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_142) B_111)))))) (forall ((C_63 tptp.int) (A_141 tptp.int) (B_110 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_63))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_141)) (tptp.hAPP_int_int _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_63)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_141) B_110)))))) (forall ((C_63 tptp.nat) (A_141 tptp.nat) (B_110 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_63))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_141)) (tptp.hAPP_nat_nat _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_63)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_141) B_110)))))) (forall ((C_63 tptp.real) (A_141 tptp.real) (B_110 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C_63))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_141)) (tptp.hAPP_real_real _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_63)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_141) B_110)))))) (forall ((C_63 tptp.code_code_numeral) (A_141 tptp.code_code_numeral) (B_110 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_63))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_141)) (tptp.hAPP_C498520661umeral _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_63)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_141) B_110)))))) (forall ((C_63 tptp.quickcheck_code_int) (A_141 tptp.quickcheck_code_int) (B_110 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_63))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_141)) (tptp.hAPP_Q1762011733de_int _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_63)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_141) B_110)))))) (forall ((C_63 tptp.rat) (A_141 tptp.rat) (B_110 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C_63))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_141)) (tptp.hAPP_rat_rat _let_1 B_110))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_63)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_141) B_110)))))) (forall ((A_140 tptp.int) (C_62 tptp.int) (B_109 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_140) C_62)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_62)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_140) B_109))))) (forall ((A_140 tptp.nat) (C_62 tptp.nat) (B_109 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_140) C_62)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_62)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_140) B_109))))) (forall ((A_140 tptp.real) (C_62 tptp.real) (B_109 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_140) C_62)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_62)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_140) B_109))))) (forall ((A_140 tptp.code_code_numeral) (C_62 tptp.code_code_numeral) (B_109 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_140) C_62)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_62)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_140) B_109))))) (forall ((A_140 tptp.quickcheck_code_int) (C_62 tptp.quickcheck_code_int) (B_109 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_140) C_62)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_62)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_140) B_109))))) (forall ((A_140 tptp.rat) (C_62 tptp.rat) (B_109 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_140) C_62)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_109) C_62))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_62)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_140) B_109))))) (forall ((A_139 tptp.int) (C_61 tptp.int) (B_108 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_139) C_61)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_61)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_139) B_108))))) (forall ((A_139 tptp.nat) (C_61 tptp.nat) (B_108 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_139) C_61)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_61)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_139) B_108))))) (forall ((A_139 tptp.real) (C_61 tptp.real) (B_108 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_139) C_61)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_61)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_139) B_108))))) (forall ((A_139 tptp.code_code_numeral) (C_61 tptp.code_code_numeral) (B_108 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_139) C_61)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_61)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_139) B_108))))) (forall ((A_139 tptp.quickcheck_code_int) (C_61 tptp.quickcheck_code_int) (B_108 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_139) C_61)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_61)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_139) B_108))))) (forall ((A_139 tptp.rat) (C_61 tptp.rat) (B_108 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_139) C_61)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_108) C_61))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_61)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_139) B_108))))) (forall ((C_60 tptp.int) (D_13 tptp.int) (A_138 tptp.int) (B_107 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_138)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_60)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_138) C_60)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_107) D_13)))))))) (forall ((C_60 tptp.nat) (D_13 tptp.nat) (A_138 tptp.nat) (B_107 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_138)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_60)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_138) C_60)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_107) D_13)))))))) (forall ((C_60 tptp.real) (D_13 tptp.real) (A_138 tptp.real) (B_107 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_138)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_60)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_138) C_60)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_107) D_13)))))))) (forall ((C_60 tptp.code_code_numeral) (D_13 tptp.code_code_numeral) (A_138 tptp.code_code_numeral) (B_107 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_138)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_60)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_138) C_60)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_107) D_13)))))))) (forall ((C_60 tptp.quickcheck_code_int) (D_13 tptp.quickcheck_code_int) (A_138 tptp.quickcheck_code_int) (B_107 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_138)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_60)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_138) C_60)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_107) D_13)))))))) (forall ((C_60 tptp.rat) (D_13 tptp.rat) (A_138 tptp.rat) (B_107 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_138) B_107)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_60) D_13)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_138)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_60)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_138) C_60)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_107) D_13)))))))) (forall ((C_59 tptp.int) (D_12 tptp.int) (A_137 tptp.int) (B_106 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_137)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_59)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_137) C_59)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_106) D_12)))))))) (forall ((C_59 tptp.nat) (D_12 tptp.nat) (A_137 tptp.nat) (B_106 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_137)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_59)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_137) C_59)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_106) D_12)))))))) (forall ((C_59 tptp.real) (D_12 tptp.real) (A_137 tptp.real) (B_106 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_137)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C_59)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_137) C_59)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_106) D_12)))))))) (forall ((C_59 tptp.code_code_numeral) (D_12 tptp.code_code_numeral) (A_137 tptp.code_code_numeral) (B_106 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_137)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) C_59)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_137) C_59)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_106) D_12)))))))) (forall ((C_59 tptp.quickcheck_code_int) (D_12 tptp.quickcheck_code_int) (A_137 tptp.quickcheck_code_int) (B_106 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_137)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) C_59)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_137) C_59)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_106) D_12)))))))) (forall ((C_59 tptp.rat) (D_12 tptp.rat) (A_137 tptp.rat) (B_106 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_137) B_106)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_59) D_12)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_137)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C_59)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_137) C_59)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_106) D_12)))))))) (forall ((C_58 tptp.int) (D_11 tptp.int) (A_136 tptp.int) (B_105 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_136) C_58)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_105) D_11))))))))) (forall ((C_58 tptp.nat) (D_11 tptp.nat) (A_136 tptp.nat) (B_105 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_136) C_58)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_105) D_11))))))))) (forall ((C_58 tptp.real) (D_11 tptp.real) (A_136 tptp.real) (B_105 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_136) C_58)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_105) D_11))))))))) (forall ((C_58 tptp.code_code_numeral) (D_11 tptp.code_code_numeral) (A_136 tptp.code_code_numeral) (B_105 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_136) C_58)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_105) D_11))))))))) (forall ((C_58 tptp.quickcheck_code_int) (D_11 tptp.quickcheck_code_int) (A_136 tptp.quickcheck_code_int) (B_105 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_136) C_58)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_105) D_11))))))))) (forall ((C_58 tptp.rat) (D_11 tptp.rat) (A_136 tptp.rat) (B_105 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_136) B_105)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_58) D_11)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_136)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_58)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_136) C_58)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_105) D_11))))))))) (forall ((C_57 tptp.int) (D_10 tptp.int) (A_135 tptp.int) (B_104 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_104)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_57)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_135) C_57)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_104) D_10)))))))) (forall ((C_57 tptp.nat) (D_10 tptp.nat) (A_135 tptp.nat) (B_104 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) B_104)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_57)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_135) C_57)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_104) D_10)))))))) (forall ((C_57 tptp.real) (D_10 tptp.real) (A_135 tptp.real) (B_104 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) B_104)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_57)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_135) C_57)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_104) D_10)))))))) (forall ((C_57 tptp.code_code_numeral) (D_10 tptp.code_code_numeral) (A_135 tptp.code_code_numeral) (B_104 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) B_104)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_57)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_135) C_57)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_104) D_10)))))))) (forall ((C_57 tptp.quickcheck_code_int) (D_10 tptp.quickcheck_code_int) (A_135 tptp.quickcheck_code_int) (B_104 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) B_104)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_57)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_135) C_57)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_104) D_10)))))))) (forall ((C_57 tptp.rat) (D_10 tptp.rat) (A_135 tptp.rat) (B_104 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_135) B_104)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_57) D_10)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) B_104)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_57)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_135) C_57)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_104) D_10)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B) A)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) B)))))) (forall ((Y_21 tptp.int) (X_27 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_27)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_21)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_21) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_21) X_27)) X_27))))))) (forall ((Y_21 tptp.real) (X_27 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_27)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_21)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_21) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_21) X_27)) X_27))))))) (forall ((Y_21 tptp.rat) (X_27 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 X_27)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Y_21)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat Y_21) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Y_21) X_27)) X_27))))))) (forall ((Y_20 tptp.int) (X_26 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_26)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_20)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_20) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_26) Y_20)) X_26))))))) (forall ((Y_20 tptp.real) (X_26 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_26)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_20)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_20) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_26) Y_20)) X_26))))))) (forall ((Y_20 tptp.rat) (X_26 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 X_26)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Y_20)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat Y_20) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_26) Y_20)) X_26))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_32 _let_93)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_92 _let_91)) (tptp.hBOOL (tptp.hAPP_real_bool _let_62 _let_90)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_89 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.one_on1645066479umeral) tptp.one_on1645066479umeral))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_88 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.one_on1684967323de_int) tptp.one_on1684967323de_int))) (tptp.hBOOL (tptp.hAPP_rat_bool _let_87 _let_86)) (forall ((A_134 tptp.int) (N_47 tptp.nat) (B_103 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_134) N_47)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_103)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_134) B_103))))) (forall ((A_134 tptp.nat) (N_47 tptp.nat) (B_103 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_134) N_47)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_103)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_134) B_103))))) (forall ((A_134 tptp.real) (N_47 tptp.nat) (B_103 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_134) N_47)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_103)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_134) B_103))))) (forall ((A_134 tptp.code_code_numeral) (N_47 tptp.nat) (B_103 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_134) N_47)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) B_103)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_134) B_103))))) (forall ((A_134 tptp.quickcheck_code_int) (N_47 tptp.nat) (B_103 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_134) N_47)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) B_103)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_134) B_103))))) (forall ((A_134 tptp.rat) (N_47 tptp.nat) (B_103 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_134) N_47)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_103) N_47))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B_103)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_134) B_103))))) (forall ((A_133 tptp.int) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_133)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_133) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 N_45)) (tptp.hAPP_nat_int _let_1 N_46)))))))) (forall ((A_133 tptp.nat) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_133)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_133) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N_45)) (tptp.hAPP_nat_nat _let_1 N_46)))))))) (forall ((A_133 tptp.real) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_133)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_133) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 N_45)) (tptp.hAPP_nat_real _let_1 N_46)))))))) (forall ((A_133 tptp.code_code_numeral) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_133)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_133) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral _let_1 N_45)) (tptp.hAPP_n1108039445umeral _let_1 N_46)))))))) (forall ((A_133 tptp.quickcheck_code_int) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_133)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_133) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int _let_1 N_45)) (tptp.hAPP_n522471361de_int _let_1 N_46)))))))) (forall ((A_133 tptp.rat) (N_46 tptp.nat) (N_45 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_133))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_46) N_45)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_133)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_133) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat _let_1 N_45)) (tptp.hAPP_nat_rat _let_1 N_46)))))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_132))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_132)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 M_19)) (tptp.hAPP_nat_int _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_132))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_132)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_19)) (tptp.hAPP_nat_nat _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_132))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_132)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 M_19)) (tptp.hAPP_nat_real _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_132))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) A_132)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral _let_1 M_19)) (tptp.hAPP_n1108039445umeral _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_132))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) A_132)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int _let_1 M_19)) (tptp.hAPP_n522471361de_int _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((M_19 tptp.nat) (N_44 tptp.nat) (A_132 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_132))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) A_132)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat _let_1 M_19)) (tptp.hAPP_nat_rat _let_1 N_44))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_19) N_44)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int _let_1 X_1)) (tptp.hAPP_nat_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 X_1)) (tptp.hAPP_nat_nat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real B))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real _let_1 X_1)) (tptp.hAPP_nat_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) B)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral _let_1 X_1)) (tptp.hAPP_n1108039445umeral _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) B)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int _let_1 X_1)) (tptp.hAPP_n522471361de_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat _let_1 X_1)) (tptp.hAPP_nat_rat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))))) (forall ((N_43 tptp.nat) (A_131 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_131)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_131) _let_1)))))) (forall ((N_43 tptp.nat) (A_131 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_131)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_131) _let_1)))))) (forall ((N_43 tptp.nat) (A_131 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_131)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_131) _let_1)))))) (forall ((N_43 tptp.nat) (A_131 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) A_131)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral _let_1) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_131) _let_1)))))) (forall ((N_43 tptp.nat) (A_131 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) A_131)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int _let_1) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_131) _let_1)))))) (forall ((N_43 tptp.nat) (A_131 tptp.rat)) (let ((_let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_131) N_43))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) A_131)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat _let_1) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_131) _let_1)))))) (forall ((N_42 tptp.nat) (A_130 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_130) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_130) N_42))))))) (forall ((N_42 tptp.nat) (A_130 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_130) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_130) N_42))))))) (forall ((N_42 tptp.nat) (A_130 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_130) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_130) N_42))))))) (forall ((N_42 tptp.nat) (A_130 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_130) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_130) N_42))))))) (forall ((N_42 tptp.nat) (A_130 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_130) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_130) N_42))))))) (forall ((N_42 tptp.nat) (A_130 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_130)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_130) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_130) N_42))))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.zero_z126310315umeral) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on1645066479umeral)) (=> (not _let_2) (= _let_1 tptp.zero_z126310315umeral)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.zero_zero_complex) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.zero_z891286103de_int) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_on1684967323de_int)) (=> (not _let_2) (= _let_1 tptp.zero_z891286103de_int)))))) (forall ((N_41 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.zero_zero_rat) N_41))) (let ((_let_2 (= N_41 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((A_129 tptp.int) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_129)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_40)) (tptp.hAPP_nat_int _let_1 N_39))))))) (forall ((A_129 tptp.nat) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_129)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_40)) (tptp.hAPP_nat_nat _let_1 N_39))))))) (forall ((A_129 tptp.real) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_129)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_40)) (tptp.hAPP_nat_real _let_1 N_39))))))) (forall ((A_129 tptp.code_code_numeral) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) A_129)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral _let_1 N_40)) (tptp.hAPP_n1108039445umeral _let_1 N_39))))))) (forall ((A_129 tptp.quickcheck_code_int) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) A_129)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int _let_1 N_40)) (tptp.hAPP_n522471361de_int _let_1 N_39))))))) (forall ((A_129 tptp.rat) (N_40 tptp.nat) (N_39 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_129))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_40) N_39)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) A_129)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat _let_1 N_40)) (tptp.hAPP_nat_rat _let_1 N_39))))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_128))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_128)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 M_18)) (tptp.hAPP_nat_int _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_128))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) A_128)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_18)) (tptp.hAPP_nat_nat _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_128))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A_128)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 M_18)) (tptp.hAPP_nat_real _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_128))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) A_128)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral _let_1 M_18)) (tptp.hAPP_n1108039445umeral _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_128))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) A_128)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int _let_1 M_18)) (tptp.hAPP_n522471361de_int _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((M_18 tptp.nat) (N_38 tptp.nat) (A_128 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_128))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) A_128)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat _let_1 M_18)) (tptp.hAPP_nat_rat _let_1 N_38))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_18) N_38)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 X_1)) (tptp.hAPP_nat_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 X_1)) (tptp.hAPP_nat_nat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real B))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 X_1)) (tptp.hAPP_nat_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral) B)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral _let_1 X_1)) (tptp.hAPP_n1108039445umeral _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int) B)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int _let_1 X_1)) (tptp.hAPP_n522471361de_int _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat _let_1 X_1)) (tptp.hAPP_nat_rat _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 _let_1))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) X)) _let_2))))) (forall ((M tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) M)) (= X tptp.zero_zero_int))))) (forall ((M tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) M)) (= A_3 tptp.zero_zero_int))))) (forall ((B_2 tptp.int) (M tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (= A_3 B_2)))))))) (forall ((P_3 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y) N))))))) (forall ((Z_1 tptp.nat) (X tptp.int) (Y tptp.nat) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 Y)) tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Y) Z_1))) tptp.one_one_int) P_3))))) (forall ((Y tptp.int) (X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong Y) tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)) tptp.zero_zero_int) P_3))))))) (forall ((V_9 tptp.int) (U_2 tptp.int) (Y_19 tptp.int) (X_25 tptp.int) (A_127 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_25) A_127)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_19) A_127)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 V_9)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int U_2) V_9) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int U_2) X_25)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int V_9) Y_19))) A_127))))))))) (forall ((V_9 tptp.real) (U_2 tptp.real) (Y_19 tptp.real) (X_25 tptp.real) (A_127 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_25) A_127)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_19) A_127)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 V_9)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real U_2) V_9) tptp.one_one_real) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real U_2) X_25)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real V_9) Y_19))) A_127))))))))) (forall ((V_9 tptp.rat) (U_2 tptp.rat) (Y_19 tptp.rat) (X_25 tptp.rat) (A_127 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat X_25) A_127)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat Y_19) A_127)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 U_2)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 V_9)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat U_2) V_9) tptp.one_one_rat) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat U_2) X_25)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat V_9) Y_19))) A_127))))))))) (forall ((N_37 tptp.nat) (A_126 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_126)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_126) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_126) _let_1)) _let_1)))))) (forall ((N_37 tptp.nat) (A_126 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_126)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_126) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_126) _let_1)) _let_1)))))) (forall ((N_37 tptp.nat) (A_126 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_126)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_126) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_126) _let_1)) _let_1)))))) (forall ((N_37 tptp.nat) (A_126 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_126)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_126) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_126) _let_1)) _let_1)))))) (forall ((N_37 tptp.nat) (A_126 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_126)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_126) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_126) _let_1)) _let_1)))))) (forall ((N_37 tptp.nat) (A_126 tptp.rat)) (let ((_let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_126) N_37))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_126)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_126) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_126) _let_1)) _let_1)))))) (forall ((A_125 tptp.int) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_125)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_125) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int _let_1 N_35)) (tptp.hAPP_nat_int _let_1 N_36)))))))) (forall ((A_125 tptp.nat) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_125)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_125) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N_35)) (tptp.hAPP_nat_nat _let_1 N_36)))))))) (forall ((A_125 tptp.real) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_125)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_125) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real _let_1 N_35)) (tptp.hAPP_nat_real _let_1 N_36)))))))) (forall ((A_125 tptp.code_code_numeral) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_125)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_125) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral _let_1 N_35)) (tptp.hAPP_n1108039445umeral _let_1 N_36)))))))) (forall ((A_125 tptp.quickcheck_code_int) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_125)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_125) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int _let_1 N_35)) (tptp.hAPP_n522471361de_int _let_1 N_36)))))))) (forall ((A_125 tptp.rat) (N_36 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_125))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_36) N_35)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_125)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_125) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat _let_1 N_35)) (tptp.hAPP_nat_rat _let_1 N_36)))))))) (forall ((A_124 tptp.int) (N_34 tptp.nat) (B_102 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_124) N_34) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_124 tptp.nat) (N_34 tptp.nat) (B_102 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_124) N_34) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_124 tptp.real) (N_34 tptp.nat) (B_102 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_124) N_34) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_124 tptp.code_code_numeral) (N_34 tptp.nat) (B_102 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_124) N_34) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_124 tptp.quickcheck_code_int) (N_34 tptp.nat) (B_102 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_124) N_34) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((A_124 tptp.rat) (N_34 tptp.nat) (B_102 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_124) N_34) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_102) N_34)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_124)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_102)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_34)) (= A_124 B_102))))))) (forall ((N_33 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_123) N_33))))))) (forall ((N_33 tptp.nat) (A_123 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_123) N_33))))))) (forall ((N_33 tptp.nat) (A_123 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_123) N_33))))))) (forall ((N_33 tptp.nat) (A_123 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_123) N_33))))))) (forall ((N_33 tptp.nat) (A_123 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_123) N_33))))))) (forall ((N_33 tptp.nat) (A_123 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_123)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_33)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_123) N_33))))))) (forall ((X_24 tptp.real) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_24) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_24) N_32))))) (forall ((X_24 tptp.code_code_numeral) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral X_24) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_24) N_32))))) (forall ((X_24 tptp.complex) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_one_complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex X_24) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_24) N_32))))) (forall ((X_24 tptp.quickcheck_code_int) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int X_24) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_24) N_32))))) (forall ((X_24 tptp.rat) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat X_24) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_24) N_32))))) (forall ((X_24 tptp.int) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_24) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_24) N_32))))) (forall ((X_24 tptp.nat) (N_32 tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_32)) (= X_24 tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_24) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_24) N_32))))) _let_83 (tptp.hBOOL (tptp.hAPP_int_bool _let_85 _let_84)) (forall ((J_2 tptp.nat) (K_2 tptp.nat) (M tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 K_2))) (let ((_let_3 (tptp.hAPP_nat_int _let_1 J_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong _let_3) _let_2) M)) (= _let_3 _let_2))))))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) M))))) (= _let_84 _let_5) (=> (not _let_83) (not _let_82)) (forall ((M tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) M)) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime _let_1)) (= (tptp.hAPP_int_int (tptp.legendre (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_1) tptp.one_one_int)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.number_number_of_int N))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 N)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 N)))))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (exists ((P_4 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_4) A_3)))))) (forall ((X_1 tptp.real)) (= (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) X_1)))) (= X_1 tptp.zero_zero_real))) (forall ((V_8 tptp.int) (W_4 tptp.int)) (= (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int V_8) W_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.number_number_of_int V_8)) (tptp.hAPP_int_int tptp.number_number_of_int W_4)))) (forall ((V_8 tptp.int) (W_4 tptp.int)) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int V_8) W_4)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.number267125858f_real V_8)) (tptp.hAPP_int_real tptp.number267125858f_real W_4)))) (forall ((V_8 tptp.int) (W_4 tptp.int)) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int V_8) W_4)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_8)) (tptp.hAPP_int_complex tptp.number528085621omplex W_4)))) (forall ((V_8 tptp.int) (W_4 tptp.int)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int V_8) W_4)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_8)) (tptp.hAPP_int_rat tptp.number_number_of_rat W_4)))) (forall ((K_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1))))) (forall ((Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) tptp.one_one_nat)) (= Ma tptp.one_one_nat))) (forall ((Z_8 tptp.real) (X_23 tptp.real) (Y_18 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real X_23))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_18)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Z_8)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y_18) Z_8))))))) (forall ((Z_8 tptp.complex) (X_23 tptp.complex) (Y_18 tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex X_23))) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 Y_18)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 Z_8)) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex Y_18) Z_8))))))) (forall ((Z_8 tptp.rat) (X_23 tptp.rat) (Y_18 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat X_23))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Y_18)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Z_8)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat Y_18) Z_8))))))) (forall ((Z_8 tptp.int) (X_23 tptp.int) (Y_18 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_23))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_18)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Y_18) Z_8))))))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) tptp.pls) K_2)) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) L_2)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) B_2) C_1) (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_1) B_2)))) (forall ((C_1 tptp.int) (D_3 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong C_1) D_3) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_2) D_3)) M))))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int M) N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)))))) (forall ((Ta tptp.real) (D tptp.real) (D_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) D_1)) (forall ((X_2 tptp.real) (K tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Ta))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real K) D_1))) Ta)))))))) (forall ((Ta tptp.complex) (D tptp.complex) (D_1 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex D) D_1)) (forall ((X_2 tptp.complex) (K tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex D))) (= (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_2) Ta))) (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_2) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex K) D_1))) Ta)))))))) (forall ((Ta tptp.rat) (D tptp.rat) (D_1 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) D_1)) (forall ((X_2 tptp.rat) (K tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D))) (= (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Ta))) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_2) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat K) D_1))) Ta)))))))) (forall ((Ta tptp.int) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int) (K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1))) Ta)))))))) (forall ((Ta tptp.real) (D tptp.real) (D_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) D_1)) (forall ((X_2 tptp.real) (K tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D))) (= (not (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real K) D_1))) Ta))))))))) (forall ((Ta tptp.complex) (D tptp.complex) (D_1 tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex D) D_1)) (forall ((X_2 tptp.complex) (K tptp.complex)) (let ((_let_1 (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex D))) (= (not (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP_complex_bool _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_2) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex K) D_1))) Ta))))))))) (forall ((Ta tptp.rat) (D tptp.rat) (D_1 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) D_1)) (forall ((X_2 tptp.rat) (K tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D))) (= (not (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_2) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat K) D_1))) Ta))))))))) (forall ((Ta tptp.int) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int) (K tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (= (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1))) Ta))))))))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D)) (= C (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B) A)) E_2)) D)))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D)) (= C (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) E_2)) D)))) (forall ((A tptp.complex) (E_2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A) E_2)) C) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B) E_2)) D)) (= C (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex B) A)) E_2)) D)))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D)) (= C (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E_2)) D)))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B)) E_2)) C) D))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B)) E_2)) C) D))) (forall ((A tptp.complex) (E_2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A) E_2)) C) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B) E_2)) D)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A) B)) E_2)) C) D))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E_2)) C) D))) (forall ((V_7 tptp.int) (B_101 tptp.int) (C_56 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int V_7)))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_101) C_56)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 B_101)) (tptp.hAPP_int_int _let_1 C_56))))) (forall ((V_7 tptp.int) (B_101 tptp.real) (C_56 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real V_7)))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_101) C_56)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_1 B_101)) (tptp.hAPP_real_real _let_1 C_56))))) (forall ((V_7 tptp.int) (B_101 tptp.complex) (C_56 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_7)))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex B_101) C_56)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex _let_1 B_101)) (tptp.hAPP_complex_complex _let_1 C_56))))) (forall ((V_7 tptp.int) (B_101 tptp.rat) (C_56 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_7)))) (= (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat B_101) C_56)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat _let_1 B_101)) (tptp.hAPP_rat_rat _let_1 C_56))))) (forall ((A_122 tptp.int) (B_100 tptp.int) (V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_6))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_122) B_100)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_122) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_100) _let_1))))) (forall ((A_122 tptp.real) (B_100 tptp.real) (V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real V_6))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_122) B_100)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_122) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_100) _let_1))))) (forall ((A_122 tptp.complex) (B_100 tptp.complex) (V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex V_6))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_122) B_100)) _let_1) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_122) _let_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_100) _let_1))))) (forall ((A_122 tptp.rat) (B_100 tptp.rat) (V_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat V_6))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A_122) B_100)) _let_1) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_122) _let_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_100) _let_1))))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) L_2)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) L_2)))) (forall ((L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int tptp.pls))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int _let_1 L_2))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_1) L)) tptp.zero_zero_int)))) (forall ((K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N)))))) (forall ((A_3 tptp.int) (R_3 tptp.int) (B_2 tptp.int) (M tptp.int) (C_1 tptp.int) (D_3 tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int R_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) (tptp.hAPP_int_int _let_1 B_2))) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C_1) (tptp.hAPP_int_int _let_1 D_3))) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C_1) N))) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int D_3) N))))))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B)) E_2)) C)) D)))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B)) E_2)) C)) D)))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E_2)) C)) D)))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B) A)) E_2)) D))))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) E_2)) D))))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E_2)) D))))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B) A)) E_2)) D))))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) E_2)) D))))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E_2)) D))))) (forall ((A tptp.int) (E_2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) E_2)) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B)) E_2)) C)) D)))) (forall ((A tptp.real) (E_2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) E_2)) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B)) E_2)) C)) D)))) (forall ((A tptp.rat) (E_2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A) E_2)) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B) E_2)) D))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E_2)) C)) D)))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1)) Ma)) (= N_1 tptp.one_one_nat)))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Ma)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) Ma)) Ma)) (= N_1 tptp.one_one_nat)))) (forall ((V_5 tptp.int) (W_3 tptp.int) (C_55 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.number_number_of_int V_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.number_number_of_int W_3)) C_55)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_5) W_3))) C_55))) (forall ((V_5 tptp.int) (W_3 tptp.int) (C_55 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.number267125858f_real V_5)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.number267125858f_real W_3)) C_55)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_5) W_3))) C_55))) (forall ((V_5 tptp.int) (W_3 tptp.int) (C_55 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_int_complex tptp.number528085621omplex V_5)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_int_complex tptp.number528085621omplex W_3)) C_55)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_5) W_3))) C_55))) (forall ((V_5 tptp.int) (W_3 tptp.int) (C_55 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat V_5)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat W_3)) C_55)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_5) W_3))) C_55))) (forall ((A_3 tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) tptp.one_one_int))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 A_3)) (=> (not (= X _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1)))))))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_2) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)))) (forall ((L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int tptp.pls) (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int tptp.min) L_2)))) (forall ((L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.bit0 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int _let_1 L_2))))) (forall ((L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int tptp.min))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int _let_1 L_2))))) (forall ((A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) _let_1)) tptp.one_one_int) P_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) _let_1) P_5))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (not (= Ma N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((S_1 tptp.nat) (T_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S_1) T_1)) (not (= S_1 T_1)))) (forall ((P_1 tptp.fun_nat_fun_nat_bool) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 N_1) Ma)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) _let_1) (=> (=> (= Ma N_1) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma)) _let_1) _let_1))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M))) (forall ((X tptp.nat) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_1)))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K_2))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (= Ma N_1)))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) K_1)) (= Ma N_1))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= M N)))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_2)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_2))))) (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) I)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) A_3)) tptp.one_one_int) P_3)) (or (= A_3 tptp.one_one_int) (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) A_3)) tptp.one_one_int) P_3)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 tptp.one_one_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) P_3)))))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat)) (= (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((P_2 tptp.bool) (P_1 tptp.bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_2 tptp.bool) (P_1 tptp.bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) tptp.zero_zero_nat)) (= N_1 tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1) tptp.zero_zero_nat) (or (= Ma tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat)))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (or (= Ma N_1) (= K_1 tptp.zero_zero_nat))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) K_1)) (or (= Ma N_1) (= K_1 tptp.zero_zero_nat)))) (forall ((I tptp.nat) (J_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J_2)) I)))) (forall ((J_2 tptp.nat) (I tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) I)) I)))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))))) (forall ((M tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) M)))))) (forall ((M tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) J_2)))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) K_2))))) (forall ((K_2 tptp.nat) (L_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) L_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) L_2)))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat) (L_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K_2) L_2)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) L_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((I tptp.nat) (J_2 tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J_2)) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K_2)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)) (not (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) (= Ma N_1)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) _let_1))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)) (exists ((K tptp.nat)) (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) K))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1))))) (forall ((M tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) M)))))) (forall ((M tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) J_2)))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) K_2))))) (forall ((K_2 tptp.nat) (L_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) L_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) L_2)))))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N)))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N))))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) K_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_2)))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) M)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) K_2))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I)) (tptp.hAPP_nat_nat _let_1 J_2)))))) (forall ((K_2 tptp.nat) (L_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) L_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) L_2)))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1)) (and (= Ma tptp.one_one_nat) (= N_1 tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1) tptp.one_one_nat) (and (= Ma tptp.one_one_nat) (= N_1 tptp.one_one_nat)))) (forall ((X_22 tptp.int) (Y_17 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_22) Y_17)) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_22) _let_2)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_17) _let_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) X_22)) Y_17)))))) (forall ((X_22 tptp.real) (Y_17 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_22) Y_17)) _let_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_22) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_17) _let_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) X_22)) Y_17)))))) (forall ((X_22 tptp.complex) (Y_17 tptp.complex)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_22) Y_17)) _let_2) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_22) _let_2)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_17) _let_2))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_int_complex tptp.number528085621omplex _let_1)) X_22)) Y_17)))))) (forall ((X_22 tptp.rat) (Y_17 tptp.rat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_22) Y_17)) _let_2) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_22) _let_2)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_17) _let_2))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat tptp.number_number_of_rat _let_1)) X_22)) Y_17)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) B_2)) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) _let_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) A_3)) B_2))) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) _let_2)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit1 _let_1))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))) (let ((_let_4 (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2))) (let ((_let_5 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1)))) (let ((_let_6 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_2)))) (let ((_let_7 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) B_2)) _let_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int _let_7 _let_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_6 (tptp.hAPP_nat_int _let_7 _let_5))) B_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_6 A_3)) (tptp.hAPP_nat_int _let_4 _let_5)))) (tptp.hAPP_nat_int _let_4 _let_3))))))))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) K_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) K_2)))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 I)) (tptp.hAPP_nat_nat _let_1 J_2))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((Ma tptp.int) (Ta tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1))) (=> (not (= K_1 tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int _let_1 Ma)) (tptp.hAPP_int_int _let_1 Ta))))))) (forall ((P_1 tptp.fun_Co1584449344l_bool) (L tptp.code_code_numeral)) (= (exists ((X_2 tptp.code_code_numeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool P_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral L) X_2)))) (exists ((X_2 tptp.code_code_numeral)) (and (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral L) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_2) tptp.zero_z126310315umeral))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_real_bool) (L tptp.real)) (= (exists ((X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool P_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real L) X_2)))) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real L) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) tptp.zero_zero_real))) (tptp.hBOOL (tptp.hAPP_real_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_complex_bool) (L tptp.complex)) (= (exists ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool P_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex L) X_2)))) (exists ((X_2 tptp.complex)) (and (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.hAPP_c1403687985x_bool tptp.dvd_dvd_complex L) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_2) tptp.zero_zero_complex))) (tptp.hBOOL (tptp.hAPP_complex_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_Qu817627884t_bool) (L tptp.quickcheck_code_int)) (= (exists ((X_2 tptp.quickcheck_code_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool P_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int L) X_2)))) (exists ((X_2 tptp.quickcheck_code_int)) (and (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int L) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_2) tptp.zero_z891286103de_int))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_rat_bool) (L tptp.rat)) (= (exists ((X_2 tptp.rat)) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat L) X_2)))) (exists ((X_2 tptp.rat)) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat L) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) tptp.zero_zero_rat))) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_int_bool) (L tptp.int)) (= (exists ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int L) X_2)))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int L) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) tptp.zero_zero_int))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_nat_bool) (L tptp.nat)) (= (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat L) X_2)))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat L) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_2) tptp.zero_zero_nat))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_76 _let_66)) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (let ((_let_2 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_1) N))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.legendre A_3) P_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_3) A_3)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3)))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)))))))))) (forall ((Ma tptp.int) (X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes Ma) X_1)) (exists ((Y_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X_1) Ma))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) _let_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) X)) Y)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)) (or (= M tptp.zero_zero_nat) (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N)) M))))) (forall ((K_1 tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_1)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) D)))))))))) (forall ((N_1 tptp.nat) (P_1 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_1)) (exists ((K tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) N_1)) (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) K)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))))))) (forall ((K_1 tptp.int) (P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_1)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) D)))))))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_2) _let_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))) (forall ((A_3 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) X_2) M)) (forall ((Y_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) Y_1) M))) (= Y_1 X_2))))))) (forall ((X tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) X))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) Y_2)) tptp.zero_zero_real)))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) X)))) (not (and _let_1 (not _let_1))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (= X_1 Y_2) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)))) (= _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1)))) (= X_1 Y_2))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)))) (= (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1)))) (and _let_1 (not (= X_1 Y_2)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1)))))) (= _let_1 _let_1))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1))) (= X_1 Y_2))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)))) (=> (not (= A_3 B_2)) (=> _let_1 (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) A_3)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (forall ((Y_2 tptp.nat) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (= X_1 Y_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (=> _let_1 (or (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (= X Y))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)))) (=> _let_1 (=> (not (= A_3 B_2)) (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) A_3)))))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (= A_3 B_2) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) C_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) C_1))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (=> (= B_2 C_1) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) M)) (= M N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)) (= X Y)))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)))))) (forall ((N tptp.nat) (K_2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_1))) (=> (= A_3 B_2) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) C_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) C_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)))))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) Z_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (=> (and _let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (not (= Y X)))) (forall ((P_1 tptp.bool) (X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_2) X_1)))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) (tptp.hBOOL P_1)))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) A_3)))) (=> (= B_2 C_1) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_1) A_3)))))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 X)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z_1)) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z_1) X))))))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) A_3)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Y)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 X)))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 Z_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 Z_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) _let_81 (forall ((Z_1 tptp.real) (W tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z_1)) (= Z_1 W)))) (forall ((K_2 tptp.real) (I tptp.real) (J_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real I))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 J_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real J_2) K_2)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 K_2)))))) (forall ((Z_1 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)) (= X_1 Y_2)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)) (not (= X_1 Y_2))))) (forall ((Z_1 tptp.real) (W tptp.real)) (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Z_1) W)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) Z_1)))) (forall ((W tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real W) W))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((L_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_2))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))))) (forall ((N tptp.nat) (J_2 tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) N)) K_2)))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (forall ((I tptp.nat) (J_2 tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) K_2))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)) N) M)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) N) M)) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((L_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((L_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) L_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) L_2))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) N)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I)) I)))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1)) (= Ma N_1)))))) (forall ((N tptp.nat) (K_2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) K_2)) (tptp.hAPP_nat_nat _let_1 N))))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1))))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_2)))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M)))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma) N_1) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I_1 tptp.nat) (J tptp.nat) (K_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J)))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_1) A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat B_2) C_1)))))) (forall ((I tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) I)) K_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2)) I)))) (forall ((I tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2)) I) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_2) I)) K_2)))) (forall ((I tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I_1) K_1) (= J (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) I_1))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N) M))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J))))) (forall ((I tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K_2))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)) K_2))))) (forall ((J tptp.nat) (K_1 tptp.nat) (I_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K_1)) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1))))) (forall ((I tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K_2)) J_2)))) (forall ((P_1 tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (forall ((D_2 tptp.nat)) (=> (= A (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) D_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))) (forall ((P_1 tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (not (or (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))) (exists ((D_2 tptp.nat)) (and (= A (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) D_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 D_2))))))))) (forall ((B_2 tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_3) B_2))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)))))) (forall ((Z_1 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.one_one_real) Z_1) Z_1)) (forall ((Z_1 tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z_1) W) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real W) Z_1))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Z1))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 Z2)) Z3) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z2) Z3))))) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Z1) Z2)) W) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z1) W)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Z2) W)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) X_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Y_2)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A) C) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B) C)) (= A B)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.hAPP_real_real _let_1 A) (tptp.hAPP_real_real _let_1 B)) (= A B))))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Z_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) Z_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Z_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y))))))) (forall ((X tptp.real) (Y tptp.real) (Z_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Z_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y))))))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Z_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)))))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Z_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Z_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_1) Z_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_2) Z_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 A_3)) (tptp.hAPP_nat_nat _let_1 B_2)))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2) C_1))))) (forall ((X_21 tptp.code_code_numeral) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_n1108039445umeral _let_1 N_31))))) (forall ((X_21 tptp.quickcheck_code_int) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_n522471361de_int _let_1 N_31))))) (forall ((X_21 tptp.rat) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_nat_rat _let_1 N_31))))) (forall ((X_21 tptp.int) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_nat_int _let_1 N_31))))) (forall ((X_21 tptp.nat) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_nat_nat _let_1 N_31))))) (forall ((X_21 tptp.real) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_nat_real _let_1 N_31))))) (forall ((X_21 tptp.complex) (N_31 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_21))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_31)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_31) tptp.one_one_nat))) X_21) (tptp.hAPP_nat_complex _let_1 N_31))))) (forall ((N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y) N))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((P_3 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_3) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X) Y))))) (forall ((A_121 tptp.int) (C_54 tptp.int) (B_99 tptp.int) (D_9 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_121) C_54)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_99) D_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_121) B_99)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C_54) D_9)))) (forall ((A_121 tptp.real) (C_54 tptp.real) (B_99 tptp.real) (D_9 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_121) C_54)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_99) D_9)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_121) B_99)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C_54) D_9)))) (forall ((A_121 tptp.complex) (C_54 tptp.complex) (B_99 tptp.complex) (D_9 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_121) C_54)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_99) D_9)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_121) B_99)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex C_54) D_9)))) (forall ((A_121 tptp.rat) (C_54 tptp.rat) (B_99 tptp.rat) (D_9 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_121) C_54)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_99) D_9)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A_121) B_99)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat C_54) D_9)))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2)) (or (= B_2 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_3) B_2))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) K_1))) (or (= K_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N_1))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) Ma) tptp.one_one_nat) (and (= N_1 tptp.one_one_nat) (= Ma tptp.one_one_nat)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Ma) N_1) tptp.zero_zero_nat) (and (not (= N_1 tptp.zero_zero_nat)) (= Ma tptp.zero_zero_nat)))) (forall ((A_3 tptp.nat) (N tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_2) N))) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) B_2))))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N)) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y))))) (forall ((X_20 tptp.int) (Y_16 tptp.int) (A_120 tptp.int) (B_98 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int X_20))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Y_16)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_120) B_98)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Y_16) B_98))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_20) A_120)) B_98))))) (forall ((X_20 tptp.real) (Y_16 tptp.real) (A_120 tptp.real) (B_98 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real X_20))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_1 Y_16)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_120) B_98)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y_16) B_98))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_20) A_120)) B_98))))) (forall ((X_20 tptp.complex) (Y_16 tptp.complex) (A_120 tptp.complex) (B_98 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex X_20))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex _let_1 Y_16)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_120) B_98)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex Y_16) B_98))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_20) A_120)) B_98))))) (forall ((X_20 tptp.rat) (Y_16 tptp.rat) (A_120 tptp.rat) (B_98 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_20))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat _let_1 Y_16)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_120) B_98)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat Y_16) B_98))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_20) A_120)) B_98))))) (forall ((X_1 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) N_1) tptp.one_one_nat) (or (= X_1 tptp.one_one_nat) (= N_1 tptp.zero_zero_nat)))) (forall ((X_19 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_19) X_19)) tptp.one_one_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_19) tptp.one_one_int)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_19) tptp.one_one_int)))) (forall ((X_19 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_19) X_19)) tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_19) tptp.one_one_real)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_19) tptp.one_one_real)))) (forall ((X_19 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_19) X_19)) tptp.one_one_complex) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_19) tptp.one_one_complex)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_19) tptp.one_one_complex)))) (forall ((X_19 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_19) X_19)) tptp.one_one_rat) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_19) tptp.one_one_rat)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_19) tptp.one_one_rat)))) (forall ((X tptp.nat) (Q_2 tptp.nat) (N tptp.nat) (R_3 tptp.nat)) (=> (= X (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Q_2) N)) R_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) R_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_3) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) X))))))) (forall ((A_3 tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_2)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_2) N) A_3) (forall ((Y_1 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y_1)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_1) N) A_3)) (= Y_1 X_2)))))))) (forall ((A_3 tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (exists ((R_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_1)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real R_1) N) A_3)))))) (forall ((M_17 tptp.int) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int M_17))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M_17) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.nat) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_17))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_17) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.real) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real M_17))) (let ((_let_2 (tptp.hAPP_nat_real _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real M_17) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.code_code_numeral) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral M_17))) (let ((_let_2 (tptp.hAPP_n1108039445umeral _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_on1645066479umeral)) (=> (not _let_3) (= _let_2 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral M_17) (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.complex) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex M_17))) (let ((_let_2 (tptp.hAPP_nat_complex _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex M_17) (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.quickcheck_code_int) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int M_17))) (let ((_let_2 (tptp.hAPP_n522471361de_int _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_on1684967323de_int)) (=> (not _let_3) (= _let_2 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int M_17) (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (forall ((M_17 tptp.rat) (N_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat M_17))) (let ((_let_2 (tptp.hAPP_nat_rat _let_1 N_30))) (let ((_let_3 (= N_30 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat M_17) (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_30) tptp.one_one_nat)))))))))) (= (tptp.hAPP_P1175774780nt_int tptp.twoSqu2000912462sum2sq (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.s) tptp.one_one_int)) _let_80) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_2) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) B_2)))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J)) U)) Ma)) N_1))))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I_1)) U)) N_1)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N_1)))))) (forall ((I tptp.nat) (J_2 tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J_2)) K_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K_2)) J_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (P_3 tptp.int) (Q_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_P1175774780nt_int tptp.twoSqu2000912462sum2sq (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_3) B_2))) (tptp.hAPP_P1175774780nt_int tptp.twoSqu2000912462sum2sq (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2))) (tptp.hAPP_P1175774780nt_int tptp.twoSqu2000912462sum2sq (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 P_3)) (tptp.hAPP_int_int _let_1 Q_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_2 Q_2)) (tptp.hAPP_int_int _let_1 P_3)))))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (or (= K_1 tptp.zero_zero_nat) (= Ma N_1))))) (forall ((I tptp.nat) (U_1 tptp.nat) (J_2 tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) U_1)) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J_2)) U_1)) K_2))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (or (= K_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) N_1)))))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1)) (= Ma (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I_1)) U)) N_1))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) I)) U_1)) N))))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I_1)) U)) N_1)))))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J)) U)) Ma) N_1)))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (J_2 tptp.nat) (I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_2) I)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_2) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I) J_2)) U_1)) M)) N)))) (forall ((U tptp.nat) (Ma tptp.nat) (N_1 tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) Ma)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J)) U)) Ma)) N_1))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.twoSqu1425020248sum2sq X_1)) (exists ((A_2 tptp.int) (B_4 tptp.int)) (= (tptp.hAPP_P1175774780nt_int tptp.twoSqu2000912462sum2sq (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_2) B_4)) X_1)))) (forall ((P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int tptp.zfact (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) P_3)))) (forall ((B_97 tptp.code_code_numeral) (A_119 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) B_97)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_119) B_97))))))) (forall ((B_97 tptp.int) (A_119 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_97)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_119) B_97))))))) (forall ((B_97 tptp.nat) (A_119 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_97)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_119) B_97))))))) (forall ((B_97 tptp.real) (A_119 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_97)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_119) B_97))))))) (forall ((B_97 tptp.quickcheck_code_int) (A_119 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) B_97)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_119) B_97))))))) (forall ((B_97 tptp.rat) (A_119 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_119)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B_97)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_119) B_97))))))) (forall ((B_96 tptp.code_code_numeral) (A_118 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_118)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_118) B_96))))))) (forall ((B_96 tptp.int) (A_118 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_118)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_118) B_96))))))) (forall ((B_96 tptp.nat) (A_118 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_118)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_118) B_96))))))) (forall ((B_96 tptp.real) (A_118 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_118)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_118) B_96))))))) (forall ((B_96 tptp.quickcheck_code_int) (A_118 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_118)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_118) B_96))))))) (forall ((B_96 tptp.rat) (A_118 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_118)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_96)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_118) B_96))))))) (forall ((B_95 tptp.code_code_numeral) (C_53 tptp.code_code_numeral) (A_117 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_117)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_95) C_53)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_95) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_117) C_53)))))) (forall ((B_95 tptp.int) (C_53 tptp.int) (A_117 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_117)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_95) C_53)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_95) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_117) C_53)))))) (forall ((B_95 tptp.nat) (C_53 tptp.nat) (A_117 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_117)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_95) C_53)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_95) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_117) C_53)))))) (forall ((B_95 tptp.real) (C_53 tptp.real) (A_117 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_117)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_95) C_53)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_95) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_117) C_53)))))) (forall ((B_95 tptp.quickcheck_code_int) (C_53 tptp.quickcheck_code_int) (A_117 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_117)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_95) C_53)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_95) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_117) C_53)))))) (forall ((B_95 tptp.rat) (C_53 tptp.rat) (A_117 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_117)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_95) C_53)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_95) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_117) C_53)))))) (forall ((B_94 tptp.code_code_numeral) (C_52 tptp.code_code_numeral) (A_116 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_94))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_116)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_116) C_52))))))) (forall ((B_94 tptp.int) (C_52 tptp.int) (A_116 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_94))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_116)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_116) C_52))))))) (forall ((B_94 tptp.nat) (C_52 tptp.nat) (A_116 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_94))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_116)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_116) C_52))))))) (forall ((B_94 tptp.real) (C_52 tptp.real) (A_116 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_94))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_116)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_116) C_52))))))) (forall ((B_94 tptp.quickcheck_code_int) (C_52 tptp.quickcheck_code_int) (A_116 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_94))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_116)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_116) C_52))))))) (forall ((B_94 tptp.rat) (C_52 tptp.rat) (A_116 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_94))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_116)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_52)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_116) C_52))))))) (forall ((B_93 tptp.code_code_numeral) (A_115 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_115) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_93) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_115) B_93)) tptp.zero_z126310315umeral))))) (forall ((B_93 tptp.int) (A_115 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_115) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_93) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_115) B_93)) tptp.zero_zero_int))))) (forall ((B_93 tptp.nat) (A_115 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_115) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_93) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_115) B_93)) tptp.zero_zero_nat))))) (forall ((B_93 tptp.real) (A_115 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_115) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_93) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_115) B_93)) tptp.zero_zero_real))))) (forall ((B_93 tptp.quickcheck_code_int) (A_115 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_115) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_93) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_115) B_93)) tptp.zero_z891286103de_int))))) (forall ((B_93 tptp.rat) (A_115 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_115) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_93) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_115) B_93)) tptp.zero_zero_rat))))) (forall ((B_92 tptp.code_code_numeral) (A_114 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_114) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_92) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_114) B_92)) tptp.zero_z126310315umeral))))) (forall ((B_92 tptp.int) (A_114 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_114) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_92) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_114) B_92)) tptp.zero_zero_int))))) (forall ((B_92 tptp.nat) (A_114 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_114) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_92) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_114) B_92)) tptp.zero_zero_nat))))) (forall ((B_92 tptp.real) (A_114 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_114) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_92) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_114) B_92)) tptp.zero_zero_real))))) (forall ((B_92 tptp.quickcheck_code_int) (A_114 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_114) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_92) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_114) B_92)) tptp.zero_z891286103de_int))))) (forall ((B_92 tptp.rat) (A_114 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_114) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_92) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_114) B_92)) tptp.zero_zero_rat))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.inv P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) P_3)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_1 A_3)) A_3))))))) (forall ((X_1 tptp.int)) (= (= tptp.zero_zero_int X_1) (= X_1 tptp.zero_zero_int))) (forall ((X_1 tptp.nat)) (= (= tptp.zero_zero_nat X_1) (= X_1 tptp.zero_zero_nat))) (forall ((X_1 tptp.real)) (= (= tptp.zero_zero_real X_1) (= X_1 tptp.zero_zero_real))) (forall ((X_1 tptp.code_code_numeral)) (= (= tptp.zero_z126310315umeral X_1) (= X_1 tptp.zero_z126310315umeral))) (forall ((X_1 tptp.complex)) (= (= tptp.zero_zero_complex X_1) (= X_1 tptp.zero_zero_complex))) (forall ((X_1 tptp.quickcheck_code_int)) (= (= tptp.zero_z891286103de_int X_1) (= X_1 tptp.zero_z891286103de_int))) (forall ((X_1 tptp.rat)) (= (= tptp.zero_zero_rat X_1) (= X_1 tptp.zero_zero_rat))) (forall ((A_113 tptp.code_code_numeral) (B_91 tptp.code_code_numeral) (C_51 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_113))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral _let_1 B_91)) C_51) (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_91) C_51))))) (forall ((A_113 tptp.int) (B_91 tptp.int) (C_51 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_113))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 B_91)) C_51) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_91) C_51))))) (forall ((A_113 tptp.nat) (B_91 tptp.nat) (C_51 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_113))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 B_91)) C_51) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_91) C_51))))) (forall ((A_113 tptp.real) (B_91 tptp.real) (C_51 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real A_113))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 B_91)) C_51) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_91) C_51))))) (forall ((A_113 tptp.complex) (B_91 tptp.complex) (C_51 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex A_113))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex _let_1 B_91)) C_51) (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex B_91) C_51))))) (forall ((A_113 tptp.quickcheck_code_int) (B_91 tptp.quickcheck_code_int) (C_51 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_113))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int _let_1 B_91)) C_51) (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_91) C_51))))) (forall ((A_113 tptp.rat) (B_91 tptp.rat) (C_51 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_113))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat _let_1 B_91)) C_51) (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat B_91) C_51))))) (forall ((B_90 tptp.code_code_numeral) (A_112 tptp.code_code_numeral) (C_50 tptp.code_code_numeral)) (=> (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_90) A_112) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.int) (A_112 tptp.int) (C_50 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_90) A_112) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.nat) (A_112 tptp.nat) (C_50 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_90) A_112) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.real) (A_112 tptp.real) (C_50 tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_90) A_112) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.complex) (A_112 tptp.complex) (C_50 tptp.complex)) (=> (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_90) A_112) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.quickcheck_code_int) (A_112 tptp.quickcheck_code_int) (C_50 tptp.quickcheck_code_int)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_90) A_112) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_50) A_112)) (= B_90 C_50))) (forall ((B_90 tptp.rat) (A_112 tptp.rat) (C_50 tptp.rat)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_90) A_112) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_50) A_112)) (= B_90 C_50))) (forall ((A_111 tptp.code_code_numeral) (B_89 tptp.code_code_numeral) (C_49 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_111))) (=> (= (tptp.hAPP_C498520661umeral _let_1 B_89) (tptp.hAPP_C498520661umeral _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.int) (B_89 tptp.int) (C_49 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_111))) (=> (= (tptp.hAPP_int_int _let_1 B_89) (tptp.hAPP_int_int _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.nat) (B_89 tptp.nat) (C_49 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_111))) (=> (= (tptp.hAPP_nat_nat _let_1 B_89) (tptp.hAPP_nat_nat _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.real) (B_89 tptp.real) (C_49 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_111))) (=> (= (tptp.hAPP_real_real _let_1 B_89) (tptp.hAPP_real_real _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.complex) (B_89 tptp.complex) (C_49 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_111))) (=> (= (tptp.hAPP_complex_complex _let_1 B_89) (tptp.hAPP_complex_complex _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.quickcheck_code_int) (B_89 tptp.quickcheck_code_int) (C_49 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_111))) (=> (= (tptp.hAPP_Q1762011733de_int _let_1 B_89) (tptp.hAPP_Q1762011733de_int _let_1 C_49)) (= B_89 C_49)))) (forall ((A_111 tptp.rat) (B_89 tptp.rat) (C_49 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_111))) (=> (= (tptp.hAPP_rat_rat _let_1 B_89) (tptp.hAPP_rat_rat _let_1 C_49)) (= B_89 C_49)))) (forall ((A_110 tptp.code_code_numeral) (B_88 tptp.code_code_numeral) (C_48 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_110))) (=> (= (tptp.hAPP_C498520661umeral _let_1 B_88) (tptp.hAPP_C498520661umeral _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.int) (B_88 tptp.int) (C_48 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_110))) (=> (= (tptp.hAPP_int_int _let_1 B_88) (tptp.hAPP_int_int _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.nat) (B_88 tptp.nat) (C_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_110))) (=> (= (tptp.hAPP_nat_nat _let_1 B_88) (tptp.hAPP_nat_nat _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.real) (B_88 tptp.real) (C_48 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_110))) (=> (= (tptp.hAPP_real_real _let_1 B_88) (tptp.hAPP_real_real _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.complex) (B_88 tptp.complex) (C_48 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_110))) (=> (= (tptp.hAPP_complex_complex _let_1 B_88) (tptp.hAPP_complex_complex _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.quickcheck_code_int) (B_88 tptp.quickcheck_code_int) (C_48 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_110))) (=> (= (tptp.hAPP_Q1762011733de_int _let_1 B_88) (tptp.hAPP_Q1762011733de_int _let_1 C_48)) (= B_88 C_48)))) (forall ((A_110 tptp.rat) (B_88 tptp.rat) (C_48 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_110))) (=> (= (tptp.hAPP_rat_rat _let_1 B_88) (tptp.hAPP_rat_rat _let_1 C_48)) (= B_88 C_48)))) (forall ((B tptp.code_code_numeral) (A tptp.code_code_numeral) (C tptp.code_code_numeral)) (= (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B) A) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C) A)) (= B C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C) A)) (= B C))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B) A) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B) A) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex C) A)) (= B C))) (forall ((B tptp.quickcheck_code_int) (A tptp.quickcheck_code_int) (C tptp.quickcheck_code_int)) (= (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B) A) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B) A) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C) A)) (= B C))) (forall ((A tptp.code_code_numeral) (B tptp.code_code_numeral) (C tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A))) (= (= (tptp.hAPP_C498520661umeral _let_1 B) (tptp.hAPP_C498520661umeral _let_1 C)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A))) (= (= (tptp.hAPP_int_int _let_1 B) (tptp.hAPP_int_int _let_1 C)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (= (tptp.hAPP_nat_nat _let_1 B) (tptp.hAPP_nat_nat _let_1 C)) (= B C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A))) (= (= (tptp.hAPP_real_real _let_1 B) (tptp.hAPP_real_real _let_1 C)) (= B C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A))) (= (= (tptp.hAPP_complex_complex _let_1 B) (tptp.hAPP_complex_complex _let_1 C)) (= B C)))) (forall ((A tptp.quickcheck_code_int) (B tptp.quickcheck_code_int) (C tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A))) (= (= (tptp.hAPP_Q1762011733de_int _let_1 B) (tptp.hAPP_Q1762011733de_int _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (= (tptp.hAPP_rat_rat _let_1 B) (tptp.hAPP_rat_rat _let_1 C)) (= B C)))) (forall ((A_109 tptp.code_code_numeral) (B_87 tptp.code_code_numeral) (C_47 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_109))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral _let_1 B_87)) C_47) (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_87) C_47))))) (forall ((A_109 tptp.int) (B_87 tptp.int) (C_47 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_109))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_87)) C_47) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_87) C_47))))) (forall ((A_109 tptp.nat) (B_87 tptp.nat) (C_47 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_109))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_87)) C_47) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_87) C_47))))) (forall ((A_109 tptp.real) (B_87 tptp.real) (C_47 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_109))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_87)) C_47) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_87) C_47))))) (forall ((A_109 tptp.complex) (B_87 tptp.complex) (C_47 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_109))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_87)) C_47) (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_87) C_47))))) (forall ((A_109 tptp.quickcheck_code_int) (B_87 tptp.quickcheck_code_int) (C_47 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_109))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int _let_1 B_87)) C_47) (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_87) C_47))))) (forall ((A_109 tptp.rat) (B_87 tptp.rat) (C_47 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_109))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat _let_1 B_87)) C_47) (tptp.hAPP_rat_rat _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_87) C_47))))) (forall ((X_1 tptp.int)) (= (= tptp.one_one_int X_1) (= X_1 tptp.one_one_int))) (forall ((X_1 tptp.nat)) (= (= tptp.one_one_nat X_1) (= X_1 tptp.one_one_nat))) (forall ((X_1 tptp.real)) (= (= tptp.one_one_real X_1) (= X_1 tptp.one_one_real))) (forall ((X_1 tptp.code_code_numeral)) (= (= tptp.one_on1645066479umeral X_1) (= X_1 tptp.one_on1645066479umeral))) (forall ((X_1 tptp.complex)) (= (= tptp.one_one_complex X_1) (= X_1 tptp.one_one_complex))) (forall ((X_1 tptp.quickcheck_code_int)) (= (= tptp.one_on1684967323de_int X_1) (= X_1 tptp.one_on1684967323de_int))) (forall ((X_1 tptp.rat)) (= (= tptp.one_one_rat X_1) (= X_1 tptp.one_one_rat))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C) D)) (= (= A B) (= C D)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) D)) (= (= A B) (= C D)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A) B) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex C) D)) (= (= A B) (= C D)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))) (forall ((A_108 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_108) tptp.zero_z126310315umeral) A_108)) (forall ((A_108 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_108) tptp.zero_zero_int) A_108)) (forall ((A_108 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_108) tptp.zero_zero_nat) A_108)) (forall ((A_108 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_108) tptp.zero_zero_real) A_108)) (forall ((A_108 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_108) tptp.zero_zero_complex) A_108)) (forall ((A_108 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_108) tptp.zero_z891286103de_int) A_108)) (forall ((A_108 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_108) tptp.zero_zero_rat) A_108)) (forall ((A_107 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_107) tptp.zero_z126310315umeral) A_107)) (forall ((A_107 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_107) tptp.zero_zero_int) A_107)) (forall ((A_107 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_107) tptp.zero_zero_nat) A_107)) (forall ((A_107 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_107) tptp.zero_zero_real) A_107)) (forall ((A_107 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_107) tptp.zero_zero_complex) A_107)) (forall ((A_107 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_107) tptp.zero_z891286103de_int) A_107)) (forall ((A_107 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_107) tptp.zero_zero_rat) A_107)) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))) (forall ((A_106 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.zero_z126310315umeral) A_106) A_106)) (forall ((A_106 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A_106) A_106)) (forall ((A_106 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A_106) A_106)) (forall ((A_106 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.zero_zero_real) A_106) A_106)) (forall ((A_106 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.zero_zero_complex) A_106) A_106)) (forall ((A_106 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.zero_z891286103de_int) A_106) A_106)) (forall ((A_106 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A_106) A_106)) (forall ((A_105 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.zero_z126310315umeral) A_105) A_105)) (forall ((A_105 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A_105) A_105)) (forall ((A_105 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A_105) A_105)) (forall ((A_105 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.zero_zero_real) A_105) A_105)) (forall ((A_105 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.zero_zero_complex) A_105) A_105)) (forall ((A_105 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.zero_z891286103de_int) A_105) A_105)) (forall ((A_105 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) A_105) A_105)) (forall ((C_46 tptp.code_code_numeral) (A_104 tptp.code_code_numeral) (B_86 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_46))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A_104)) (tptp.hAPP_C498520661umeral _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_104) B_86))))) (forall ((C_46 tptp.int) (A_104 tptp.int) (B_86 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_46))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_104)) (tptp.hAPP_int_int _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_104) B_86))))) (forall ((C_46 tptp.nat) (A_104 tptp.nat) (B_86 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_46))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_104)) (tptp.hAPP_nat_nat _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_104) B_86))))) (forall ((C_46 tptp.real) (A_104 tptp.real) (B_86 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_46))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_104)) (tptp.hAPP_real_real _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_104) B_86))))) (forall ((C_46 tptp.quickcheck_code_int) (A_104 tptp.quickcheck_code_int) (B_86 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_46))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A_104)) (tptp.hAPP_Q1762011733de_int _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_104) B_86))))) (forall ((C_46 tptp.rat) (A_104 tptp.rat) (B_86 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_46))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_104)) (tptp.hAPP_rat_rat _let_1 B_86))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_104) B_86))))) (forall ((A_103 tptp.code_code_numeral) (C_45 tptp.code_code_numeral) (B_85 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_103) C_45)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_85) C_45))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_103) B_85)))) (forall ((A_103 tptp.int) (C_45 tptp.int) (B_85 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_103) C_45)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_85) C_45))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_103) B_85)))) (forall ((A_103 tptp.nat) (C_45 tptp.nat) (B_85 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_103) C_45)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_85) C_45))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_103) B_85)))) (forall ((A_103 tptp.real) (C_45 tptp.real) (B_85 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_103) C_45)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_85) C_45))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_103) B_85)))) (forall ((A_103 tptp.quickcheck_code_int) (C_45 tptp.quickcheck_code_int) (B_85 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_103) C_45)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_85) C_45))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_103) B_85)))) (forall ((A_103 tptp.rat) (C_45 tptp.rat) (B_85 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_103) C_45)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_85) C_45))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_103) B_85)))) (forall ((C_44 tptp.code_code_numeral) (D_8 tptp.code_code_numeral) (A_102 tptp.code_code_numeral) (B_84 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral C_44) D_8)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_102) C_44)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_84) D_8)))))) (forall ((C_44 tptp.int) (D_8 tptp.int) (A_102 tptp.int) (B_84 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_44) D_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_102) C_44)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_84) D_8)))))) (forall ((C_44 tptp.nat) (D_8 tptp.nat) (A_102 tptp.nat) (B_84 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_44) D_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_102) C_44)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_84) D_8)))))) (forall ((C_44 tptp.real) (D_8 tptp.real) (A_102 tptp.real) (B_84 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_44) D_8)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_102) C_44)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_84) D_8)))))) (forall ((C_44 tptp.quickcheck_code_int) (D_8 tptp.quickcheck_code_int) (A_102 tptp.quickcheck_code_int) (B_84 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int C_44) D_8)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_102) C_44)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_84) D_8)))))) (forall ((C_44 tptp.rat) (D_8 tptp.rat) (A_102 tptp.rat) (B_84 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_102) B_84)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_44) D_8)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_102) C_44)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_84) D_8)))))) (forall ((C_43 tptp.code_code_numeral) (A_101 tptp.code_code_numeral) (B_83 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_43))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_101) B_83)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A_101)) (tptp.hAPP_C498520661umeral _let_1 B_83)))))) (forall ((C_43 tptp.int) (A_101 tptp.int) (B_83 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_43))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_101) B_83)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_101)) (tptp.hAPP_int_int _let_1 B_83)))))) (forall ((C_43 tptp.nat) (A_101 tptp.nat) (B_83 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_43))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_101) B_83)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_101)) (tptp.hAPP_nat_nat _let_1 B_83)))))) (forall ((C_43 tptp.real) (A_101 tptp.real) (B_83 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_43))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_101) B_83)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_101)) (tptp.hAPP_real_real _let_1 B_83)))))) (forall ((C_43 tptp.quickcheck_code_int) (A_101 tptp.quickcheck_code_int) (B_83 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_43))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_101) B_83)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A_101)) (tptp.hAPP_Q1762011733de_int _let_1 B_83)))))) (forall ((C_43 tptp.rat) (A_101 tptp.rat) (B_83 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_43))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_101) B_83)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A_101)) (tptp.hAPP_rat_rat _let_1 B_83)))))) (forall ((C_42 tptp.code_code_numeral) (A_100 tptp.code_code_numeral) (B_82 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_100) B_82)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_100) C_42)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_82) C_42))))) (forall ((C_42 tptp.int) (A_100 tptp.int) (B_82 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_100) B_82)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_100) C_42)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_82) C_42))))) (forall ((C_42 tptp.nat) (A_100 tptp.nat) (B_82 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_100) B_82)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_100) C_42)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_82) C_42))))) (forall ((C_42 tptp.real) (A_100 tptp.real) (B_82 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_100) B_82)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_100) C_42)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_82) C_42))))) (forall ((C_42 tptp.quickcheck_code_int) (A_100 tptp.quickcheck_code_int) (B_82 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_100) B_82)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_100) C_42)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_82) C_42))))) (forall ((C_42 tptp.rat) (A_100 tptp.rat) (B_82 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_100) B_82)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_100) C_42)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_82) C_42))))) (forall ((C tptp.code_code_numeral) (A tptp.code_code_numeral) (B tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C))) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral _let_1 A)) (tptp.hAPP_C498520661umeral _let_1 B))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A)) (tptp.hAPP_nat_nat _let_1 B))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B))))) (forall ((C tptp.quickcheck_code_int) (A tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C))) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int _let_1 A)) (tptp.hAPP_Q1762011733de_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.code_code_numeral) (C tptp.code_code_numeral) (B tptp.code_code_numeral)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A) C)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B) C))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B) C))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)))) (forall ((A tptp.quickcheck_code_int) (C tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A) C)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B) C))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) B)))) (forall ((C_41 tptp.code_code_numeral) (A_99 tptp.code_code_numeral) (B_81 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_41))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_99)) (tptp.hAPP_C498520661umeral _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_99) B_81))))) (forall ((C_41 tptp.int) (A_99 tptp.int) (B_81 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_41))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_99)) (tptp.hAPP_int_int _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_99) B_81))))) (forall ((C_41 tptp.nat) (A_99 tptp.nat) (B_81 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_41))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_99)) (tptp.hAPP_nat_nat _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_99) B_81))))) (forall ((C_41 tptp.real) (A_99 tptp.real) (B_81 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_41))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_99)) (tptp.hAPP_real_real _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_99) B_81))))) (forall ((C_41 tptp.quickcheck_code_int) (A_99 tptp.quickcheck_code_int) (B_81 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_41))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_99)) (tptp.hAPP_Q1762011733de_int _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_99) B_81))))) (forall ((C_41 tptp.rat) (A_99 tptp.rat) (B_81 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_41))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_99)) (tptp.hAPP_rat_rat _let_1 B_81))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_99) B_81))))) (forall ((A_98 tptp.code_code_numeral) (C_40 tptp.code_code_numeral) (B_80 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_98) C_40)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_80) C_40))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_98) B_80)))) (forall ((A_98 tptp.int) (C_40 tptp.int) (B_80 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_98) C_40)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_80) C_40))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_98) B_80)))) (forall ((A_98 tptp.nat) (C_40 tptp.nat) (B_80 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_98) C_40)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_80) C_40))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_98) B_80)))) (forall ((A_98 tptp.real) (C_40 tptp.real) (B_80 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_98) C_40)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_80) C_40))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_98) B_80)))) (forall ((A_98 tptp.quickcheck_code_int) (C_40 tptp.quickcheck_code_int) (B_80 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_98) C_40)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_80) C_40))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_98) B_80)))) (forall ((A_98 tptp.rat) (C_40 tptp.rat) (B_80 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_98) C_40)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_80) C_40))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_98) B_80)))) (forall ((C_39 tptp.code_code_numeral) (D_7 tptp.code_code_numeral) (A_97 tptp.code_code_numeral) (B_79 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral C_39) D_7)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_97) C_39)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_79) D_7)))))) (forall ((C_39 tptp.int) (D_7 tptp.int) (A_97 tptp.int) (B_79 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_39) D_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_97) C_39)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_79) D_7)))))) (forall ((C_39 tptp.nat) (D_7 tptp.nat) (A_97 tptp.nat) (B_79 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_39) D_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_97) C_39)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_79) D_7)))))) (forall ((C_39 tptp.real) (D_7 tptp.real) (A_97 tptp.real) (B_79 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_39) D_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_97) C_39)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_79) D_7)))))) (forall ((C_39 tptp.quickcheck_code_int) (D_7 tptp.quickcheck_code_int) (A_97 tptp.quickcheck_code_int) (B_79 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int C_39) D_7)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_97) C_39)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_79) D_7)))))) (forall ((C_39 tptp.rat) (D_7 tptp.rat) (A_97 tptp.rat) (B_79 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_97) B_79)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_39) D_7)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_97) C_39)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_79) D_7)))))) (forall ((C_38 tptp.code_code_numeral) (A_96 tptp.code_code_numeral) (B_78 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_38))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_96) B_78)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A_96)) (tptp.hAPP_C498520661umeral _let_1 B_78)))))) (forall ((C_38 tptp.int) (A_96 tptp.int) (B_78 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_38))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_96) B_78)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A_96)) (tptp.hAPP_int_int _let_1 B_78)))))) (forall ((C_38 tptp.nat) (A_96 tptp.nat) (B_78 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_38))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_96) B_78)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A_96)) (tptp.hAPP_nat_nat _let_1 B_78)))))) (forall ((C_38 tptp.real) (A_96 tptp.real) (B_78 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C_38))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_96) B_78)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_96)) (tptp.hAPP_real_real _let_1 B_78)))))) (forall ((C_38 tptp.quickcheck_code_int) (A_96 tptp.quickcheck_code_int) (B_78 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_38))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_96) B_78)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A_96)) (tptp.hAPP_Q1762011733de_int _let_1 B_78)))))) (forall ((C_38 tptp.rat) (A_96 tptp.rat) (B_78 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C_38))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_96) B_78)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A_96)) (tptp.hAPP_rat_rat _let_1 B_78)))))) (forall ((C_37 tptp.code_code_numeral) (A_95 tptp.code_code_numeral) (B_77 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_95) B_77)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_95) C_37)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_77) C_37))))) (forall ((C_37 tptp.int) (A_95 tptp.int) (B_77 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_95) B_77)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_95) C_37)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_77) C_37))))) (forall ((C_37 tptp.nat) (A_95 tptp.nat) (B_77 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_95) B_77)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_95) C_37)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_77) C_37))))) (forall ((C_37 tptp.real) (A_95 tptp.real) (B_77 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_95) B_77)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_95) C_37)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_77) C_37))))) (forall ((C_37 tptp.quickcheck_code_int) (A_95 tptp.quickcheck_code_int) (B_77 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_95) B_77)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_95) C_37)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_77) C_37))))) (forall ((C_37 tptp.rat) (A_95 tptp.rat) (B_77 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_95) B_77)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_95) C_37)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_77) C_37))))) (forall ((C tptp.code_code_numeral) (A tptp.code_code_numeral) (B tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C))) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral _let_1 A)) (tptp.hAPP_C498520661umeral _let_1 B))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 A)) (tptp.hAPP_nat_nat _let_1 B))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real C))) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B))))) (forall ((C tptp.quickcheck_code_int) (A tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C))) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int _let_1 A)) (tptp.hAPP_Q1762011733de_int _let_1 B))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat _let_1 A)) (tptp.hAPP_rat_rat _let_1 B))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.code_code_numeral) (C tptp.code_code_numeral) (B tptp.code_code_numeral)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A) C)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B) C))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) C)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B) C))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.quickcheck_code_int) (C tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A) C)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B) C))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B) tptp.zero_zero_int) (= A B))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B) tptp.zero_zero_real) (= A B))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A) B) tptp.zero_zero_complex) (= A B))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B) tptp.zero_zero_rat) (= A B))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.real) (B tptp.real)) (= (= A B) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A B) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B) tptp.zero_zero_rat))) (forall ((A_94 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_94) A_94) tptp.zero_zero_int)) (forall ((A_94 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_94) A_94) tptp.zero_zero_real)) (forall ((A_94 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_94) A_94) tptp.zero_zero_complex)) (forall ((A_94 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A_94) A_94) tptp.zero_zero_rat)) (forall ((A_93 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_93) tptp.zero_zero_int) A_93)) (forall ((A_93 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_93) tptp.zero_zero_real) A_93)) (forall ((A_93 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_93) tptp.zero_zero_complex) A_93)) (forall ((A_93 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A_93) tptp.zero_zero_rat) A_93)) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C) D))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) D)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat C) D)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) B)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C) D))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) D)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat C) D)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C) D))))) (forall ((A_92 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_92) tptp.one_one_int) A_92)) (forall ((A_92 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_92) tptp.one_one_nat) A_92)) (forall ((A_92 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_92) tptp.one_one_real) A_92)) (forall ((A_92 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_92) tptp.one_on1645066479umeral) A_92)) (forall ((A_92 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_92) tptp.one_one_complex) A_92)) (forall ((A_92 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_92) tptp.one_on1684967323de_int) A_92)) (forall ((A_92 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_92) tptp.one_one_rat) A_92)) (forall ((A_91 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_91) tptp.one_one_int) A_91)) (forall ((A_91 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_91) tptp.one_one_nat) A_91)) (forall ((A_91 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_91) tptp.one_one_real) A_91)) (forall ((A_91 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_91) tptp.one_on1645066479umeral) A_91)) (forall ((A_91 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_91) tptp.one_one_complex) A_91)) (forall ((A_91 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_91) tptp.one_on1684967323de_int) A_91)) (forall ((A_91 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_91) tptp.one_one_rat) A_91)) (forall ((A_90 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) A_90) A_90)) (forall ((A_90 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A_90) A_90)) (forall ((A_90 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.one_one_real) A_90) A_90)) (forall ((A_90 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral tptp.one_on1645066479umeral) A_90) A_90)) (forall ((A_90 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.one_one_complex) A_90) A_90)) (forall ((A_90 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int tptp.one_on1684967323de_int) A_90) A_90)) (forall ((A_90 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A_90) A_90)) (forall ((A_89 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) A_89) A_89)) (forall ((A_89 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A_89) A_89)) (forall ((A_89 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.one_one_real) A_89) A_89)) (forall ((A_89 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral tptp.one_on1645066479umeral) A_89) A_89)) (forall ((A_89 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.one_one_complex) A_89) A_89)) (forall ((A_89 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int tptp.one_on1684967323de_int) A_89) A_89)) (forall ((A_89 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A_89) A_89)) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.inv P_3) A_3)) _let_1))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.inv P_3) A_3)))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) _let_1)) (not (= (tptp.hAPP_int_int (tptp.inv P_3) A_3) _let_1))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= (tptp.hAPP_int_int (tptp.inv P_3) A_3) tptp.one_one_int)))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= A_3 (tptp.hAPP_int_int (tptp.inv P_3) A_3))))))) (forall ((A_88 tptp.int) (B_76 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_88) B_76)) B_76) A_88)) (forall ((A_88 tptp.real) (B_76 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_88) B_76)) B_76) A_88)) (forall ((A_88 tptp.complex) (B_76 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_88) B_76)) B_76) A_88)) (forall ((A_88 tptp.rat) (B_76 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_88) B_76)) B_76) A_88)) (forall ((A_87 tptp.int) (B_75 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_87) B_75)) B_75) A_87)) (forall ((A_87 tptp.real) (B_75 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_87) B_75)) B_75) A_87)) (forall ((A_87 tptp.complex) (B_75 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_87) B_75)) B_75) A_87)) (forall ((A_87 tptp.rat) (B_75 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A_87) B_75)) B_75) A_87)) (forall ((A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (not (= (tptp.hAPP_int_int (tptp.inv P_3) A_3) tptp.zero_zero_int)))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_int_int (tptp.inv P_3) A_3))) tptp.one_one_int) P_3)))))) (forall ((B_74 tptp.code_code_numeral) (A_86 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_86) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_74) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_86) B_74)) tptp.zero_z126310315umeral))))) (forall ((B_74 tptp.int) (A_86 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_86) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_74) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_86) B_74)) tptp.zero_zero_int))))) (forall ((B_74 tptp.nat) (A_86 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_86) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_74) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_86) B_74)) tptp.zero_zero_nat))))) (forall ((B_74 tptp.real) (A_86 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_86) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_74) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_86) B_74)) tptp.zero_zero_real))))) (forall ((B_74 tptp.quickcheck_code_int) (A_86 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_86) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_74) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_86) B_74)) tptp.zero_z891286103de_int))))) (forall ((B_74 tptp.rat) (A_86 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_86) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_74) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_86) B_74)) tptp.zero_zero_rat))))) (forall ((B_73 tptp.code_code_numeral) (A_85 tptp.code_code_numeral) (C_36 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_73))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) C_36)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_85) C_36))))))) (forall ((B_73 tptp.int) (A_85 tptp.int) (C_36 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_73))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) C_36)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_85) C_36))))))) (forall ((B_73 tptp.nat) (A_85 tptp.nat) (C_36 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_73))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C_36)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_85) C_36))))))) (forall ((B_73 tptp.real) (A_85 tptp.real) (C_36 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_73))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) C_36)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_85) C_36))))))) (forall ((B_73 tptp.quickcheck_code_int) (A_85 tptp.quickcheck_code_int) (C_36 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_73))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) C_36)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_85) C_36))))))) (forall ((B_73 tptp.rat) (A_85 tptp.rat) (C_36 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_73))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C_36)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_85)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_85) C_36))))))) (forall ((B_72 tptp.code_code_numeral) (C_35 tptp.code_code_numeral) (A_84 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral B_72))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) A_84)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_84) C_35))))))) (forall ((B_72 tptp.int) (C_35 tptp.int) (A_84 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_72))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_84)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_84) C_35))))))) (forall ((B_72 tptp.nat) (C_35 tptp.nat) (A_84 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_72))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A_84)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_84) C_35))))))) (forall ((B_72 tptp.real) (C_35 tptp.real) (A_84 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_72))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_84)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_84) C_35))))))) (forall ((B_72 tptp.quickcheck_code_int) (C_35 tptp.quickcheck_code_int) (A_84 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int B_72))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) A_84)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_84) C_35))))))) (forall ((B_72 tptp.rat) (C_35 tptp.rat) (A_84 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat B_72))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A_84)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 C_35)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_84) C_35))))))) (forall ((Y_2 tptp.code_code_numeral) (X_1 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 Y_2)) (= (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_1) Y_2) tptp.zero_z126310315umeral) (and (= X_1 tptp.zero_z126310315umeral) (= Y_2 tptp.zero_z126310315umeral))))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_2)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_1) Y_2) tptp.zero_zero_int) (and (= X_1 tptp.zero_zero_int) (= Y_2 tptp.zero_zero_int))))))) (forall ((Y_2 tptp.nat) (X_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_2)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_1) Y_2) tptp.zero_zero_nat) (and (= X_1 tptp.zero_zero_nat) (= Y_2 tptp.zero_zero_nat))))))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.zero_zero_real))))))) (forall ((Y_2 tptp.quickcheck_code_int) (X_1 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 Y_2)) (= (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_1) Y_2) tptp.zero_z891286103de_int) (and (= X_1 tptp.zero_z891286103de_int) (= Y_2 tptp.zero_z891286103de_int))))))) (forall ((Y_2 tptp.rat) (X_1 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 Y_2)) (= (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_1) Y_2) tptp.zero_zero_rat) (and (= X_1 tptp.zero_zero_rat) (= Y_2 tptp.zero_zero_rat))))))) (forall ((B_71 tptp.code_code_numeral) (A_83 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_83) B_71))))))) (forall ((B_71 tptp.int) (A_83 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_83) B_71))))))) (forall ((B_71 tptp.nat) (A_83 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_83) B_71))))))) (forall ((B_71 tptp.real) (A_83 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_83) B_71))))))) (forall ((B_71 tptp.quickcheck_code_int) (A_83 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_83) B_71))))))) (forall ((B_71 tptp.rat) (A_83 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_83)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_71)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_83) B_71))))))) (forall ((A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A))))) (forall ((B_70 tptp.code_code_numeral) (A_82 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_82) tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral B_70) tptp.zero_z126310315umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_82) B_70)) tptp.zero_z126310315umeral))))) (forall ((B_70 tptp.int) (A_82 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_82) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_70) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_82) B_70)) tptp.zero_zero_int))))) (forall ((B_70 tptp.nat) (A_82 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_82) tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat B_70) tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_82) B_70)) tptp.zero_zero_nat))))) (forall ((B_70 tptp.real) (A_82 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_82) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B_70) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_82) B_70)) tptp.zero_zero_real))))) (forall ((B_70 tptp.quickcheck_code_int) (A_82 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_82) tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int B_70) tptp.zero_z891286103de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_82) B_70)) tptp.zero_z891286103de_int))))) (forall ((B_70 tptp.rat) (A_82 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_82) tptp.zero_zero_rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat B_70) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_82) B_70)) tptp.zero_zero_rat))))) (forall ((B_69 tptp.code_code_numeral) (A_81 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_81) B_69))))))) (forall ((B_69 tptp.int) (A_81 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_81) B_69))))))) (forall ((B_69 tptp.nat) (A_81 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_81) B_69))))))) (forall ((B_69 tptp.real) (A_81 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_81) B_69))))))) (forall ((B_69 tptp.quickcheck_code_int) (A_81 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_81) B_69))))))) (forall ((B_69 tptp.rat) (A_81 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_81)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_69)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_81) B_69))))))) (forall ((A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) A))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A))))) (forall ((C_34 tptp.code_code_numeral) (D_6 tptp.code_code_numeral) (A_80 tptp.code_code_numeral) (B_68 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral C_34) D_6)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_80) C_34)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_68) D_6)))))) (forall ((C_34 tptp.int) (D_6 tptp.int) (A_80 tptp.int) (B_68 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int C_34) D_6)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_80) C_34)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_68) D_6)))))) (forall ((C_34 tptp.nat) (D_6 tptp.nat) (A_80 tptp.nat) (B_68 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat C_34) D_6)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_80) C_34)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_68) D_6)))))) (forall ((C_34 tptp.real) (D_6 tptp.real) (A_80 tptp.real) (B_68 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real C_34) D_6)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_80) C_34)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_68) D_6)))))) (forall ((C_34 tptp.quickcheck_code_int) (D_6 tptp.quickcheck_code_int) (A_80 tptp.quickcheck_code_int) (B_68 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int C_34) D_6)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_80) C_34)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_68) D_6)))))) (forall ((C_34 tptp.rat) (D_6 tptp.rat) (A_80 tptp.rat) (B_68 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_80) B_68)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat C_34) D_6)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_80) C_34)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_68) D_6)))))) (forall ((C_33 tptp.code_code_numeral) (D_5 tptp.code_code_numeral) (A_79 tptp.code_code_numeral) (B_67 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral C_33) D_5)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_79) C_33)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_67) D_5)))))) (forall ((C_33 tptp.int) (D_5 tptp.int) (A_79 tptp.int) (B_67 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_33) D_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_79) C_33)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_67) D_5)))))) (forall ((C_33 tptp.nat) (D_5 tptp.nat) (A_79 tptp.nat) (B_67 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_33) D_5)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_79) C_33)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_67) D_5)))))) (forall ((C_33 tptp.real) (D_5 tptp.real) (A_79 tptp.real) (B_67 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_33) D_5)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_79) C_33)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_67) D_5)))))) (forall ((C_33 tptp.quickcheck_code_int) (D_5 tptp.quickcheck_code_int) (A_79 tptp.quickcheck_code_int) (B_67 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int C_33) D_5)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_79) C_33)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_67) D_5)))))) (forall ((C_33 tptp.rat) (D_5 tptp.rat) (A_79 tptp.rat) (B_67 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_79) B_67)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat C_33) D_5)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat A_79) C_33)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat B_67) D_5)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A) B)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A) B)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((N tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.zfact N))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N) (tptp.hAPP_int_int tptp.zfact (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int N) tptp.one_one_int))))))))) (forall ((B tptp.int) (A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.inv P_5) B)) _let_1)))))))) (forall ((B tptp.int) (A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.inv P_5) B)) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) _let_1))))))))))) (forall ((J_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong J_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_3) A_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_int_int (tptp.multInv P_3) J_2))) P_3)))))))))) (forall ((P_1 tptp.fun_int_bool) (I_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (forall ((X_1 tptp.int) (P_1 tptp.fun_int_bool)) (=> (forall ((A_2 tptp.int)) (=> (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_2) tptp.one_one_int)))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 A_2)))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_1)))) (forall ((P_1 tptp.fun_int_bool) (I_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_1) tptp.one_one_int))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (forall ((P_1 tptp.fun_int_bool) (K_1 tptp.int) (I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (forall ((J_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int) (K_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_int_int (tptp.multInv P_3) K_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong J_2) _let_1) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int J_2) K_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) K_2)) P_3))))) (forall ((J_2 tptp.int) (K_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.multInv P_3) J_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int J_2) K_2)) A_3) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 J_2)) K_2)) (tptp.hAPP_int_int _let_1 A_3)) P_3))))) (forall ((P_5 tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))))) (forall ((B tptp.int) (P_5 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) tptp.one_one_int)) P_5))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))))))) (forall ((B tptp.int) (A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)))))) (forall ((B tptp.int) (A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) _let_1))))))) (forall ((B tptp.int) (P_5 tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int B))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A) tptp.one_one_int)) P_5)))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) (or (= B A) (= B (tptp.hAPP_int_int (tptp.inv P_5) A)))))))) (forall ((X tptp.int) (Y tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) Y) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_1 X)) (tptp.hAPP_int_int _let_1 Y)) P_3)))))) (forall ((B tptp.int) (A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5)))))))) (forall ((A_3 tptp.int) (J_2 tptp.int) (K_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong J_2) K_2) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 J_2))) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 K_2))) P_3))))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.multInv P_3) X)) tptp.zero_zero_int) P_3))))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_1 X))) X) P_3))))))) (forall ((Y tptp.int) (X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong X))) (let ((_let_2 (tptp.multInv P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong Y) tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_2 X)) (tptp.hAPP_int_int _let_2 Y)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 Y) P_3)))))))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (let ((_let_2 (tptp.hAPP_int_int _let_1 X))) (let ((_let_3 (tptp.hAPP_int_int _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong _let_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) _let_2)) _let_3)) P_3))))))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (let ((_let_2 (tptp.hAPP_int_int _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) _let_2)) (tptp.hAPP_int_int _let_1 _let_2))) X) P_3)))))))) (forall ((J_2 tptp.int) (K_2 tptp.int) (A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong J_2))) (let ((_let_2 (tptp.multInv P_3))) (let ((_let_3 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong K_2) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int _let_2 J_2))) (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int _let_2 K_2))) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 K_2) P_3)))))))))))) (forall ((A_3 tptp.int) (J_2 tptp.int) (K_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.multInv P_3))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (let ((_let_3 (tptp.zcong K_2))) (let ((_let_4 (tptp.zcong J_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_3 tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_4 tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_4 (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 K_2))) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_3 (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 J_2))) P_3)))))))))))) (forall ((J_2 tptp.int) (A_3 tptp.int) (K_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int J_2) K_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong K_2) tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_int_int (tptp.multInv P_3) K_2))) K_2)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_1 A_3) P_3)))))))) (forall ((K_2 tptp.int) (A_3 tptp.int) (J_2 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.multInv P_3) J_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong J_2) tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_2 J_2)) K_2)) (tptp.hAPP_int_int _let_2 A_3)) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) _let_1)) P_3))))))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) (tptp.hAPP_int_int (tptp.multInv P_3) X))) tptp.one_one_int) P_3)))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.multInv P_3) X)) X)) tptp.one_one_int) P_3)))))) (forall ((P_1 tptp.fun_int_bool) (K_1 tptp.int) (I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1) tptp.one_one_int))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M_1)) (tptp.hAPP_nat_nat F N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F Ma)) K_1)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) K_1)))))) (forall ((P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (= (tptp.hAPP_i1948725293t_bool tptp.d22set _let_1) (tptp.hAPP_i1948725293t_bool (tptp.wset _let_1) P_5))))) (forall ((N_1 tptp.nat) (P_1 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_1)) (exists ((K tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_1)) (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) K)) (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 K))))))) (forall ((I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (exists ((K tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K) J_2))))) (forall ((D tptp.code_code_numeral) (Sa tptp.code_code_numeral)) (exists ((Z tptp.code_code_numeral)) (forall ((X_2 tptp.code_code_numeral)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral D) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (Sa tptp.real)) (exists ((Z tptp.real)) (forall ((X_2 tptp.real)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.quickcheck_code_int) (Sa tptp.quickcheck_code_int)) (exists ((Z tptp.quickcheck_code_int)) (forall ((X_2 tptp.quickcheck_code_int)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int D) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (Sa tptp.rat)) (exists ((Z tptp.rat)) (forall ((X_2 tptp.rat)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (Sa tptp.int)) (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (Sa tptp.nat)) (exists ((Z tptp.nat)) (forall ((X_2 tptp.nat)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.code_code_numeral) (Sa tptp.code_code_numeral)) (exists ((Z tptp.code_code_numeral)) (forall ((X_2 tptp.code_code_numeral)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral D) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (Sa tptp.real)) (exists ((Z tptp.real)) (forall ((X_2 tptp.real)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.quickcheck_code_int) (Sa tptp.quickcheck_code_int)) (exists ((Z tptp.quickcheck_code_int)) (forall ((X_2 tptp.quickcheck_code_int)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int D) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (Sa tptp.rat)) (exists ((Z tptp.rat)) (forall ((X_2 tptp.rat)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (Sa tptp.int)) (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (Sa tptp.nat)) (exists ((Z tptp.nat)) (forall ((X_2 tptp.nat)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.code_code_numeral) (Sa tptp.code_code_numeral)) (exists ((Z tptp.code_code_numeral)) (forall ((X_2 tptp.code_code_numeral)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral D) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (Sa tptp.real)) (exists ((Z tptp.real)) (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.quickcheck_code_int) (Sa tptp.quickcheck_code_int)) (exists ((Z tptp.quickcheck_code_int)) (forall ((X_2 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int D) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (Sa tptp.rat)) (exists ((Z tptp.rat)) (forall ((X_2 tptp.rat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (Sa tptp.int)) (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Z)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (Sa tptp.nat)) (exists ((Z tptp.nat)) (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) Z)) (= _let_1 _let_1)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool tptp.d22set A)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool tptp.d22set A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool tptp.d22set A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool tptp.d22set A)))))) (forall ((D tptp.code_code_numeral) (Sa tptp.code_code_numeral)) (exists ((Z tptp.code_code_numeral)) (forall ((X_2 tptp.code_code_numeral)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral D) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (Sa tptp.real)) (exists ((Z tptp.real)) (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.dvd_dvd_real D) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.quickcheck_code_int) (Sa tptp.quickcheck_code_int)) (exists ((Z tptp.quickcheck_code_int)) (forall ((X_2 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int D) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (Sa tptp.rat)) (exists ((Z tptp.rat)) (forall ((X_2 tptp.rat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.dvd_dvd_rat D) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (Sa tptp.int)) (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) X_2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (Sa tptp.nat)) (exists ((Z tptp.nat)) (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Z) X_2)) (= _let_1 _let_1)))))) (forall ((A tptp.int) (B tptp.int) (N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) N_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B))))) (forall ((A_3 tptp.int) (N tptp.nat) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) N))) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_3) B_2))))) (forall ((A tptp.nat) (B tptp.nat) (N_1 tptp.nat)) (=> (not (= N_1 tptp.zero_zero_nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A) N_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (M tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (=> (= (tptp.hAPP_nat_nat _let_1 N) (tptp.hAPP_nat_nat _let_1 M)) (= N M))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((X_18 tptp.real) (Y_15 tptp.real) (A_78 tptp.real) (B_66 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y_15) B_66))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real A_78))) (let ((_let_3 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_18) A_78)))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_18) Y_15)) (tptp.hAPP_real_real _let_2 B_66)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_3 _let_1)) (tptp.hAPP_real_real _let_3 B_66))) (tptp.hAPP_real_real _let_2 _let_1))))))) (forall ((X_18 tptp.complex) (Y_15 tptp.complex) (A_78 tptp.complex) (B_66 tptp.complex)) (let ((_let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex Y_15) B_66))) (let ((_let_2 (tptp.hAPP_c172932010omplex tptp.times_times_complex A_78))) (let ((_let_3 (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_18) A_78)))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_18) Y_15)) (tptp.hAPP_complex_complex _let_2 B_66)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_3 _let_1)) (tptp.hAPP_complex_complex _let_3 B_66))) (tptp.hAPP_complex_complex _let_2 _let_1))))))) (forall ((B_65 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.zero_zero_real) B_65) tptp.zero_zero_real)) (forall ((B_65 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.zero_zero_complex) B_65) tptp.zero_zero_complex)) (forall ((Y_14 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.zero_zero_real) Y_14) tptp.zero_zero_real)) (forall ((Y_14 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.zero_zero_complex) Y_14) tptp.zero_zero_complex)) (forall ((A_77 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_77) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_77 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_77) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((X_17 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_17) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X_17 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_17) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A_76 tptp.real) (B_64 tptp.real) (B_63 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real A_76))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_64) B_63)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 B_64)) (tptp.hAPP_real_real _let_1 B_63))))) (forall ((A_76 tptp.complex) (B_64 tptp.complex) (B_63 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex A_76))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_64) B_63)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 B_64)) (tptp.hAPP_complex_complex _let_1 B_63))))) (forall ((Xa_4 tptp.real) (X_16 tptp.real) (Y_13 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Xa_4))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_16) Y_13)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 X_16)) (tptp.hAPP_real_real _let_1 Y_13))))) (forall ((Xa_4 tptp.complex) (X_16 tptp.complex) (Y_13 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Xa_4))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_16) Y_13)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex _let_1 X_16)) (tptp.hAPP_complex_complex _let_1 Y_13))))) (forall ((A_75 tptp.real) (A_74 tptp.real) (B_62 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_75) A_74)) B_62) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_75) B_62)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_74) B_62)))) (forall ((A_75 tptp.complex) (A_74 tptp.complex) (B_62 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_75) A_74)) B_62) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_75) B_62)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_74) B_62)))) (forall ((X_15 tptp.real) (Y_12 tptp.real) (Ya_2 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_15) Y_12)) Ya_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_15) Ya_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_12) Ya_2)))) (forall ((X_15 tptp.complex) (Y_12 tptp.complex) (Ya_2 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_15) Y_12)) Ya_2) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_15) Ya_2)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Y_12) Ya_2)))) (forall ((X_14 tptp.real) (Y_11 tptp.real) (Ya_1 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_14) Y_11)) Ya_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_14) Ya_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y_11) Ya_1)))) (forall ((X_14 tptp.complex) (Y_11 tptp.complex) (Ya_1 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_14) Y_11)) Ya_1) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_14) Ya_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Y_11) Ya_1)))) (forall ((A_73 tptp.real) (A_72 tptp.real) (B_61 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_73) A_72)) B_61) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_73) B_61)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_72) B_61)))) (forall ((A_73 tptp.complex) (A_72 tptp.complex) (B_61 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex A_73) A_72)) B_61) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_73) B_61)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_72) B_61)))) (forall ((Xa_3 tptp.real) (X_13 tptp.real) (Y_10 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real Xa_3))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_13) Y_10)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_1 X_13)) (tptp.hAPP_real_real _let_1 Y_10))))) (forall ((Xa_3 tptp.complex) (X_13 tptp.complex) (Y_10 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex Xa_3))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_13) Y_10)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex _let_1 X_13)) (tptp.hAPP_complex_complex _let_1 Y_10))))) (forall ((A_71 tptp.real) (B_60 tptp.real) (B_59 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real A_71))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_60) B_59)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_1 B_60)) (tptp.hAPP_real_real _let_1 B_59))))) (forall ((A_71 tptp.complex) (B_60 tptp.complex) (B_59 tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex A_71))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex B_60) B_59)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex _let_1 B_60)) (tptp.hAPP_complex_complex _let_1 B_59))))) (forall ((A_3 tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_3)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) tptp.zero_zero_nat)))))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)))))) (forall ((A tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A_3)) (= A_3 tptp.zero_zero_nat))) (forall ((A_3 tptp.nat)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) tptp.one_one_nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_3)))))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A_3))) (forall ((A tptp.nat)) (= (not (= A tptp.one_one_nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat tptp.one_one_nat) A)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)))))) (forall ((A tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= A tptp.one_one_nat))) (forall ((A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) tptp.one_one_nat)) (= A_3 tptp.one_one_nat))) (forall ((P_5 tptp.int)) (= (tptp.hAPP_i1948725293t_bool tptp.sr P_5) (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) P_5))))) (forall ((V_2 tptp.int) (W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_3 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 V_2))) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1))) tptp.one_one_int))) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_3 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))) tptp.one_one_int)))))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_2) tptp.one_one_int)) A_3))) tptp.one_one_int))))) (forall ((X tptp.int) (Y tptp.int) (M tptp.int)) (let ((_let_1 (tptp.standardRes M))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 X)) (tptp.hAPP_int_int _let_1 Y))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)) M))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_2 (tptp.negDivAlg tptp.one_one_int _let_1))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_3)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (and (=> _let_4 (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_3))) (=> (not _let_4) (= _let_2 (tptp.hAPP_P1975530577nt_int (tptp.adjust _let_1) (tptp.negDivAlg tptp.one_one_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) _let_1)))))))))))) (forall ((X_1 tptp.int) (K_1 tptp.int)) (=> (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K_1)) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 B_2))) (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_2) A_3)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) A_3))))) (forall ((A_70 tptp.int) (B_58 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_70) B_58))) (= (tptp.hAPP_int_int (tptp.div_mod_int _let_1) B_58) _let_1))) (forall ((A_70 tptp.nat) (B_58 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat A_70) B_58))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_1) B_58) _let_1))) (forall ((A_70 tptp.code_code_numeral) (B_58 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_70) B_58))) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral _let_1) B_58) _let_1))) (forall ((A_70 tptp.quickcheck_code_int) (B_58 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_70) B_58))) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int _let_1) B_58) _let_1))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)) B_2) tptp.zero_zero_int)) (forall ((A_3 tptp.int)) (and (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) tptp.zero_zero_int) tptp.zero_zero_int) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) tptp.zero_zero_int) A_3))) (forall ((A_69 tptp.int) (B_57 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.div_mod_int A_69) B_57)) B_57) tptp.zero_zero_int)) (forall ((A_69 tptp.nat) (B_57 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_69) B_57)) B_57) tptp.zero_zero_nat)) (forall ((A_69 tptp.code_code_numeral) (B_57 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_69) B_57)) B_57) tptp.zero_z126310315umeral)) (forall ((A_69 tptp.quickcheck_code_int) (B_57 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_69) B_57)) B_57) tptp.zero_z891286103de_int)) (forall ((X_1 tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) (tptp.hAPP_i1948725293t_bool tptp.sr P_5))) (= (tptp.hAPP_int_int (tptp.standardRes P_5) X_1) X_1))) (forall ((M tptp.int) (X tptp.int)) (= (tptp.hAPP_int_int (tptp.standardRes M) X) (tptp.hAPP_int_int (tptp.div_mod_int X) M))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2)) C_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) C_1))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) C_1)) (tptp.hAPP_int_int (tptp.div_mod_int B_2) C_1))) C_1)))) (forall ((A_68 tptp.int) (B_56 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.div_mod_int A_68) B_56)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_68) B_56)) B_56)) A_68)) (forall ((A_68 tptp.nat) (B_56 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_68) B_56)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_68) B_56)) B_56)) A_68)) (forall ((A_68 tptp.code_code_numeral) (B_56 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_68) B_56)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_68) B_56)) B_56)) A_68)) (forall ((A_68 tptp.quickcheck_code_int) (B_56 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_68) B_56)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_68) B_56)) B_56)) A_68)) (forall ((B_55 tptp.int) (A_67 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_55) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_67) B_55))) (tptp.hAPP_int_int (tptp.div_mod_int A_67) B_55)) A_67)) (forall ((B_55 tptp.nat) (A_67 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_55) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_67) B_55))) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_67) B_55)) A_67)) (forall ((B_55 tptp.code_code_numeral) (A_67 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_55) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_67) B_55))) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_67) B_55)) A_67)) (forall ((B_55 tptp.quickcheck_code_int) (A_67 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_55) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_67) B_55))) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_67) B_55)) A_67)) (forall ((A_66 tptp.int) (B_54 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_66) B_54)) B_54)) (tptp.hAPP_int_int (tptp.div_mod_int A_66) B_54)) A_66)) (forall ((A_66 tptp.nat) (B_54 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_66) B_54)) B_54)) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_66) B_54)) A_66)) (forall ((A_66 tptp.code_code_numeral) (B_54 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_66) B_54)) B_54)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_66) B_54)) A_66)) (forall ((A_66 tptp.quickcheck_code_int) (B_54 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_66) B_54)) B_54)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_66) B_54)) A_66)) (forall ((B_53 tptp.int) (A_65 tptp.int) (C_32 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_53) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_65) B_53))) (tptp.hAPP_int_int (tptp.div_mod_int A_65) B_53))) C_32) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_65) C_32))) (forall ((B_53 tptp.nat) (A_65 tptp.nat) (C_32 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_53) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_65) B_53))) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_65) B_53))) C_32) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_65) C_32))) (forall ((B_53 tptp.code_code_numeral) (A_65 tptp.code_code_numeral) (C_32 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_53) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_65) B_53))) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_65) B_53))) C_32) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_65) C_32))) (forall ((B_53 tptp.quickcheck_code_int) (A_65 tptp.quickcheck_code_int) (C_32 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_53) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_65) B_53))) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_65) B_53))) C_32) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_65) C_32))) (forall ((A_64 tptp.int) (B_52 tptp.int) (C_31 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_64) B_52)) B_52)) (tptp.hAPP_int_int (tptp.div_mod_int A_64) B_52))) C_31) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_64) C_31))) (forall ((A_64 tptp.nat) (B_52 tptp.nat) (C_31 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_64) B_52)) B_52)) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_64) B_52))) C_31) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_64) C_31))) (forall ((A_64 tptp.code_code_numeral) (B_52 tptp.code_code_numeral) (C_31 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_64) B_52)) B_52)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_64) B_52))) C_31) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_64) C_31))) (forall ((A_64 tptp.quickcheck_code_int) (B_52 tptp.quickcheck_code_int) (C_31 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_64) B_52)) B_52)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_64) B_52))) C_31) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_64) C_31))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2))) (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 B_2)) C_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) C_1))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_2) C_1))) C_1))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2))) (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))) K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) K_2))) (forall ((A_3 tptp.int) (B_2 tptp.int) (K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) B_2)) (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))) K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) K_2))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int M) N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int M) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int M) N)) N)))) (forall ((N tptp.int) (M tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int M) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int M) (tptp.hAPP_int_int (tptp.div_mod_int M) N)))) (forall ((A_63 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_63) A_63) tptp.zero_zero_int)) (forall ((A_63 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat A_63) A_63) tptp.zero_zero_nat)) (forall ((A_63 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_63) A_63) tptp.zero_z126310315umeral)) (forall ((A_63 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_63) A_63) tptp.zero_z891286103de_int)) (forall ((A_62 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_62) tptp.zero_zero_int) A_62)) (forall ((A_62 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat A_62) tptp.zero_zero_nat) A_62)) (forall ((A_62 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_62) tptp.zero_z126310315umeral) A_62)) (forall ((A_62 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_62) tptp.zero_z891286103de_int) A_62)) (forall ((A_61 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.zero_zero_int) A_61) tptp.zero_zero_int)) (forall ((A_61 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat tptp.zero_zero_nat) A_61) tptp.zero_zero_nat)) (forall ((A_61 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral tptp.zero_z126310315umeral) A_61) tptp.zero_z126310315umeral)) (forall ((A_61 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int tptp.zero_z891286103de_int) A_61) tptp.zero_z891286103de_int)) (forall ((L_2 tptp.int) (K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_2) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) L_2)) (= (tptp.negDivAlg K_2 L_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int K_2) L_2)) (tptp.hAPP_int_int (tptp.div_mod_int K_2) L_2)))))) (forall ((A_60 tptp.int) (B_51 tptp.int) (C_30 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_60))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_51)) C_30) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_51) C_30))) C_30)))) (forall ((A_60 tptp.nat) (B_51 tptp.nat) (C_30 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_60))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 B_51)) C_30) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat B_51) C_30))) C_30)))) (forall ((A_60 tptp.code_code_numeral) (B_51 tptp.code_code_numeral) (C_30 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_60))) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 B_51)) C_30) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_51) C_30))) C_30)))) (forall ((A_60 tptp.quickcheck_code_int) (B_51 tptp.quickcheck_code_int) (C_30 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_60))) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 B_51)) C_30) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_51) C_30))) C_30)))) (forall ((A_59 tptp.int) (B_50 tptp.int) (C_29 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_59) B_50)) C_29) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.div_mod_int A_59) C_29)) B_50)) C_29))) (forall ((A_59 tptp.nat) (B_50 tptp.nat) (C_29 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_59) B_50)) C_29) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_59) C_29)) B_50)) C_29))) (forall ((A_59 tptp.code_code_numeral) (B_50 tptp.code_code_numeral) (C_29 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_59) B_50)) C_29) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_59) C_29)) B_50)) C_29))) (forall ((A_59 tptp.quickcheck_code_int) (B_50 tptp.quickcheck_code_int) (C_29 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_59) B_50)) C_29) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_59) C_29)) B_50)) C_29))) (forall ((A_58 tptp.int) (B_49 tptp.int) (C_28 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_58) B_49)) C_28) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.div_mod_int A_58) C_28)) (tptp.hAPP_int_int (tptp.div_mod_int B_49) C_28))) C_28))) (forall ((A_58 tptp.nat) (B_49 tptp.nat) (C_28 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_58) B_49)) C_28) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_58) C_28)) (tptp.hAPP_nat_nat (tptp.div_mod_nat B_49) C_28))) C_28))) (forall ((A_58 tptp.code_code_numeral) (B_49 tptp.code_code_numeral) (C_28 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_58) B_49)) C_28) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_58) C_28)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_49) C_28))) C_28))) (forall ((A_58 tptp.quickcheck_code_int) (B_49 tptp.quickcheck_code_int) (C_28 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_58) B_49)) C_28) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_58) C_28)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_49) C_28))) C_28))) (forall ((C_27 tptp.int) (A_57 tptp.int) (B_48 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_27))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 A_57)) (tptp.hAPP_int_int _let_1 B_48)) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_57) B_48))))) (forall ((C_27 tptp.nat) (A_57 tptp.nat) (B_48 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_27))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 A_57)) (tptp.hAPP_nat_nat _let_1 B_48)) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat A_57) B_48))))) (forall ((C_27 tptp.code_code_numeral) (A_57 tptp.code_code_numeral) (B_48 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_27))) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 A_57)) (tptp.hAPP_C498520661umeral _let_1 B_48)) (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_57) B_48))))) (forall ((C_27 tptp.quickcheck_code_int) (A_57 tptp.quickcheck_code_int) (B_48 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_27))) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 A_57)) (tptp.hAPP_Q1762011733de_int _let_1 B_48)) (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_57) B_48))))) (forall ((A_56 tptp.int) (C_26 tptp.int) (B_47 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_56) C_26)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_47) C_26)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.div_mod_int A_56) B_47)) C_26))) (forall ((A_56 tptp.nat) (C_26 tptp.nat) (B_47 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_56) C_26)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_47) C_26)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_56) B_47)) C_26))) (forall ((A_56 tptp.code_code_numeral) (C_26 tptp.code_code_numeral) (B_47 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_56) C_26)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_47) C_26)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_56) B_47)) C_26))) (forall ((A_56 tptp.quickcheck_code_int) (C_26 tptp.quickcheck_code_int) (B_47 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_56) C_26)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_47) C_26)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_56) B_47)) C_26))) (forall ((A_55 tptp.int) (C_25 tptp.int) (B_46 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.div_mod_int A_55) C_25)) B_46)) C_25) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_55) B_46)) C_25))) (forall ((A_55 tptp.nat) (C_25 tptp.nat) (B_46 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_55) C_25)) B_46)) C_25) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_55) B_46)) C_25))) (forall ((A_55 tptp.code_code_numeral) (C_25 tptp.code_code_numeral) (B_46 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_55) C_25)) B_46)) C_25) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_55) B_46)) C_25))) (forall ((A_55 tptp.quickcheck_code_int) (C_25 tptp.quickcheck_code_int) (B_46 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_55) C_25)) B_46)) C_25) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_55) B_46)) C_25))) (forall ((B_45 tptp.int) (B_44 tptp.int) (A_54 tptp.int) (C_24 tptp.int) (A_53 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int A_54) C_24) (tptp.hAPP_int_int (tptp.div_mod_int A_53) C_24)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int B_45) C_24) (tptp.hAPP_int_int (tptp.div_mod_int B_44) C_24)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_54) B_45)) C_24) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_53) B_44)) C_24))))) (forall ((B_45 tptp.nat) (B_44 tptp.nat) (A_54 tptp.nat) (C_24 tptp.nat) (A_53 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat A_54) C_24) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_53) C_24)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat B_45) C_24) (tptp.hAPP_nat_nat (tptp.div_mod_nat B_44) C_24)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_54) B_45)) C_24) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_53) B_44)) C_24))))) (forall ((B_45 tptp.code_code_numeral) (B_44 tptp.code_code_numeral) (A_54 tptp.code_code_numeral) (C_24 tptp.code_code_numeral) (A_53 tptp.code_code_numeral)) (=> (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_54) C_24) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_53) C_24)) (=> (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_45) C_24) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_44) C_24)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_54) B_45)) C_24) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_53) B_44)) C_24))))) (forall ((B_45 tptp.quickcheck_code_int) (B_44 tptp.quickcheck_code_int) (A_54 tptp.quickcheck_code_int) (C_24 tptp.quickcheck_code_int) (A_53 tptp.quickcheck_code_int)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_54) C_24) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_53) C_24)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_45) C_24) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_44) C_24)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_54) B_45)) C_24) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_53) B_44)) C_24))))) (forall ((B_43 tptp.int) (B_42 tptp.int) (A_52 tptp.int) (C_23 tptp.int) (A_51 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int A_52) C_23) (tptp.hAPP_int_int (tptp.div_mod_int A_51) C_23)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int B_43) C_23) (tptp.hAPP_int_int (tptp.div_mod_int B_42) C_23)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_52) B_43)) C_23) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_51) B_42)) C_23))))) (forall ((B_43 tptp.nat) (B_42 tptp.nat) (A_52 tptp.nat) (C_23 tptp.nat) (A_51 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat A_52) C_23) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_51) C_23)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat B_43) C_23) (tptp.hAPP_nat_nat (tptp.div_mod_nat B_42) C_23)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_52) B_43)) C_23) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_51) B_42)) C_23))))) (forall ((B_43 tptp.code_code_numeral) (B_42 tptp.code_code_numeral) (A_52 tptp.code_code_numeral) (C_23 tptp.code_code_numeral) (A_51 tptp.code_code_numeral)) (=> (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_52) C_23) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_51) C_23)) (=> (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_43) C_23) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_42) C_23)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_52) B_43)) C_23) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_51) B_42)) C_23))))) (forall ((B_43 tptp.quickcheck_code_int) (B_42 tptp.quickcheck_code_int) (A_52 tptp.quickcheck_code_int) (C_23 tptp.quickcheck_code_int) (A_51 tptp.quickcheck_code_int)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_52) C_23) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_51) C_23)) (=> (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_43) C_23) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_42) C_23)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_52) B_43)) C_23) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_51) B_42)) C_23))))) (forall ((A_50 tptp.int) (C_22 tptp.int) (B_41 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.div_mod_int A_50) C_22)) B_41)) C_22) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_50) B_41)) C_22))) (forall ((A_50 tptp.nat) (C_22 tptp.nat) (B_41 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_50) C_22)) B_41)) C_22) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_50) B_41)) C_22))) (forall ((A_50 tptp.code_code_numeral) (C_22 tptp.code_code_numeral) (B_41 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_50) C_22)) B_41)) C_22) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_50) B_41)) C_22))) (forall ((A_50 tptp.quickcheck_code_int) (C_22 tptp.quickcheck_code_int) (B_41 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_50) C_22)) B_41)) C_22) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_50) B_41)) C_22))) (forall ((A_49 tptp.int) (B_40 tptp.int) (C_21 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_49))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_40) C_21))) C_21) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_40)) C_21)))) (forall ((A_49 tptp.nat) (B_40 tptp.nat) (C_21 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_49))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat B_40) C_21))) C_21) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 B_40)) C_21)))) (forall ((A_49 tptp.code_code_numeral) (B_40 tptp.code_code_numeral) (C_21 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_49))) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_40) C_21))) C_21) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 B_40)) C_21)))) (forall ((A_49 tptp.quickcheck_code_int) (B_40 tptp.quickcheck_code_int) (C_21 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_49))) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_40) C_21))) C_21) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 B_40)) C_21)))) (forall ((A_48 tptp.int) (B_39 tptp.int) (C_20 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_48) B_39)) C_20) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.div_mod_int A_48) C_20)) (tptp.hAPP_int_int (tptp.div_mod_int B_39) C_20))) C_20))) (forall ((A_48 tptp.nat) (B_39 tptp.nat) (C_20 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_48) B_39)) C_20) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_48) C_20)) (tptp.hAPP_nat_nat (tptp.div_mod_nat B_39) C_20))) C_20))) (forall ((A_48 tptp.code_code_numeral) (B_39 tptp.code_code_numeral) (C_20 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_48) B_39)) C_20) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_48) C_20)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_39) C_20))) C_20))) (forall ((A_48 tptp.quickcheck_code_int) (B_39 tptp.quickcheck_code_int) (C_20 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_48) B_39)) C_20) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_48) C_20)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_39) C_20))) C_20))) (forall ((A_47 tptp.int) (B_38 tptp.int) (C_19 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_47) B_38)) C_19) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.div_mod_int A_47) C_19)) B_38)) C_19))) (forall ((A_47 tptp.nat) (B_38 tptp.nat) (C_19 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_47) B_38)) C_19) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_47) C_19)) B_38)) C_19))) (forall ((A_47 tptp.code_code_numeral) (B_38 tptp.code_code_numeral) (C_19 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_47) B_38)) C_19) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_47) C_19)) B_38)) C_19))) (forall ((A_47 tptp.quickcheck_code_int) (B_38 tptp.quickcheck_code_int) (C_19 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_47) B_38)) C_19) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_47) C_19)) B_38)) C_19))) (forall ((A_46 tptp.int) (B_37 tptp.int) (C_18 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_46))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_37)) C_18) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_37) C_18))) C_18)))) (forall ((A_46 tptp.nat) (B_37 tptp.nat) (C_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_46))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 B_37)) C_18) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat B_37) C_18))) C_18)))) (forall ((A_46 tptp.code_code_numeral) (B_37 tptp.code_code_numeral) (C_18 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_46))) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 B_37)) C_18) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_37) C_18))) C_18)))) (forall ((A_46 tptp.quickcheck_code_int) (B_37 tptp.quickcheck_code_int) (C_18 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_46))) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 B_37)) C_18) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_37) C_18))) C_18)))) (forall ((B_36 tptp.int) (A_45 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_36) A_45)) B_36) (tptp.hAPP_int_int (tptp.div_mod_int A_45) B_36))) (forall ((B_36 tptp.nat) (A_45 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_36) A_45)) B_36) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_45) B_36))) (forall ((B_36 tptp.code_code_numeral) (A_45 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_36) A_45)) B_36) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_45) B_36))) (forall ((B_36 tptp.quickcheck_code_int) (A_45 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_36) A_45)) B_36) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_45) B_36))) (forall ((A_44 tptp.int) (B_35 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_44) B_35)) B_35) (tptp.hAPP_int_int (tptp.div_mod_int A_44) B_35))) (forall ((A_44 tptp.nat) (B_35 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_44) B_35)) B_35) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_44) B_35))) (forall ((A_44 tptp.code_code_numeral) (B_35 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_44) B_35)) B_35) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_44) B_35))) (forall ((A_44 tptp.quickcheck_code_int) (B_35 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_44) B_35)) B_35) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_44) B_35))) (forall ((B_34 tptp.int) (B_33 tptp.int) (A_43 tptp.int) (C_17 tptp.int) (A_42 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int A_43) C_17) (tptp.hAPP_int_int (tptp.div_mod_int A_42) C_17)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int B_34) C_17) (tptp.hAPP_int_int (tptp.div_mod_int B_33) C_17)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_43) B_34)) C_17) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_42) B_33)) C_17))))) (forall ((A_41 tptp.int) (B_32 tptp.int) (C_16 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_41) B_32)) C_16) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int A_41) C_16)) (tptp.hAPP_int_int (tptp.div_mod_int B_32) C_16))) C_16))) (forall ((A_40 tptp.int) (B_31 tptp.int) (C_15 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_40) B_31)) C_15) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int A_40) C_15)) B_31)) C_15))) (forall ((A_39 tptp.int) (B_30 tptp.int) (C_14 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_39))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_30)) C_14) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_30) C_14))) C_14)))) (forall ((Ma tptp.code_code_numeral) (K_1 tptp.code_code_numeral) (N_1 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral K_1))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral Ma) N_1))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 Ma)))))) (forall ((Ma tptp.quickcheck_code_int) (K_1 tptp.quickcheck_code_int) (N_1 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int Ma) N_1))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 Ma)))))) (forall ((Ma tptp.int) (K_1 tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Ma) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ma)))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Ma) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)))))) (forall ((A_38 tptp.code_code_numeral) (C_13 tptp.code_code_numeral) (B_29 tptp.code_code_numeral)) (let ((_let_1 (tptp.div_mo1740067990umeral A_38))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral C_13) B_29)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral _let_1 B_29)) C_13) (tptp.hAPP_C498520661umeral _let_1 C_13))))) (forall ((A_38 tptp.quickcheck_code_int) (C_13 tptp.quickcheck_code_int) (B_29 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.div_mo231679042de_int A_38))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int C_13) B_29)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int _let_1 B_29)) C_13) (tptp.hAPP_Q1762011733de_int _let_1 C_13))))) (forall ((A_38 tptp.int) (C_13 tptp.int) (B_29 tptp.int)) (let ((_let_1 (tptp.div_mod_int A_38))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C_13) B_29)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_29)) C_13) (tptp.hAPP_int_int _let_1 C_13))))) (forall ((A_38 tptp.nat) (C_13 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (tptp.div_mod_nat A_38))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_13) B_29)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 B_29)) C_13) (tptp.hAPP_nat_nat _let_1 C_13))))) (forall ((N_29 tptp.code_code_numeral) (K_6 tptp.code_code_numeral) (M_16 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral K_6))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 M_16)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 N_29)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral M_16) N_29))))))) (forall ((N_29 tptp.quickcheck_code_int) (K_6 tptp.quickcheck_code_int) (M_16 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int K_6))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 M_16)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 N_29)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int M_16) N_29))))))) (forall ((N_29 tptp.int) (K_6 tptp.int) (M_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_6))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_29)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M_16) N_29))))))) (forall ((N_29 tptp.nat) (K_6 tptp.nat) (M_16 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_29)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M_16) N_29))))))) (forall ((K_5 tptp.code_code_numeral) (M_15 tptp.code_code_numeral) (N_28 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral K_5))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral M_15) N_28))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 N_28)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 M_15)))))) (forall ((K_5 tptp.quickcheck_code_int) (M_15 tptp.quickcheck_code_int) (N_28 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int K_5))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int M_15) N_28))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 N_28)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 M_15)))))) (forall ((K_5 tptp.int) (M_15 tptp.int) (N_28 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M_15) N_28))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_28)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M_15)))))) (forall ((K_5 tptp.nat) (M_15 tptp.nat) (N_28 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M_15) N_28))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_28)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_15)))))) (forall ((B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int tptp.zero_zero_int) B_2) tptp.zero_zero_int)) (forall ((A_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) A_3) tptp.zero_zero_int)) (forall ((B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.zero_zero_int) B_2) tptp.zero_zero_int)) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_2)) C_1) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_2) C_1))) C_1)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int B_2) C_1))) C_1) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_2)) C_1)))) (forall ((X tptp.int) (M tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int X) M)) Y)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y)) M))) (forall ((X tptp.int) (Y tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X))) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Y) M))) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 Y)) M)))) (forall ((X tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) (tptp.hAPP_int_int (tptp.div_mod_int X) M)) M))) (forall ((X tptp.int) (M tptp.int) (Y tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int X) M) (tptp.hAPP_int_int (tptp.div_mod_int Y) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) Y) M)))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.div_mod_int A) Ma)) (tptp.hAPP_int_int (tptp.div_mod_int B) Ma)) Ma)))) (forall ((N tptp.int) (F_3 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int F_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N))))))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int M) N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((X tptp.int) (M tptp.int) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.div_mod_int X) M)) Y)) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) Y)) M))) (forall ((A_37 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_37) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_37 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_37) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_37 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_37) tptp.zero_z126310315umeral) tptp.zero_z126310315umeral)) (forall ((A_37 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_37) tptp.zero_z891286103de_int) tptp.zero_z891286103de_int)) (forall ((A_36 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int tptp.zero_zero_int) A_36) tptp.zero_zero_int)) (forall ((A_36 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat tptp.zero_zero_nat) A_36) tptp.zero_zero_nat)) (forall ((A_36 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral tptp.zero_z126310315umeral) A_36) tptp.zero_z126310315umeral)) (forall ((A_36 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int tptp.zero_z891286103de_int) A_36) tptp.zero_z891286103de_int)) (forall ((A_35 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_35) tptp.one_one_int) A_35)) (forall ((A_35 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_35) tptp.one_one_nat) A_35)) (forall ((A_35 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_35) tptp.one_on1645066479umeral) A_35)) (forall ((A_35 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_35) tptp.one_on1684967323de_int) A_35)) (forall ((C tptp.code_code_numeral) (A tptp.code_code_numeral) (B tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 C)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B) A)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral C) A))) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral B) C))))))) (forall ((C tptp.quickcheck_code_int) (A tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 C)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B) A)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int C) A))) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int B) C))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int C) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B) C))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat C) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B) C))))))) (forall ((R_3 tptp.int) (S_1 tptp.int) (T_1 tptp.int) (R_5 tptp.int) (S_3 tptp.int) (M tptp.int) (T_2 tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int R_5) R_3)))) (=> (= R_5 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_3) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T_2) N))) (=> (= R_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_1) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T_1) N))) (= (tptp.hAPP_int_int (tptp.div_mod_int R_5) R_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int S_3) (tptp.hAPP_int_int _let_1 S_1))) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int T_2) (tptp.hAPP_int_int _let_1 T_1))) N))))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_3) B_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) M)))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) M)) (tptp.hAPP_int_int (tptp.div_mod_int B_2) M))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2)) tptp.zOdd))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2)) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)))) (forall ((X tptp.int) (M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) (tptp.hAPP_int_int (tptp.standardRes M) X)) M))) (forall ((B_28 tptp.int) (A_34 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_28) A_34)) B_28) tptp.zero_zero_int)) (forall ((B_28 tptp.nat) (A_34 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_28) A_34)) B_28) tptp.zero_zero_nat)) (forall ((B_28 tptp.code_code_numeral) (A_34 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_28) A_34)) B_28) tptp.zero_z126310315umeral)) (forall ((B_28 tptp.quickcheck_code_int) (A_34 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_28) A_34)) B_28) tptp.zero_z891286103de_int)) (forall ((A_33 tptp.int) (B_27 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_33) B_27)) B_27) tptp.zero_zero_int)) (forall ((A_33 tptp.nat) (B_27 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_33) B_27)) B_27) tptp.zero_zero_nat)) (forall ((A_33 tptp.code_code_numeral) (B_27 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_33) B_27)) B_27) tptp.zero_z126310315umeral)) (forall ((A_33 tptp.quickcheck_code_int) (B_27 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_33) B_27)) B_27) tptp.zero_z891286103de_int)) (forall ((A_32 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_32) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A_32 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat A_32) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A_32 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_32) tptp.one_on1645066479umeral) tptp.zero_z126310315umeral)) (forall ((A_32 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_32) tptp.one_on1684967323de_int) tptp.zero_z891286103de_int)) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.div_mod_int A_3))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) C_1))) (tptp.hAPP_int_int _let_1 B_2))))))) (forall ((A_31 tptp.int) (C_12 tptp.int) (B_26 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_31) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C_12) B_26))) B_26) (tptp.hAPP_int_int (tptp.div_mod_int A_31) B_26))) (forall ((A_31 tptp.nat) (C_12 tptp.nat) (B_26 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_31) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_12) B_26))) B_26) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_31) B_26))) (forall ((A_31 tptp.code_code_numeral) (C_12 tptp.code_code_numeral) (B_26 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_31) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_12) B_26))) B_26) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_31) B_26))) (forall ((A_31 tptp.quickcheck_code_int) (C_12 tptp.quickcheck_code_int) (B_26 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_31) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_12) B_26))) B_26) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_31) B_26))) (forall ((A_30 tptp.int) (B_25 tptp.int) (C_11 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_30) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_25) C_11))) B_25) (tptp.hAPP_int_int (tptp.div_mod_int A_30) B_25))) (forall ((A_30 tptp.nat) (B_25 tptp.nat) (C_11 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_30) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_25) C_11))) B_25) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_30) B_25))) (forall ((A_30 tptp.code_code_numeral) (B_25 tptp.code_code_numeral) (C_11 tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_30) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_25) C_11))) B_25) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_30) B_25))) (forall ((A_30 tptp.quickcheck_code_int) (B_25 tptp.quickcheck_code_int) (C_11 tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_30) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_25) C_11))) B_25) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_30) B_25))) (forall ((A_29 tptp.code_code_numeral) (B_24 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_29) B_24)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B_24) A_29) tptp.zero_z126310315umeral))) (forall ((A_29 tptp.quickcheck_code_int) (B_24 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_29) B_24)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B_24) A_29) tptp.zero_z891286103de_int))) (forall ((A_29 tptp.int) (B_24 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_29) B_24)) (= (tptp.hAPP_int_int (tptp.div_mod_int B_24) A_29) tptp.zero_zero_int))) (forall ((A_29 tptp.nat) (B_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_29) B_24)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat B_24) A_29) tptp.zero_zero_nat))) (forall ((A tptp.code_code_numeral) (B tptp.code_code_numeral)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A) B)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral B) A) tptp.zero_z126310315umeral))) (forall ((A tptp.quickcheck_code_int) (B tptp.quickcheck_code_int)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A) B)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int B) A) tptp.zero_z891286103de_int))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B)) (= (tptp.hAPP_int_int (tptp.div_mod_int B) A) tptp.zero_zero_int))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat B) A) tptp.zero_zero_nat))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) B)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) B)) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((A_3 tptp.int)) (=> (not (= A_3 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) A_3) tptp.one_one_int))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y))))))) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 V_2))) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_int tptp.number_number_of_int W)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)) B_2)))) (forall ((K_2 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int M) K_2)) M)))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.div_mod_int X) Y))))))) (forall ((Ma tptp.int) (D tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int Ma) D) tptp.zero_zero_int) (exists ((Q_4 tptp.int)) (= Ma (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int D) Q_4))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) M)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int M) N)) M))) (forall ((X_1 tptp.int) (N_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.div_mod_int X_1) N_1) (tptp.hAPP_int_int (tptp.div_mod_int Y_2) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2))))) (forall ((A_28 tptp.int) (B_23 tptp.int) (C_10 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_10))) (=> (not (= C_10 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 A_28)) (tptp.hAPP_int_int _let_1 B_23)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_28) B_23))))) (forall ((A_28 tptp.nat) (B_23 tptp.nat) (C_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_10))) (=> (not (= C_10 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 A_28)) (tptp.hAPP_nat_nat _let_1 B_23)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_28) B_23))))) (forall ((A_28 tptp.code_code_numeral) (B_23 tptp.code_code_numeral) (C_10 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_10))) (=> (not (= C_10 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral _let_1 A_28)) (tptp.hAPP_C498520661umeral _let_1 B_23)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_28) B_23))))) (forall ((A_28 tptp.quickcheck_code_int) (B_23 tptp.quickcheck_code_int) (C_10 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_10))) (=> (not (= C_10 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int _let_1 A_28)) (tptp.hAPP_Q1762011733de_int _let_1 B_23)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_28) B_23))))) (forall ((A_27 tptp.int) (B_22 tptp.int) (C_9 tptp.int)) (=> (not (= C_9 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_27) C_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_22) C_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_27) B_22)))) (forall ((A_27 tptp.nat) (B_22 tptp.nat) (C_9 tptp.nat)) (=> (not (= C_9 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_27) C_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_22) C_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_27) B_22)))) (forall ((A_27 tptp.code_code_numeral) (B_22 tptp.code_code_numeral) (C_9 tptp.code_code_numeral)) (=> (not (= C_9 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_27) C_9)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_22) C_9)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_27) B_22)))) (forall ((A_27 tptp.quickcheck_code_int) (B_22 tptp.quickcheck_code_int) (C_9 tptp.quickcheck_code_int)) (=> (not (= C_9 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_27) C_9)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_22) C_9)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_27) B_22)))) (forall ((A_26 tptp.int) (B_21 tptp.int)) (=> (not (= B_21 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_21) A_26)) B_21) A_26))) (forall ((A_26 tptp.nat) (B_21 tptp.nat)) (=> (not (= B_21 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_21) A_26)) B_21) A_26))) (forall ((A_26 tptp.code_code_numeral) (B_21 tptp.code_code_numeral)) (=> (not (= B_21 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_21) A_26)) B_21) A_26))) (forall ((A_26 tptp.quickcheck_code_int) (B_21 tptp.quickcheck_code_int)) (=> (not (= B_21 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_21) A_26)) B_21) A_26))) (forall ((A_25 tptp.int) (B_20 tptp.int)) (=> (not (= B_20 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_25) B_20)) B_20) A_25))) (forall ((A_25 tptp.nat) (B_20 tptp.nat)) (=> (not (= B_20 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_25) B_20)) B_20) A_25))) (forall ((A_25 tptp.code_code_numeral) (B_20 tptp.code_code_numeral)) (=> (not (= B_20 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_25) B_20)) B_20) A_25))) (forall ((A_25 tptp.quickcheck_code_int) (B_20 tptp.quickcheck_code_int)) (=> (not (= B_20 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_25) B_20)) B_20) A_25))) (forall ((A_24 tptp.int) (B_19 tptp.int) (C_8 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_8))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 A_24)) (tptp.hAPP_int_int _let_1 B_19)))) (let ((_let_3 (= C_8 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_24) B_19)))))))) (forall ((A_24 tptp.nat) (B_19 tptp.nat) (C_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_8))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 A_24)) (tptp.hAPP_nat_nat _let_1 B_19)))) (let ((_let_3 (= C_8 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_24) B_19)))))))) (forall ((A_24 tptp.code_code_numeral) (B_19 tptp.code_code_numeral) (C_8 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_8))) (let ((_let_2 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral _let_1 A_24)) (tptp.hAPP_C498520661umeral _let_1 B_19)))) (let ((_let_3 (= C_8 tptp.zero_z126310315umeral))) (and (=> _let_3 (= _let_2 tptp.zero_z126310315umeral)) (=> (not _let_3) (= _let_2 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_24) B_19)))))))) (forall ((A_24 tptp.quickcheck_code_int) (B_19 tptp.quickcheck_code_int) (C_8 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_8))) (let ((_let_2 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int _let_1 A_24)) (tptp.hAPP_Q1762011733de_int _let_1 B_19)))) (let ((_let_3 (= C_8 tptp.zero_z891286103de_int))) (and (=> _let_3 (= _let_2 tptp.zero_z891286103de_int)) (=> (not _let_3) (= _let_2 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_24) B_19)))))))) (forall ((A_23 tptp.int)) (=> (not (= A_23 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_23) A_23) tptp.one_one_int))) (forall ((A_23 tptp.nat)) (=> (not (= A_23 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_23) A_23) tptp.one_one_nat))) (forall ((A_23 tptp.code_code_numeral)) (=> (not (= A_23 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_23) A_23) tptp.one_on1645066479umeral))) (forall ((A_23 tptp.quickcheck_code_int)) (=> (not (= A_23 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_23) A_23) tptp.one_on1684967323de_int))) (forall ((Z_7 tptp.code_code_numeral) (W_2 tptp.code_code_numeral) (Y_9 tptp.code_code_numeral) (X_12 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral Y_9) X_12)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral Z_7) W_2)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral X_12) Y_9)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral W_2) Z_7)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_12) W_2)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral Y_9) Z_7)))))) (forall ((Z_7 tptp.quickcheck_code_int) (W_2 tptp.quickcheck_code_int) (Y_9 tptp.quickcheck_code_int) (X_12 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int Y_9) X_12)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int Z_7) W_2)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int X_12) Y_9)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int W_2) Z_7)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_12) W_2)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int Y_9) Z_7)))))) (forall ((Z_7 tptp.int) (W_2 tptp.int) (Y_9 tptp.int) (X_12 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Y_9) X_12)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_7) W_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_12) Y_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int W_2) Z_7)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_12) W_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y_9) Z_7)))))) (forall ((Z_7 tptp.nat) (W_2 tptp.nat) (Y_9 tptp.nat) (X_12 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_9) X_12)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z_7) W_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X_12) Y_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat W_2) Z_7)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_12) W_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Y_9) Z_7)))))) (forall ((C_7 tptp.code_code_numeral) (A_22 tptp.code_code_numeral) (B_18 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_22) B_18)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B_18) A_22)) C_7) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_18) C_7)) A_22)))) (forall ((C_7 tptp.quickcheck_code_int) (A_22 tptp.quickcheck_code_int) (B_18 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_22) B_18)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B_18) A_22)) C_7) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_18) C_7)) A_22)))) (forall ((C_7 tptp.int) (A_22 tptp.int) (B_18 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_22) B_18)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_18) A_22)) C_7) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_18) C_7)) A_22)))) (forall ((C_7 tptp.nat) (A_22 tptp.nat) (B_18 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_22) B_18)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_18) A_22)) C_7) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_18) C_7)) A_22)))) (forall ((A_21 tptp.code_code_numeral) (B_17 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_21) B_17)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B_17) A_21)) A_21) B_17))) (forall ((A_21 tptp.quickcheck_code_int) (B_17 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_21) B_17)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B_17) A_21)) A_21) B_17))) (forall ((A_21 tptp.int) (B_17 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_21) B_17)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_17) A_21)) A_21) B_17))) (forall ((A_21 tptp.nat) (B_17 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_21) B_17)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_17) A_21)) A_21) B_17))) (forall ((A_20 tptp.code_code_numeral) (C_6 tptp.code_code_numeral) (B_16 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_20))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral C_6) B_16)) (= (tptp.hAPP_C498520661umeral _let_1 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B_16) C_6)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral _let_1 B_16)) C_6))))) (forall ((A_20 tptp.quickcheck_code_int) (C_6 tptp.quickcheck_code_int) (B_16 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_20))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int C_6) B_16)) (= (tptp.hAPP_Q1762011733de_int _let_1 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B_16) C_6)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int _let_1 B_16)) C_6))))) (forall ((A_20 tptp.int) (C_6 tptp.int) (B_16 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_20))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C_6) B_16)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_16) C_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 B_16)) C_6))))) (forall ((A_20 tptp.nat) (C_6 tptp.nat) (B_16 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_20))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C_6) B_16)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_16) C_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 B_16)) C_6))))) (forall ((A_19 tptp.code_code_numeral) (B_15 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A_19) B_15)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_19) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B_15) A_19)) B_15))) (forall ((A_19 tptp.quickcheck_code_int) (B_15 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A_19) B_15)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_19) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B_15) A_19)) B_15))) (forall ((A_19 tptp.int) (B_15 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_19) B_15)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_19) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_15) A_19)) B_15))) (forall ((A_19 tptp.nat) (B_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_19) B_15)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_19) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_15) A_19)) B_15))) (forall ((Y_8 tptp.code_code_numeral) (Z_6 tptp.code_code_numeral) (X_11 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral Z_6))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 X_11)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 Y_8)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral X_11) Y_8)) Z_6) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral X_11) Z_6)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral Y_8) Z_6))))))) (forall ((Y_8 tptp.quickcheck_code_int) (Z_6 tptp.quickcheck_code_int) (X_11 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int Z_6))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 X_11)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 Y_8)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int X_11) Y_8)) Z_6) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int X_11) Z_6)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int Y_8) Z_6))))))) (forall ((Y_8 tptp.int) (Z_6 tptp.int) (X_11 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_6))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_11)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_8)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_11) Y_8)) Z_6) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_11) Z_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int Y_8) Z_6))))))) (forall ((Y_8 tptp.nat) (Z_6 tptp.nat) (X_11 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Z_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_11)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_8)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_11) Y_8)) Z_6) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X_11) Z_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat Y_8) Z_6))))))) (forall ((N_27 tptp.nat) (Y_7 tptp.code_code_numeral) (X_10 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral Y_7) X_10)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral X_10) Y_7)) N_27) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_10) N_27)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_7) N_27))))) (forall ((N_27 tptp.nat) (Y_7 tptp.quickcheck_code_int) (X_10 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int Y_7) X_10)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int X_10) Y_7)) N_27) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_10) N_27)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_7) N_27))))) (forall ((N_27 tptp.nat) (Y_7 tptp.int) (X_10 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Y_7) X_10)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_10) Y_7)) N_27) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_10) N_27)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_7) N_27))))) (forall ((N_27 tptp.nat) (Y_7 tptp.nat) (X_10 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y_7) X_10)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X_10) Y_7)) N_27) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_10) N_27)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_7) N_27))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (N_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N_1) K_1)) (tptp.hAPP_int_int (tptp.div_mod_int N_1) K_1))) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) tptp.zero_zero_int)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 I_2) J_1))))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (N_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N_1) K_1)) (tptp.hAPP_int_int (tptp.div_mod_int N_1) K_1))) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J_1) K_1)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 I_2) J_1))))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral X_1))) (let ((_let_2 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral Y_2))) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral _let_1) _let_2)) (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral _let_2) _let_1) tptp.zero_z126310315umeral))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int X_1))) (let ((_let_2 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int Y_2))) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int _let_1) _let_2)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int _let_2) _let_1) tptp.zero_z891286103de_int))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int X_1))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_1) _let_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat X_1))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat Y_2))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) _let_2)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_2) _let_1) tptp.zero_zero_nat))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.standardRes P_3) X)) P_3)))) (forall ((Ma tptp.int) (X_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.standardRes Ma) X_1) tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_1) tptp.zero_zero_int) Ma)))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_1) tptp.zero_zero_int) P_5))) (not (= (tptp.hAPP_int_int (tptp.standardRes P_5) X_1) tptp.zero_zero_int)))) (forall ((K_2 tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) K_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) K_2)) X))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (A_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) A_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_5) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (A_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) A_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_5) B_2)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_3)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) tptp.zero_zero_int)))) (forall ((B_2 tptp.int) (B_5 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 B_5)) (tptp.hAPP_int_int _let_1 B_2)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) B_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) tptp.zero_zero_int)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) tptp.zero_zero_int))))) (forall ((B_2 tptp.int) (B_5 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 B_2)) (tptp.hAPP_int_int _let_1 B_5)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) B))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))))))) (forall ((I_1 tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int I_1) K_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_1)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)))))) (forall ((I_1 tptp.int) (K_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int I_1) K_1) tptp.zero_zero_int) (or (= K_1 tptp.zero_zero_int) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) I_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) K_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_1)))))) (forall ((X tptp.int) (Y tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y) Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Z_1)) Y))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int _let_1 B_2)) C_1))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) A_3)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) A_3)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 tptp.zero_zero_int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 _let_1))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)) tptp.zero_zero_int)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) B_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) A_3)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) B_2)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (= (tptp.hAPP_int_int (tptp.div_mod_int A) Ma) (tptp.hAPP_int_int (tptp.div_mod_int B) Ma))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.div_mod_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) B_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int _let_1 B_2)) M) (tptp.hAPP_int_int _let_1 M)))))) (forall ((A_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) tptp.zero_zero_int)) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int X_1))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int Y_2))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int _let_1) _let_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))) (forall ((A_18 tptp.int) (C_5 tptp.int) (B_14 tptp.int)) (=> (not (= B_14 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_18) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C_5) B_14))) B_14) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_5) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_18) B_14))))) (forall ((A_18 tptp.nat) (C_5 tptp.nat) (B_14 tptp.nat)) (=> (not (= B_14 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_18) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C_5) B_14))) B_14) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_5) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_18) B_14))))) (forall ((A_18 tptp.code_code_numeral) (C_5 tptp.code_code_numeral) (B_14 tptp.code_code_numeral)) (=> (not (= B_14 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_18) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C_5) B_14))) B_14) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_5) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_18) B_14))))) (forall ((A_18 tptp.quickcheck_code_int) (C_5 tptp.quickcheck_code_int) (B_14 tptp.quickcheck_code_int)) (=> (not (= B_14 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_18) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C_5) B_14))) B_14) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_5) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_18) B_14))))) (forall ((A_17 tptp.int) (C_4 tptp.int) (B_13 tptp.int)) (=> (not (= B_13 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_17) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_13) C_4))) B_13) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_4) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_17) B_13))))) (forall ((A_17 tptp.nat) (C_4 tptp.nat) (B_13 tptp.nat)) (=> (not (= B_13 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_17) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_13) C_4))) B_13) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_4) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_17) B_13))))) (forall ((A_17 tptp.code_code_numeral) (C_4 tptp.code_code_numeral) (B_13 tptp.code_code_numeral)) (=> (not (= B_13 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_17) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B_13) C_4))) B_13) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral C_4) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_17) B_13))))) (forall ((A_17 tptp.quickcheck_code_int) (C_4 tptp.quickcheck_code_int) (B_13 tptp.quickcheck_code_int)) (=> (not (= B_13 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_17) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B_13) C_4))) B_13) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int C_4) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_17) B_13))))) (forall ((A_16 tptp.int) (B_12 tptp.int)) (=> (not (= B_12 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_12) A_16)) B_12) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_16) B_12)) tptp.one_one_int)))) (forall ((A_16 tptp.nat) (B_12 tptp.nat)) (=> (not (= B_12 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_12) A_16)) B_12) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_16) B_12)) tptp.one_one_nat)))) (forall ((A_16 tptp.code_code_numeral) (B_12 tptp.code_code_numeral)) (=> (not (= B_12 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral B_12) A_16)) B_12) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_16) B_12)) tptp.one_on1645066479umeral)))) (forall ((A_16 tptp.quickcheck_code_int) (B_12 tptp.quickcheck_code_int)) (=> (not (= B_12 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int B_12) A_16)) B_12) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_16) B_12)) tptp.one_on1684967323de_int)))) (forall ((A_15 tptp.int) (B_11 tptp.int)) (=> (not (= B_11 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_15) B_11)) B_11) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_15) B_11)) tptp.one_one_int)))) (forall ((A_15 tptp.nat) (B_11 tptp.nat)) (=> (not (= B_11 tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_15) B_11)) B_11) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_15) B_11)) tptp.one_one_nat)))) (forall ((A_15 tptp.code_code_numeral) (B_11 tptp.code_code_numeral)) (=> (not (= B_11 tptp.zero_z126310315umeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral A_15) B_11)) B_11) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_15) B_11)) tptp.one_on1645066479umeral)))) (forall ((A_15 tptp.quickcheck_code_int) (B_11 tptp.quickcheck_code_int)) (=> (not (= B_11 tptp.zero_z891286103de_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int A_15) B_11)) B_11) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_15) B_11)) tptp.one_on1684967323de_int)))) (forall ((D tptp.code_code_numeral) (B tptp.code_code_numeral) (C tptp.code_code_numeral) (A tptp.code_code_numeral)) (=> (not (= A tptp.zero_z126310315umeral)) (=> (not (= C tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A) B)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral C) D)) (= (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B) A) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral D) C)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral B) C) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A) D)))))))) (forall ((D tptp.quickcheck_code_int) (B tptp.quickcheck_code_int) (C tptp.quickcheck_code_int) (A tptp.quickcheck_code_int)) (=> (not (= A tptp.zero_z891286103de_int)) (=> (not (= C tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A) B)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int C) D)) (= (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B) A) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int D) C)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int B) C) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A) D)))))))) (forall ((D tptp.int) (B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int C) D)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int D) C)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) C) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) D)))))))) (forall ((D tptp.nat) (B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat C) D)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat D) C)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B) C) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A) D)))))))) (forall ((C tptp.code_code_numeral) (B tptp.code_code_numeral) (A tptp.code_code_numeral)) (=> (not (= A tptp.zero_z126310315umeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.dvd_dv174992974umeral A) B)) (= (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral B) A) C) (= B (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral C) A)))))) (forall ((C tptp.quickcheck_code_int) (B tptp.quickcheck_code_int) (A tptp.quickcheck_code_int)) (=> (not (= A tptp.zero_z891286103de_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.dvd_dv1760642554de_int A) B)) (= (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int B) A) C) (= B (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int C) A)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A) B)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B) A) C) (= B (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C) A)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A) B)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B) A) C) (= B (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat C) A)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y))) X)))) (forall ((X_1 tptp.int) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) N_1)) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd))))) (forall ((B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_1) B_2) _let_1)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) _let_1))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.standardRes P_3) X))))) (forall ((P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_5)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int P_5) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int)) _let_1))))))) (forall ((X1_2 tptp.int) (X2 tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.standardRes Ma))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (= (tptp.hAPP_int_int _let_1 X1_2) (tptp.hAPP_int_int _let_1 X2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X1_2) X2) Ma)))))) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 V_2))) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_int tptp.number_number_of_int W))))) (forall ((X tptp.int) (Y tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Y) Z_1)) Z_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Z_1)) Y))))) (forall ((A_14 tptp.int) (B_10 tptp.int) (Y tptp.int) (R_7 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_10)))) (=> (= A_14 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_10) Y)) R_7)) (=> (and (=> _let_1 (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_7) B_10)))) (=> (not _let_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_10) R_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_7) tptp.zero_zero_int))))) (=> (not (= B_10 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_14) B_10) Y)))))) (forall ((P_1 tptp.fun_int_bool) (N_1 tptp.int) (K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N_1) K_1))) (and (=> (= K_1 tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool P_1 tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J_1) K_1)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.zero_zero_int)) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) tptp.zero_zero_int)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)))))))) (forall ((A_14 tptp.int) (B_10 tptp.int) (Q_9 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_10)))) (=> (= A_14 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_10) Q_9)) Y)) (=> (and (=> _let_1 (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) B_10)))) (=> (not _let_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_10) Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int))))) (=> (not (= B_10 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_14) B_10) Y)))))) (forall ((Q_2 tptp.int) (B_2 tptp.int) (R_3 tptp.int) (C_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_3) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) (tptp.hAPP_int_int (tptp.div_mod_int Q_2) C_1))) R_3)) tptp.zero_zero_int)))))) (forall ((Q_2 tptp.int) (B_2 tptp.int) (R_3 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_3) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_2) C_1))) R_3)))))))) (forall ((Q_2 tptp.int) (B_2 tptp.int) (R_3 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_2) C_1))) R_3)) (tptp.hAPP_int_int _let_1 C_1)))))))) (forall ((Q_2 tptp.int) (B_2 tptp.int) (R_3 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) (tptp.hAPP_int_int (tptp.div_mod_int Q_2) C_1))) R_3)))))))) (forall ((P_1 tptp.fun_int_bool) (N_1 tptp.int) (K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.div_mod_int N_1) K_1))) (and (=> (= K_1 tptp.zero_zero_int) (tptp.hBOOL (tptp.hAPP_int_bool P_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_1)) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J_1) K_1)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 J_1))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.zero_zero_int)) (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J_1) tptp.zero_zero_int)) (= N_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 J_1)))))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int X_1) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2)) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))))) (forall ((B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) B_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_2) tptp.one_one_int)))) (forall ((V_2 tptp.int) (W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 V_2))) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_2) _let_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))))))))) (forall ((B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (= (tptp.negDivAlg _let_1 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_2) tptp.one_one_int))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.negDivAlg A_3 B_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2))) (let ((_let_3 (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))))) (and (=> _let_3 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_2))) (=> (not _let_3) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B_2) (tptp.negDivAlg A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_2)))))))))) (forall ((P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int P_5) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5))))) (forall ((W tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_3 (tptp.negDivAlg _let_2 _let_1))) (let ((_let_4 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_2) _let_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_4)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (and (=> _let_5 (= _let_3 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_4))) (=> (not _let_5) (= _let_3 (tptp.hAPP_P1975530577nt_int (tptp.adjust _let_1) (tptp.negDivAlg _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) _let_1))))))))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.negDivAlg A_3 B_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (and (=> _let_3 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_2))) (=> (not _let_3) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B_2) (tptp.negDivAlg A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_2))))))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_int_int _let_1 B_2))) (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_2) tptp.one_one_int)) A_3))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (not (forall ((K tptp.int)) (not (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K)) tptp.one_one_int))))))) (forall ((X_1 tptp.int) (A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.standardRes P_5) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) (tptp.hAPP_int_int (tptp.multInv P_5) X_1)))) _let_1)))))))) (forall ((A_13 tptp.int) (B_9 tptp.int)) (= A_13 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_13) B_9)) B_9)) (tptp.hAPP_int_int (tptp.div_mod_int A_13) B_9)))) (forall ((A_13 tptp.nat) (B_9 tptp.nat)) (= A_13 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_13) B_9)) B_9)) (tptp.hAPP_nat_nat (tptp.div_mod_nat A_13) B_9)))) (forall ((A_13 tptp.code_code_numeral) (B_9 tptp.code_code_numeral)) (= A_13 (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral A_13) B_9)) B_9)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral A_13) B_9)))) (forall ((A_13 tptp.quickcheck_code_int) (B_9 tptp.quickcheck_code_int)) (= A_13 (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int A_13) B_9)) B_9)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int A_13) B_9)))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_3) A_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int tptp.zfact _let_2)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_2) _let_1)))) P_3))))))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_3) X))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) _let_1)))) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) P_3)))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.posDivAlg A_3 B_2))) (let ((_let_2 (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A_3))) (=> (not _let_2) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B_2) (tptp.posDivAlg A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_2))))))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_2 (tptp.posDivAlg tptp.one_one_int _let_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) _let_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (and (=> _let_3 (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_3) (= _let_2 (tptp.hAPP_P1975530577nt_int (tptp.adjust _let_1) (tptp.posDivAlg tptp.one_one_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) _let_1))))))))))) (forall ((X tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X) tptp.zero_zero_int) P_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_3) X)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) _let_1)))) tptp.one_one_int) P_3)))))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_3) B_2)) C_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_2) C_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.div_mod_nat B_2) C_1))) C_1)))) (forall ((X_1 tptp.int) (Y_2 tptp.int) (P_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_b1463609396nt_int tptp.if_int P_1) X_1) Y_2)))) (let ((_let_2 (tptp.hBOOL P_1))) (and (=> _let_2 (= (tptp.hAPP_int_nat tptp.nat_1 X_1) _let_1)) (=> (not _let_2) (= (tptp.hAPP_int_nat tptp.nat_1 Y_2) _let_1)))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.div_mod_nat A_3))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3) B_2)) C_1))) (tptp.hAPP_nat_nat _let_1 B_2)))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 B_2)) C_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_2) C_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat B_2) C_1))) C_1))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) N)))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) K_2))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) M))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 B_2)) C_1)))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)) M))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)) K_2) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K_2)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.div_mod_int X) Y)) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.div_mod_int X) Y))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N)))) (let ((_let_3 (= K_2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)))))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (= (tptp.hAPP_int_int (tptp.standardRes P_5) X_1) X_1))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)) N)))) (= tptp.zero_zero_nat _let_77) (= _let_77 tptp.zero_zero_nat) (forall ((Ma tptp.nat) (D tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.div_mod_nat Ma) D) tptp.zero_zero_nat) (exists ((Q_4 tptp.nat)) (= Ma (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat D) Q_4))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_2)) (= (= (tptp.hAPP_int_nat tptp.nat_1 X_1) (tptp.hAPP_int_nat tptp.nat_1 Y_2)) (= X_1 Y_2)))))) (forall ((P_1 tptp.fun_nat_bool)) (= (forall ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X1))) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_int_nat tptp.nat_1 X_2))))))) (forall ((P_1 tptp.fun_nat_bool)) (= (exists ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X1))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_int_nat tptp.nat_1 X_2))))))) (forall ((Z_3 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_3)) (= (= (tptp.hAPP_int_nat tptp.nat_1 Z_2) (tptp.hAPP_int_nat tptp.nat_1 Z_3)) (= Z_2 Z_3)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N))))))) (forall ((K_2 tptp.nat) (N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) N)) M)) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N))) (forall ((V_2 tptp.int)) (= (tptp.hAPP_int_nat tptp.number_number_of_nat V_2) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2)))) (forall ((W tptp.int)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.number_number_of_int W)) (tptp.hAPP_int_nat tptp.number_number_of_nat W))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))) (= tptp.one_one_nat _let_71) (forall ((X_1 tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_i1948725293t_bool tptp.sr P_5)))))) (forall ((K_2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M))))))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) N) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M)) N) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) M))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)) N)))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_nat tptp.nat_1 Z_1) tptp.zero_zero_nat))) (forall ((I_1 tptp.int)) (= (= (tptp.hAPP_int_nat tptp.nat_1 I_1) tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) tptp.zero_zero_int)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 W_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2))))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 W_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.nat_1 X_1)) (tptp.hAPP_int_nat tptp.nat_1 Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_2))))))) (forall ((B_2 tptp.int)) (= (tptp.posDivAlg tptp.zero_zero_int B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.zero_zero_int))) (forall ((P_5 tptp.int)) (= (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5) (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) P_5))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_1) tptp.zero_zero_int) P_5))))) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (= K_1 tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N_1) K_1))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (not _let_1) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_1)) (=> (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1) I_2)) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2)))))))))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Z_2)))) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat) (K_1 tptp.nat)) (let ((_let_1 (= K_1 tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat N_1) K_1))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_1))) (=> (not _let_1) (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) K_1)) (=> (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_1) I_2)) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 J_1)))))))))) (forall ((Q_2 tptp.nat) (R_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_3) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Q_2) C_1))) R_3)) (tptp.hAPP_nat_nat _let_1 C_1))))))) (= _let_70 (tptp.hAPP_int_nat tptp.nat_1 _let_10)) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 X_1)) (tptp.hAPP_int_nat tptp.nat_1 Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2))))))) (forall ((Z_2 tptp.int) (W_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) W_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 W_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2))))) (forall ((Z_2 tptp.int) (W_1 tptp.int)) (=> (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) W_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_2))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.nat_1 W_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_2))))) (forall ((Z_4 tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.nat_1 Z_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_4))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (forall ((Z_4 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_4)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.nat_1 Z_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_4))))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_2)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_int_nat tptp.nat_1 X_1)) (tptp.hAPP_int_nat tptp.nat_1 Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_1) Y_2))))))) (forall ((Z_1 tptp.int) (Z_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_4) Z_1)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_1) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_int_nat tptp.nat_1 Z_1)) (tptp.hAPP_int_nat tptp.nat_1 Z_4)))))) (forall ((N tptp.nat) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_int_nat tptp.nat_1 X)) N) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N))))) (forall ((N tptp.nat) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Z_1) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_int_nat tptp.nat_1 Z_1)) N)))) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) (= _let_3 _let_68) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 P_3))) (let ((_let_2 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) P_3)) (= (tptp.hAPP_nat_int _let_2 _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) (tptp.hAPP_nat_int _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_1) (tptp.hAPP_int_nat tptp.nat_1 X_1)) _let_1))))) (forall ((X tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) X))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)))) tptp.one_one_int) P_3))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (forall ((Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Ma) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 tptp.one_one_nat)))) (forall ((P_3 tptp.int) (X tptp.int)) (= (tptp.hAPP_int_int (tptp.multInv P_3) X) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (forall ((L_2 tptp.int) (K_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 L_2)) (= (tptp.posDivAlg K_2 L_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int K_2) L_2)) (tptp.hAPP_int_int (tptp.div_mod_int K_2) L_2))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) _let_1))))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) P_3)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_int_nat tptp.nat_1 P_3)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) _let_2))))))) (forall ((P_3 tptp.int) (A_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.inv P_3) A_3) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) P_3))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int _let_1))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) _let_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) (tptp.hAPP_int_nat tptp.nat_1 _let_3)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_2) _let_3))))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.standardRes P_5) X_1)) _let_1))))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.standardRes P_5) X_1)) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_1) tptp.zero_zero_int) P_5)))))) (forall ((Y_2 tptp.int) (X_1 tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.standardRes P_5) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2))) _let_1)))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) tptp.zero_zero_int) P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) _let_1)))) P_3))))))) (forall ((X_1 tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) _let_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.standardRes P_5) (tptp.hAPP_int_int (tptp.multInv P_5) X_1))) _let_1))))))) (forall ((A_3 tptp.int) (P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.legendre A_3) P_3)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int)) _let_1)))) P_3)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.posDivAlg A_3 B_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) B_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (and (=> _let_2 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A_3))) (=> (not _let_2) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B_2) (tptp.posDivAlg A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_2)))))))))) (forall ((W tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int W))) (let ((_let_3 (tptp.posDivAlg _let_2 _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_2) _let_1)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (and (=> _let_4 (= _let_3 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) _let_2))) (=> (not _let_4) (= _let_3 (tptp.hAPP_P1975530577nt_int (tptp.adjust _let_1) (tptp.posDivAlg _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) _let_1)))))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 _let_1))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.div_mod_nat M) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_2))))) (or (= _let_3 tptp.zero_zero_nat) (= _let_3 tptp.one_one_nat) (= _let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2)) (= _let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 _let_1)))))))) (forall ((I tptp.int) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.nat_aux I) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.nat_1 I)) N))) (forall ((M_14 tptp.int) (D_4 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int M_14) D_4) tptp.zero_zero_int) (exists ((Q_4 tptp.int)) (= M_14 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int D_4) Q_4))))) (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat Y) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y) X)) (exists ((Q_4 tptp.nat)) (= X (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) Q_4))))))) (forall ((P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (= (tptp.hAPP_int_nat tptp.phi P_3) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3) tptp.one_one_int))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.negDivAlg A B))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) B))) (let ((_let_3 (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.negDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A) B))) (and (=> _let_3 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) _let_2))) (=> (not _let_3) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B) (tptp.negDivAlg A (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B))))))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.nat_tr876908586nt_nat tptp.nat_1) _let_76)) (forall ((F tptp.fun_int_nat) (A_1 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.nat_tr876908586nt_nat F) A_1))) (forall ((F tptp.fun_nat_int) (A_1 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.nat_tr160667106at_int F) A_1))) (forall ((F tptp.fun_int_nat) (A_1 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.nat_tr876908586nt_nat F) A_1))) (forall ((F tptp.fun_nat_int) (A_1 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.nat_tr160667106at_int F) A_1))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Z_2 tptp.real)) (= (= X_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y_2) Z_2)) (= Y_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Z_2)))) (forall ((P_1 tptp.fun_int_fun_int_bool) (A0 tptp.int) (A1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.negDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool P_1 A_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.negDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_2) B_4))) (=> (=> (not (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_2) B_4))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_4) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_4)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_4)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.posDivAlg A B))) (let ((_let_2 (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.posDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A) B))) (and (=> _let_2 (= _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A))) (=> (not _let_2) (= _let_1 (tptp.hAPP_P1975530577nt_int (tptp.adjust B) (tptp.posDivAlg A (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B)))))))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (A0 tptp.int) (A1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.posDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool P_1 A_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.posDivAlg_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_2) B_4))) (=> (=> (not (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_2) B_4)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_4) tptp.zero_zero_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) B_4)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_4)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((M tptp.nat) (D_3 tptp.nat) (R_3 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) D_3) R_3) (exists ((Q_4 tptp.nat)) (= M (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat R_3) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Q_4) D_3)))))) (forall ((X_1 tptp.nat) (N_1 tptp.nat) (Y_2 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X_1) N_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat Y_2) N_1)) (exists ((Q1 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_1) (tptp.hAPP_nat_nat _let_1 Q1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_2) (tptp.hAPP_nat_nat _let_1 Q2))))))) (forall ((M_14 tptp.nat) (D_4 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M_14) D_4) tptp.zero_zero_nat) (exists ((Q_4 tptp.nat)) (= M_14 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat D_4) Q_4))))) (forall ((C_1 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= B_2 tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) C_1)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 (tptp.hAPP_int_int _let_1 C_1)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int Q_2) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.div_mod_int Q_2) C_1))) R_3))))))))) (forall ((Q_8 tptp.int) (R_5 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.divmod_int_rel A_3 B_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_8) R_5))) (=> (not (= B_2 tptp.zero_zero_int)) (= R_3 R_5)))))) (forall ((Q_8 tptp.int) (R_5 tptp.int) (A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.divmod_int_rel A_3 B_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool _let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_8) R_5))) (=> (not (= B_2 tptp.zero_zero_int)) (= Q_2 Q_8)))))) (forall ((A_3 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 A_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= A_3 tptp.zero_zero_int)) (= R_3 tptp.zero_zero_int)))) (forall ((B_2 tptp.int)) (=> (not (= B_2 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel tptp.zero_zero_int B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.zero_zero_int))))) (forall ((A_3 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 A_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= A_3 tptp.zero_zero_int)) (= Q_2 tptp.one_one_int)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= B_2 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) Q_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= B_2 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) R_3)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.negDivAlg A_3 B_2)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (not (= B_2 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)) (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.posDivAlg A_3 B_2)))))) (forall ((B_2 tptp.int) (Bq tptp.int) (Br tptp.int) (A_3 tptp.int) (C_1 tptp.int) (Aq tptp.int) (Ar tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ar) Br))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 C_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Aq) Ar))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel B_2 C_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Bq) Br))) (=> (not (= C_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_3) B_2) C_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Aq) Bq)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_1) C_1))) (tptp.hAPP_int_int (tptp.div_mod_int _let_1) C_1))))))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)))) (=> (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) Q_2)) R_3)) (=> (and (=> _let_1 (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int R_3) B_2)))) (=> (not _let_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) R_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_3) tptp.zero_zero_int))))) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int) (Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3))) (let ((_let_2 (tptp.hAPP_int_int _let_1 R_3))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel B_2 C_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2) R_3))) (=> (not (= C_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel (tptp.hAPP_int_int _let_1 B_2) C_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Q_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_2) C_1))) (tptp.hAPP_int_int (tptp.div_mod_int _let_2) C_1))))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.nat_tsub X) Y))))))) (forall ((P_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_3))) (let ((_let_3 (tptp.hAPP_int_int tptp.bit0 _let_1))) (let ((_let_4 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int tptp.number_number_of_int _let_3))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 _let_3))) P_3)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_4) _let_4) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int _let_2 tptp.one_one_int))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 _let_1))))))))))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) _let_1))) tptp.one_one_int) X)))) (forall ((K_2 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_i769753017umeral tptp.number1443263063umeral _let_1))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) (tptp.code_int_of (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral K_2) _let_2))))) (let ((_let_4 (tptp.code_int_of K_2))) (let ((_let_5 (= (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral K_2) _let_2) tptp.zero_z126310315umeral))) (let ((_let_6 (= K_2 tptp.zero_z126310315umeral))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_3) tptp.one_one_int))))))))))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) (tptp.hAPP_int_nat tptp.nat_1 X_1)) tptp.one_one_int)))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int _let_1) _let_1))))) (forall ((X_9 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_int_nat tptp.nat_1 X_9)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_9)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_9))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1))))) (forall ((I_1 tptp.nat) (J tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((I_2 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat F J_1))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_1)) (tptp.hAPP_nat_nat F J)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((K_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) K_2))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.nat_tsub (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X) Y)))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.minus_1690775515umeral tptp.zero_z126310315umeral) tptp.one_on1645066479umeral) tptp.zero_z126310315umeral) (forall ((N_26 tptp.nat)) (= (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_26))) (forall ((N_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26))) (= (tptp.hAPP_int_int tptp.number_number_of_int _let_1) _let_1))) (forall ((N_26 tptp.nat)) (= (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_26))) (forall ((N_26 tptp.nat)) (= (tptp.hAPP_int_complex tptp.number528085621omplex (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N_26))) (forall ((N_26 tptp.nat)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_26)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_26))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.hAPP_nat_nat tptp.suc X) (tptp.hAPP_nat_nat tptp.suc Y)) (= X Y))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int Ma) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral Ma) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex Ma) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N_1)) (= Ma N_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat Ma) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_1)) (= Ma N_1))) (forall ((Nat_5 tptp.nat) (Nat_4 tptp.nat)) (= (= (tptp.hAPP_nat_nat tptp.suc Nat_5) (tptp.hAPP_nat_nat tptp.suc Nat_4)) (= Nat_5 Nat_4))) (forall ((N tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc N) N))) (forall ((N tptp.nat)) (not (= N (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_nat_real tptp.semiri132038758t_real M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral tptp.one_on1645066479umeral) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex tptp.one_one_complex) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int tptp.one_on1684967323de_int) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_13)))) (forall ((M_13 tptp.nat)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_nat_nat tptp.suc M_13)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_13)))) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_43) tptp.one_one_int) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z_2)) (exists ((N_2 tptp.nat)) (= Z_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N_2))))))) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))) (forall ((M tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M)))) (forall ((Nat_3 tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc Nat_3) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((Nat_2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc Nat_2)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.hAPP_nat_nat tptp.suc M)))) (forall ((N tptp.nat)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) N)) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))) (= M N))))) (forall ((K_2 tptp.nat) (I tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_2) K_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I)) K_2))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc M))) (= M N))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc Ma))) (= N_1 Ma))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc Ma)) (tptp.hAPP_nat_nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= Ma N_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_nat_nat tptp.suc Ma))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat _let_1 N))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) N)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N_1)) Ma)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N_1)) (= Ma _let_1)))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_nat_nat tptp.suc Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) Ma)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N))) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K_1)))) (= (= (tptp.hAPP_nat_nat _let_1 Ma) (tptp.hAPP_nat_nat _let_1 N_1)) (= Ma N_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hAPP_nat_nat tptp.suc K_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K_2))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N))) N))) (forall ((X_1 tptp.nat) (N_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_2) _let_1)) (= X_1 Y_2)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int tptp.zero_zero_int)) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int tptp.one_one_int))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y_2))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y)) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y)))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)))) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_1) Y_2))) (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)))) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2))) (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))))))) (forall ((N tptp.nat) (X tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)))))) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int tptp.one_one_int) tptp.zEven))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2)) tptp.zEven)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2)) tptp.zEven)) (or (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_1) Y_2)) tptp.zEven))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2)) tptp.zEven)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2)) tptp.zEven))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zOdd))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zEven))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (or (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zEven))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zOdd)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zEven)))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (not (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 tptp.zEven)))))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_12)))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_12)))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_12)))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.semiri132038758t_real M_12)))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_12)))) (forall ((M_12 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_12)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_25)))) (forall ((N_25 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_25)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_11)) tptp.zero_zero_rat)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_11)) tptp.zero_z891286103de_int)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_11)) tptp.zero_z126310315umeral)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_11)) tptp.zero_zero_real)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_11)) tptp.zero_zero_nat)))) (forall ((M_11 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_11)) tptp.zero_zero_int)))) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int tptp.zero_zero_nat) tptp.zero_z891286103de_int) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral tptp.zero_zero_nat) tptp.zero_z126310315umeral) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) _let_75 (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_10)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_10)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_10)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_10)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_10)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_10 tptp.nat) (N_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_10)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_24))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_10) N_24)))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_9)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_23))))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_9)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_23))))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_9)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_23))))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_9)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_23))))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_9)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_23))))) (forall ((M_9 tptp.nat) (N_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_9) N_23)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_9)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_23))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral Ma)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat Ma)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int Ma)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral Ma)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int Ma)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat Ma)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat Ma)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.semiri132038758t_real Ma)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.plus_p1627245867umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_8)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_8)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_8)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_nat_complex tptp.semiri2020571505omplex M_8)) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_8)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_8)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_22)))) (forall ((M_8 tptp.nat) (N_22 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_8) N_22)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_8)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_22)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_7)) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_7)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_7)) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex tptp.semiri2020571505omplex M_7)) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_7)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_7)) (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_21)))) (forall ((M_7 tptp.nat) (N_21 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_7) N_21)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_7)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_21)))) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat tptp.one_one_nat) tptp.one_one_rat) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int tptp.one_one_nat) tptp.one_on1684967323de_int) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex tptp.one_one_nat) tptp.one_one_complex) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral tptp.one_one_nat) tptp.one_on1645066479umeral) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat tptp.one_one_nat) tptp.one_one_nat) _let_73 _let_75 (forall ((N_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1) tptp.zero_zero_int) (= N_1 tptp.zero_zero_nat))) (= tptp.zero_zero_int _let_74) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_nat_complex tptp.semiri2020571505omplex M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.semiri984289939at_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat tptp.semiri984289939at_nat M_6)) N_20))) (forall ((M_6 tptp.nat) (N_20 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M_6) N_20)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_6)) N_20))) (forall ((K_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_2)) tptp.zero_zero_int)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((Z_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Z_1)))) (forall ((P_1 tptp.fun_int_bool)) (= (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)))) (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((P_1 tptp.fun_int_bool)) (= (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)))) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat tptp.zero_zero_rat) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_zero_rat)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int tptp.zero_z891286103de_int) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_z891286103de_int)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.zero_zero_complex) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_zero_complex)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral tptp.zero_z126310315umeral) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_z126310315umeral)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_zero_real)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_zero_nat)) (forall ((N_19 tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) (tptp.hAPP_nat_nat tptp.suc N_19)) tptp.zero_zero_int)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)))) (forall ((W_1 tptp.int) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z_2)) (exists ((N_2 tptp.nat)) (= Z_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))))) (forall ((A_12 tptp.quickcheck_code_int) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_12))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 N_18)) A_12)))) (forall ((A_12 tptp.code_code_numeral) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_12))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 N_18)) A_12)))) (forall ((A_12 tptp.rat) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_12))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 N_18)) A_12)))) (forall ((A_12 tptp.complex) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_12))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 N_18)) A_12)))) (forall ((A_12 tptp.real) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_12))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 N_18)) A_12)))) (forall ((A_12 tptp.nat) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_12))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N_18)) A_12)))) (forall ((A_12 tptp.int) (N_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_12))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat tptp.suc N_18)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 N_18)) A_12)))) (forall ((A_11 tptp.quickcheck_code_int) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_11))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int A_11) (tptp.hAPP_n522471361de_int _let_1 N_17))))) (forall ((A_11 tptp.code_code_numeral) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_11))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral A_11) (tptp.hAPP_n1108039445umeral _let_1 N_17))))) (forall ((A_11 tptp.rat) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_11))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat A_11) (tptp.hAPP_nat_rat _let_1 N_17))))) (forall ((A_11 tptp.complex) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex A_11))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex A_11) (tptp.hAPP_nat_complex _let_1 N_17))))) (forall ((A_11 tptp.real) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real A_11))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_11) (tptp.hAPP_nat_real _let_1 N_17))))) (forall ((A_11 tptp.nat) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_11))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_11) (tptp.hAPP_nat_nat _let_1 N_17))))) (forall ((A_11 tptp.int) (N_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_11))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat tptp.suc N_17)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_11) (tptp.hAPP_nat_int _let_1 N_17))))) (forall ((X_8 tptp.quickcheck_code_int) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_8))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 Q_7)) X_8) (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.code_code_numeral) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_8))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 Q_7)) X_8) (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.rat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_8))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 Q_7)) X_8) (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.complex) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_8))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 Q_7)) X_8) (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.real) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_8))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 Q_7)) X_8) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.nat) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_8))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Q_7)) X_8) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_8 tptp.int) (Q_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_8))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 Q_7)) X_8) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_7))))) (forall ((X_7 tptp.quickcheck_code_int) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_7))) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_7) (tptp.hAPP_n522471361de_int _let_1 Q_6)) (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.code_code_numeral) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_7))) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_7) (tptp.hAPP_n1108039445umeral _let_1 Q_6)) (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.rat) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_7))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_7) (tptp.hAPP_nat_rat _let_1 Q_6)) (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.complex) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_7))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_7) (tptp.hAPP_nat_complex _let_1 Q_6)) (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.real) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_7))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_7) (tptp.hAPP_nat_real _let_1 Q_6)) (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_7))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_7) (tptp.hAPP_nat_nat _let_1 Q_6)) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_7 tptp.int) (Q_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_7))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_7) (tptp.hAPP_nat_int _let_1 Q_6)) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_6))))) (forall ((X_6 tptp.quickcheck_code_int) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int X_6))) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int X_6) (tptp.hAPP_n522471361de_int _let_1 Q_5))))) (forall ((X_6 tptp.code_code_numeral) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral X_6))) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral X_6) (tptp.hAPP_n1108039445umeral _let_1 Q_5))))) (forall ((X_6 tptp.rat) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_6))) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X_6) (tptp.hAPP_nat_rat _let_1 Q_5))))) (forall ((X_6 tptp.complex) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_6))) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X_6) (tptp.hAPP_nat_complex _let_1 Q_5))))) (forall ((X_6 tptp.real) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_6))) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X_6) (tptp.hAPP_nat_real _let_1 Q_5))))) (forall ((X_6 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_6))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_6) (tptp.hAPP_nat_nat _let_1 Q_5))))) (forall ((X_6 tptp.int) (Q_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_6))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat tptp.suc Q_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_6) (tptp.hAPP_nat_int _let_1 Q_5))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat) (Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) Z_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) Z_1))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X) Y)))) _let_73 (= tptp.one_one_int _let_72) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) (tptp.hAPP_nat_nat tptp.suc _let_1))) (or (= X tptp.zero_zero_nat) (= X _let_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat tptp.suc N_1))) (or (= Ma tptp.zero_zero_nat) (exists ((J_1 tptp.nat)) (and (= Ma (tptp.hAPP_nat_nat tptp.suc J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J_1) N_1))))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= N_1 tptp.zero_zero_nat))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (exists ((M_1 tptp.nat)) (= N_1 (tptp.hAPP_nat_nat tptp.suc M_1))))) (forall ((Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) _let_1)) (= Ma _let_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1) _let_1) (or (and (= Ma _let_1) (= N_1 tptp.zero_zero_nat)) (and (= Ma tptp.zero_zero_nat) (= N_1 _let_1)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1)) (or (and (= Ma _let_1) (= N_1 tptp.zero_zero_nat)) (and (= Ma tptp.zero_zero_nat) (= N_1 _let_1)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1) _let_1) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) (exists ((K tptp.nat)) (= N_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) K)))))) (forall ((I tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) I))))) (forall ((I tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) M))))) (= tptp.one_one_nat _let_43) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_nat_nat tptp.suc Ma))) (= N_1 Ma)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc M)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Ma)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1)))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N_1)) Ma)))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.hAPP_nat_nat tptp.suc M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc K_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Ma)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) N_1))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N)) tptp.one_one_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 tptp.one_one_nat)) N)))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int A_3)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int B_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) Y)))) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) Ma) _let_1) (or (= Ma tptp.zero_zero_nat) (= X_1 _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat _let_1) N) _let_1))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)))) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N)))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.div_mod_nat A_3) B_2)) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int A_3)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int B_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))) (forall ((X_1 tptp.nat) (N_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_2) _let_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2))))) (forall ((N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y) (tptp.hAPP_nat_nat tptp.suc N))))))) (forall ((X_1 tptp.nat) (N_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_2) _let_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_2))))) (forall ((X_1 tptp.int) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) N_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (not (= N_1 tptp.zero_zero_nat))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zEven))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zOdd))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) tptp.zEven))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) tptp.zOdd))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2)) tptp.zOdd))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2)) tptp.zOdd))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) Y_2)) tptp.zEven))))) (forall ((N_16 tptp.nat) (M_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_16) M_5)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_5) N_16)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat M_5)) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_16))))) (forall ((N_16 tptp.nat) (M_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_16) M_5)) (= (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_5) N_16)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_nat_complex tptp.semiri2020571505omplex M_5)) (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N_16))))) (forall ((N_16 tptp.nat) (M_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_16) M_5)) (= (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_5) N_16)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real tptp.semiri132038758t_real M_5)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_16))))) (forall ((N_16 tptp.nat) (M_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_16) M_5)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_5) N_16)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_5)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_16))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) tptp.zero_zero_int)) (= N_1 tptp.zero_zero_nat))) (forall ((A_10 tptp.rat) (N_15 tptp.nat) (B_8 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_10) _let_2) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_10 tptp.quickcheck_code_int) (N_15 tptp.nat) (B_8 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_10) _let_2) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_10 tptp.code_code_numeral) (N_15 tptp.nat) (B_8 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_10) _let_2) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_10 tptp.real) (N_15 tptp.nat) (B_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_10) _let_2) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_10 tptp.nat) (N_15 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_10) _let_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_10 tptp.int) (N_15 tptp.nat) (B_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_15))) (=> (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_10) _let_2) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_8) _let_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_10)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_8)) (= A_10 B_8))))))) (forall ((A_9 tptp.rat) (N_14 tptp.nat) (B_7 tptp.rat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_9) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B_7)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat A_9) B_7)))))) (forall ((A_9 tptp.quickcheck_code_int) (N_14 tptp.nat) (B_7 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_9) _let_1)) (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) B_7)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int A_9) B_7)))))) (forall ((A_9 tptp.code_code_numeral) (N_14 tptp.nat) (B_7 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_9) _let_1)) (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) B_7)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral A_9) B_7)))))) (forall ((A_9 tptp.real) (N_14 tptp.nat) (B_7 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_9) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) B_7)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_9) B_7)))))) (forall ((A_9 tptp.nat) (N_14 tptp.nat) (B_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_9) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_9) B_7)))))) (forall ((A_9 tptp.int) (N_14 tptp.nat) (B_7 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_14))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_9) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_7) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_9) B_7)))))) (forall ((N_13 tptp.nat) (A_8 tptp.rat)) (let ((_let_1 (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_rat_bool _let_1 (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((N_13 tptp.nat) (A_8 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.one_on1684967323de_int))) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool _let_1 (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((N_13 tptp.nat) (A_8 tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.one_on1645066479umeral))) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool _let_1 (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((N_13 tptp.nat) (A_8 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((N_13 tptp.nat) (A_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((N_13 tptp.nat) (A_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_8) (tptp.hAPP_nat_nat tptp.suc N_13))))))) (forall ((Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 Z_1)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)))) (and (=> _let_2 (= _let_1 Z_1)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Ma tptp.nat) (Z_2 tptp.int)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) Z_2) (and (= Ma (tptp.hAPP_int_nat tptp.nat_1 Z_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_2))))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 Z_1)) Z_1))) (forall ((Ma tptp.nat) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) Z_2)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N) M) (= N (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N) K_2) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) K_2)))))))) (forall ((M tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K_2))) (=> (not (= M _let_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K_2))))))) (forall ((M tptp.nat) (K_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (=> (not (= M (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K_2))) (=> (not (= M _let_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) M)))))) (forall ((I tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat tptp.suc I))) N)))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) N))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)))))) (= _let_71 _let_43) (forall ((M tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K_2)) (tptp.hAPP_nat_nat tptp.suc J_2))))) (forall ((M tptp.nat) (K_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) J_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_2) K_2))) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc J_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2) M))))) (forall ((N tptp.nat) (I tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 I)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat I) N)))))) (forall ((K_2 tptp.nat) (N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) N)) M))) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc M)) N))) (= tptp.zero_z126310315umeral (tptp.hAPP_i769753017umeral tptp.number1443263063umeral tptp.pls)) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) (tptp.hAPP_n522471361de_int tptp.semiri1424489471de_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) (tptp.hAPP_n1108039445umeral tptp.semiri1619134803umeral N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.semiri132038758t_real N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat tptp.semiri984289939at_nat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((X_1 tptp.int) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) N_1)) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_1) tptp.one_one_int)) tptp.zEven)))) (= _let_10 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_70)) (forall ((K_2 tptp.nat) (I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) K_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J_2))))))) (forall ((N_12 tptp.nat) (R_6 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R_6)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat R_6) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_12 tptp.nat) (R_6 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int tptp.zero_z891286103de_int) R_6)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int R_6) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_12 tptp.nat) (R_6 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral tptp.zero_z126310315umeral) R_6)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral R_6) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le565307924umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_12 tptp.nat) (R_6 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real R_6) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_12 tptp.nat) (R_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) R_6)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat R_6) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_12 tptp.nat) (R_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) R_6)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_6) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int R_6) (tptp.hAPP_nat_nat tptp.suc N_12))) R_6))))) (forall ((N_11 tptp.nat) (A_7 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_7)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat A_7) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_one_rat))))) (forall ((N_11 tptp.nat) (A_7 tptp.quickcheck_code_int)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int tptp.zero_z891286103de_int) A_7)) (=> (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int A_7) tptp.one_on1684967323de_int)) (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int (tptp.hAPP_n522471361de_int (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_on1684967323de_int))))) (forall ((N_11 tptp.nat) (A_7 tptp.code_code_numeral)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral tptp.zero_z126310315umeral) A_7)) (=> (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral A_7) tptp.one_on1645066479umeral)) (tptp.hBOOL (tptp.hAPP_C24501650l_bool (tptp.hAPP_C10902773l_bool tptp.ord_le1304079648umeral (tptp.hAPP_n1108039445umeral (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_on1645066479umeral))))) (forall ((N_11 tptp.nat) (A_7 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_7)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_7) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_one_real))))) (forall ((N_11 tptp.nat) (A_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) A_7)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_7) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_one_nat))))) (forall ((N_11 tptp.nat) (A_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_7)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_7) tptp.one_one_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_7) (tptp.hAPP_nat_nat tptp.suc N_11))) tptp.one_one_int))))) (forall ((P_1 tptp.fun_nat_bool) (I_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_int_nat tptp.nat_1 I_1))) (and (forall ((N_2 tptp.nat)) (=> (= I_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_2)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))))) (forall ((Ma tptp.nat) (W_1 tptp.int)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) W_1)))) (= (= Ma (tptp.hAPP_int_nat tptp.nat_1 W_1)) (and (=> _let_1 (= W_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (forall ((W_1 tptp.int) (Ma tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) W_1)))) (= (= (tptp.hAPP_int_nat tptp.nat_1 W_1) Ma) (and (=> _let_1 (= W_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (forall ((Ma tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V))) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) _let_1) (and (= Ma (tptp.hAPP_int_nat tptp.nat_1 _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)))))) (= _let_70 (tptp.hAPP_nat_nat tptp.suc _let_67)) (= _let_69 _let_43) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N))) (forall ((Y_6 tptp.quickcheck_code_int) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_Q125967240de_int tptp.power_881366806de_int Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int (tptp.hAPP_n522471361de_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.code_code_numeral) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_C471253896umeral tptp.power_2100829034umeral Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.times_1655362735umeral (tptp.hAPP_n1108039445umeral _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.rat) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_nat_rat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.complex) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_nat_complex _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.real) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.nat) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((Y_6 tptp.int) (P_6 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_6))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_6) N_10)) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc N_10)) P_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_10) P_6))) Y_6))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N))))))))) (forall ((M tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) K_2)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) M))) K_2) tptp.one_one_nat))) (forall ((A_3 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc A_3)) C_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat _let_1) C_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat A_3) C_1)) (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_1) C_1))) C_1))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.nat_tsub X) Y))))))) (= _let_8 (tptp.hAPP_nat_int tptp.semiri1621563631at_int _let_3)) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) X)) (= (tptp.hAPP_int_int (tptp.nat_tsub X) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((Ma tptp.nat) (W_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) W_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 W_1)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)))))) (forall ((X_5 tptp.rat) (Y_5 tptp.rat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat X_5) _let_1)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat Y_5) _let_1)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X_5) Y_5)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X_5) Y_5))))) (forall ((X_5 tptp.complex) (Y_5 tptp.complex)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X_5) _let_1)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex Y_5) _let_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X_5) Y_5)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X_5) Y_5))))) (forall ((X_5 tptp.real) (Y_5 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_5) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_5) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_5) Y_5)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_5) Y_5))))) (forall ((X_5 tptp.int) (Y_5 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_5) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int Y_5) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_5) Y_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_5) Y_5))))) (forall ((P_1 tptp.fun_int_bool) (X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X_1) Y_2)))) (and (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_2) X_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 tptp.zero_zero_int)))))) (= _let_3 _let_67) (= _let_67 _let_3) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.number_number_of_nat tptp.pls)) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Z_2)))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M))) _let_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) _let_1))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M))) _let_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) _let_1)))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_int_nat tptp.nat_1 Z_1)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z_1))))) (forall ((M tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M)))) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M)))) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N)))) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N))))) (forall ((M tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat V_2))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M)))) _let_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) _let_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc M)))) N) (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.div_mod_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc N)))) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N))))) (forall ((Q_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Q_1)) Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_1))))) (= Q_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat Ma) N_1)))))) (forall ((P_1 tptp.fun_nat_bool) (Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat Ma) N_1))) (or (and (= N_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (exists ((Q_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 Q_4)) Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc Q_4)))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 Q_4)))))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N)))))) (forall ((N_9 tptp.nat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_nat_rat tptp.semiri151668891at_rat N_9)) (tptp.hAPP_nat_rat (tptp.hAPP_rat_fun_nat_rat tptp.power_power_rat (tptp.hAPP_int_rat tptp.number_number_of_rat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_9)))) (forall ((N_9 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.semiri132038758t_real N_9)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_9)))) (forall ((N_9 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_9)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_9)))) (forall ((V_4 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_rat tptp.semiri151668891at_rat (tptp.hAPP_int_nat tptp.number_number_of_nat V_4)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int V_4))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_rat tptp.number_number_of_rat V_4))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((V_4 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_complex tptp.semiri2020571505omplex (tptp.hAPP_int_nat tptp.number_number_of_nat V_4)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int V_4))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_complex tptp.number528085621omplex V_4))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((V_4 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_real tptp.semiri132038758t_real (tptp.hAPP_int_nat tptp.number_number_of_nat V_4)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int V_4))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_real tptp.number267125858f_real V_4))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((V_4 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.number_number_of_nat V_4)))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int V_4))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 tptp.zero_zero_int))))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (exists ((Y_1 tptp.int)) (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Y_1))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1)))) (forall ((Z_2 tptp.int) (Ma tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_2)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_int_nat tptp.nat_1 Z_2)) Ma)) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)))) (=> (not _let_1) (= Ma tptp.zero_zero_nat)))))) (forall ((X_1 tptp.int) (K_1 tptp.int)) (=> (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (or (= N tptp.zero_zero_nat) (= N (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))) (= _let_68 _let_67) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (= (tptp.hAPP_int_int (tptp.div_mod_int X_1) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_int))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) _let_1)) X)))) (= tptp.one_on1645066479umeral (tptp.hAPP_i769753017umeral tptp.number1443263063umeral _let_1)) (forall ((A_6 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_6))) (= (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_8))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_6) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat _let_2 N_8)) _let_1)))))) (forall ((A_6 tptp.int) (N_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_6))) (= (tptp.hAPP_nat_int _let_2 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N_8))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_6) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_2 N_8)) _let_1)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.nat_tsub X) Y))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y) X)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1))) N))) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)))) _let_2))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) N))) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) _let_1))) _let_2))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (= (tptp.hAPP_int_int (tptp.div_mod_int X_1) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.zero_zero_int))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_1) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int Y_2) _let_1))))))) (forall ((K_2 tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_nat_int _let_1 M)) K_2) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) Y_2)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_1) _let_1)) Y_2))))) (forall ((X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_1) _let_1)) X_1)))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_1) Y_2)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X_1) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int Y_2) _let_1))))))) (forall ((V_3 tptp.int)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int V_3))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 Y_2)) (=> (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_2) tptp.zEven))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1)) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.nat_1 Y_2))))))))) (forall ((X_1 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1))) (exists ((Y_1 tptp.int)) (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Y_1)) tptp.one_one_int))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) _let_1)) tptp.one_one_int))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) _let_1))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N))) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat)) _let_1)))) (forall ((M tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int M))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) M)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int _let_1 tptp.one_one_int)))))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (not (forall ((K tptp.int)) (not (= X_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) K))))))) (forall ((I_1 tptp.nat) (P_1 tptp.fun_nat_bool) (P_5 tptp.nat)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) P_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc I_2)) P_5)))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) P_5)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)))))) (forall ((N tptp.nat) (A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (exists ((R_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_1)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real R_1) (tptp.hAPP_nat_nat tptp.suc N)) A_3))))) (forall ((K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K_2)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (= K_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))))) (forall ((J tptp.nat) (I_1 tptp.nat) (P_1 tptp.fun_nat_bool) (P_5 tptp.nat)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) P_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.suc I_2)) P_5)))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) P_5)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) P_5)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 J))))))) (forall ((N_1 tptp.nat) (N_7 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat F N_2)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) N_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat F N_1)) (tptp.hAPP_nat_nat F N_7)))))) (forall ((P_1 tptp.fun_nat_bool) (I_1 tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 J)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 I_1)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (P_1 tptp.bool)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat P_1) X_1) Y_2)))) (let ((_let_2 (tptp.hBOOL P_1))) (and (=> _let_2 (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) _let_1)) (=> (not _let_2) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2) _let_1)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_2)) (= X_1 Y_2))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (= Ma N_1))) (forall ((N tptp.nat) (I tptp.code_code_numeral)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.code_nat_of_aux I) N))) (let ((_let_2 (= I tptp.zero_z126310315umeral))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.code_nat_of_aux (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.minus_1690775515umeral I) tptp.one_on1645066479umeral)) (tptp.hAPP_nat_nat tptp.suc N)))))))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z_1)) (not (forall ((M_1 tptp.nat)) (not (= Z_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1))))))) (forall ((K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (not (forall ((N_2 tptp.nat)) (not (= K_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2))))))) (forall ((K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (exists ((N_2 tptp.nat)) (= K_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (exists ((K tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)))))) (forall ((N_1 tptp.nat) (N_7 tptp.nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.hAPP_nat_nat F N_1))) (let ((_let_2 (tptp.hAPP_nat_nat F N_7))) (=> (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat F N_2))) (let ((_let_2 (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_2)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_2) _let_1))))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) N_7)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_2) _let_1))))))))) (forall ((N_1 tptp.nat) (Ma tptp.nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.hAPP_nat_nat F N_1))) (let ((_let_2 (tptp.hAPP_nat_nat F Ma))) (=> (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat F N_2))) (let ((_let_2 (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc N_2)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_2) _let_1))))))) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_2) _let_1)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma))))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (exists ((M_1 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M_1))))) (forall ((V_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_3))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_2) (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.div_mod_int tptp.one_one_int) _let_1)))))))))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg tptp.zero_zero_int))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg tptp.one_one_int))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))))) (forall ((Z_5 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg Z_5)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_5) tptp.zero_zero_int)))) (forall ((X_1 tptp.int)) (= (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg X_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 W_1)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int W_1))))) (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_66))) (forall ((W_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 W_1)))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int W_1))))) (forall ((Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg Z_1)) (= (tptp.hAPP_int_nat tptp.nat_1 Z_1) tptp.zero_zero_nat))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_65)) (forall ((Z_1 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg Z_1))) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 Z_1)) Z_1))) (forall ((V_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (= (tptp.hAPP_int_nat tptp.number_number_of_nat V_2) tptp.zero_zero_nat))) (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (let ((_let_3 (tptp.hAPP_int_int tptp.number_number_of_int V))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_3)))) (= (= (tptp.hAPP_int_nat tptp.number_number_of_nat V) (tptp.hAPP_int_nat tptp.number_number_of_nat V_1)) (and (=> _let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int))) (=> (not _let_4) (and (=> _let_2 (= _let_3 tptp.zero_zero_int)) (=> (not _let_2) (= V V_1))))))))))) (forall ((V_3 tptp.int) (K_2 tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)) K_2))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)))) (let ((_let_3 (tptp.hAPP_nat_nat _let_2 _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_3))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_2))))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat _let_2 K_2))) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_2) V_3))) K_2)))))))))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_1) (tptp.hAPP_int_int tptp.number_number_of_int V_3)))))))))) (forall ((W tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) _let_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_2)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) _let_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_2) _let_1)))))))))) (forall ((N tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) N))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N))) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_1) N))))))))) (forall ((V_3 tptp.int) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int V_3))) (let ((_let_2 (tptp.hAPP_int_int tptp.number_number_of_int V_2))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat V_2))) (let ((_let_4 (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_3) (tptp.hAPP_int_nat tptp.number_number_of_nat V_3)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_2)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_6) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1)))))))))))))) (forall ((N tptp.nat) (V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) N)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_2))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N))) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.succ V_2))) N))))))) (forall ((P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int)))) (forall ((Z_1 tptp.int)) (not (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (not (= Z_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2))))))) (forall ((I_1 tptp.nat) (P_1 tptp.fun_nat_bool) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 K_1)) (=> (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_2)))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat K_1) I_1)))))) (forall ((N tptp.nat) (M_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N)) M_4)) (exists ((M_1 tptp.nat)) (= M_4 (tptp.hAPP_nat_nat tptp.suc M_1))))) (= (tptp.hAPP_int_int tptp.succ tptp.pls) _let_1) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.succ (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.succ K_2)))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.succ (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit1 K_2))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.succ K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) tptp.one_one_int))) (= (tptp.hAPP_int_int tptp.succ tptp.min) tptp.pls) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) tptp.min) (tptp.hAPP_int_int tptp.succ K_2))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) (tptp.hAPP_int_int tptp.succ L_2))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) tptp.one_one_nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.succ V_2)))))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_2) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.succ V_2)))))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_2))))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.succ V_2)))))))) (forall ((J tptp.int) (A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_5) A))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong J) tptp.zero_zero_int) P_5))) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.multInvPair A P_5) J)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))))))))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_5) A))) (forall ((X_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_2) (tptp.setS A P_5))) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int X_2) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))))) (forall ((I tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K_2)) (=> (not (= K_2 (tptp.hAPP_nat_nat tptp.suc I))) (not (forall ((J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_1)) (not (= K_2 (tptp.hAPP_nat_nat tptp.suc J_1))))))))) (forall ((I tptp.nat) (K_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc I)) K_2)) (not (forall ((J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J_1)) (not (= K_2 (tptp.hAPP_nat_nat tptp.suc J_1)))))))) (forall ((A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_5) A))) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_f521865025ol_nat tptp.finite1876863882t_bool (tptp.setS A P_5))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int)) _let_1)))))))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (= (tptp.comple219730294t_bool (tptp.setS A P_5)) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5)))))) (forall ((D2 tptp.real) (D1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D2)) (exists ((E tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real E))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D1)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 D2))))))))) (forall ((X tptp.real) (Y tptp.real) (Xa_2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Xa_2) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Ya) _let_1)))))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat_1 tptp.nat)) (not (= Y (tptp.hAPP_nat_nat tptp.suc Nat_1))))))) (forall ((P_1 tptp.fun_nat_bool) (K_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 K_1)) (=> (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_2)))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real tptp.sqrt X_1) (tptp.hAPP_real_real tptp.sqrt Y_2)) (= X_1 Y_2))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_real_real tptp.sqrt Y))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sqrt X_1)) (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.sqrt X_1) tptp.zero_zero_real) (= X_1 tptp.zero_zero_real))) (= (tptp.hAPP_real_real tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_real_real tptp.sqrt Y))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt X_1)) (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_real_real tptp.sqrt Y)))) (forall ((X tptp.real) (K_2 tptp.nat)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) K_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sqrt X)) K_2))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.sqrt X_1) tptp.one_one_real) (= X_1 tptp.one_one_real))) (= (tptp.hAPP_real_real tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.hAPP_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt X)))))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sqrt X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.zero_zero_real)))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt X)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (not (= (tptp.hAPP_real_real tptp.sqrt X) tptp.zero_zero_real)))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt X)))))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sqrt X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.one_one_real)))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2))))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sqrt Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) Y)))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 _let_53)) (tptp.hBOOL (tptp.hAPP_real_bool _let_62 _let_53)) (tptp.hBOOL (tptp.hAPP_real_bool _let_64 _let_53)) (forall ((Y tptp.real) (X tptp.real)) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.hAPP_real_real tptp.sqrt X) Y)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sqrt X_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((A_3 tptp.real) (C_1 tptp.real) (B_2 tptp.real) (D_3 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) C_1)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_2) D_3)) _let_1)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_3) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_2) _let_1)))) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real C_1) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real D_3) _let_1)))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))) (forall ((X tptp.real) (Y tptp.real) (Xa_2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Xa_2) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Ya) _let_1))))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sqrt _let_2)) _let_1) _let_2)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real) (U_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (let ((_let_3 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real U_1) (tptp.hAPP_int_real tptp.number267125858f_real _let_1)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) U_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) _let_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_2)))) U_1)))))))))))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.comple219730294t_bool (tptp.setS A P_5)))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N (tptp.hAPP_nat_nat tptp.suc M_1))))) (forall ((N_1 tptp.nat) (P_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat)) (=> (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat tptp.suc N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_1))))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 R_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real A_3) R_3)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sqrt X)) (tptp.hAPP_real_real tptp.sqrt Y)))) (forall ((A tptp.int) (P_5 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5)))) (forall ((A tptp.int) (P_5 tptp.int) (X_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_2) (tptp.setS A P_5))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int X_2)))) (forall ((A tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool tptp.d22set A)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X_1) Y_2))) (and (or (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2))) (or (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_2) tptp.zero_zero_real))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) Y)))) (forall ((P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5))))) (forall ((U_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) U_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real U_1) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) U_1)))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) B_2)) _let_1)) A_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_2) A_3)) _let_1)))) (forall ((B_2 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_2) A_3)) _let_1)) A_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_2) A_3)) _let_1)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1) X))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real Y_2))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (= X_1 (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 Z_2))) (= (tptp.hAPP_real_real _let_2 X_1) (tptp.hAPP_real_real _let_1 Z_2)))))) (forall ((B_2 tptp.complex) (A_3 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex B_2) A_3))) (tptp.hAPP_complex_real tptp.norm_norm_complex B_2))) (tptp.hAPP_complex_real tptp.norm_norm_complex A_3)))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.setS A P_5))))) (forall ((K_1 tptp.nat) (L tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) L)) (exists ((N_2 tptp.nat)) (= L (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) N_2))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_real_real F A))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real F B)))) (let ((_let_3 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real _let_2 _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real _let_1) (tptp.hAPP_real_real _let_3 A)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_3 B))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real))) (= (tptp.hAPP_real_real tptp.arctan X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real _let_2 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)))))))))))) (forall ((Ma tptp.nat) (No tptp.nat) (F tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F N_2)) (tptp.hAPP_nat_real F (tptp.hAPP_nat_nat tptp.suc N_2))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F Ma)) (tptp.hAPP_nat_real F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) No)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.arctan X)) (tptp.hAPP_real_real tptp.arctan Y))))) (= (tptp.hAPP_real_real tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.arctan X)) (tptp.hAPP_real_real tptp.arctan Y))))) (forall ((X tptp.real) (N tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int N)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natceiling (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_int_real tptp.number267125858f_real N))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natceiling X)) (tptp.hAPP_int_nat tptp.number_number_of_nat N)))))) (forall ((Y tptp.real) (X tptp.real) (U_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (let ((_let_3 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real U_1) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_int_real tptp.number267125858f_real _let_1))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real X)) _let_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real Y)) _let_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_2)))) U_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1)))))) tptp.one_one_real)))) (forall ((X tptp.real) (N tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int N)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_int_real tptp.number267125858f_real N))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natfloor X)) (tptp.hAPP_int_nat tptp.number_number_of_nat N)))))) (forall ((R_3 tptp.real)) (= (tptp.hAPP_real_real tptp.norm_norm_real R_3) (tptp.hAPP_real_real tptp.abs_abs_real R_3))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) X)) (tptp.hAPP_real_real tptp.abs_abs_real X))) (= (tptp.natfloor tptp.zero_zero_real) tptp.zero_zero_nat) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.natfloor X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natfloor X)) (tptp.natfloor Y))))) (forall ((N tptp.int)) (= (tptp.natfloor (tptp.hAPP_int_real tptp.number267125858f_real N)) (tptp.hAPP_int_nat tptp.number_number_of_nat N))) (= (tptp.natfloor tptp.one_one_real) tptp.one_one_nat) (= (tptp.natceiling tptp.zero_zero_real) tptp.zero_zero_nat) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.natceiling X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natceiling X)) (tptp.natceiling Y))))) (forall ((N tptp.int)) (= (tptp.natceiling (tptp.hAPP_int_real tptp.number267125858f_real N)) (tptp.hAPP_int_nat tptp.number_number_of_nat N))) (= (tptp.natceiling tptp.one_one_real) tptp.one_one_nat) (forall ((X tptp.real) (Y tptp.real) (C_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real C_1) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real C_1) (tptp.hAPP_real_real tptp.abs_abs_real Y)))) (= X tptp.zero_zero_real)))) (forall ((X tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.abs_abs_real X)) tptp.one_one_real)) X)))) (forall ((U_1 tptp.real) (V_2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (= X Y) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real U_1)) V_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) U_1)) Y))) V_2))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.natfloor X) tptp.zero_zero_nat))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_real_real tptp.abs_abs_real X))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.natceiling X) tptp.zero_zero_nat))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X_1)))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natceiling X_1)) tptp.one_one_nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.one_one_real)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hAPP_real_real tptp.abs_abs_real X))) (forall ((B_2 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.natfloor A_3)) (tptp.natfloor B_2))) (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3) B_2)))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) tptp.one_one_real)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natfloor X)) tptp.one_one_nat)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real Y)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.arctan X)) (tptp.hAPP_real_real tptp.arctan Y)) (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natceiling (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natceiling X)) tptp.one_one_nat)))) (forall ((X_1 tptp.real) (N_1 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int N_1)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.number_number_of_nat N_1)) (tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real N_1)) X_1)))))) (forall ((X_1 tptp.real) (N_1 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int N_1)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natceiling X_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat N_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.hAPP_int_real tptp.number267125858f_real N_1))))))) (forall ((B_2 tptp.real) (A_3 tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) B_2)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((Y_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y_1))) D_2)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_3) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_1) B_2)))))))))) (forall ((B_2 tptp.real) (A_3 tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) B_2)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((Y_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y_1))) D_2)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_1) B_2)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) _let_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))))))))) (= _let_37 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_36) (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real _let_27 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit1 _let_2)))))) (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real _let_27 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 _let_9))))))))))) (not (= tptp.pi tptp.zero_zero_real)) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int M))) (= (tptp.hAPP_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int B_2) A_3)) (= (tptp.hAPP_int_int tptp.abs_abs_int A_3) (tptp.hAPP_int_int tptp.abs_abs_int B_2))))) (forall ((D_3 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int tptp.abs_abs_int D_3)) D_3))) (forall ((D_3 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_3) (tptp.hAPP_int_int tptp.abs_abs_int D_3)))) (forall ((M tptp.int) (N tptp.int)) (=> (= (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N)) tptp.one_one_int) (= (tptp.hAPP_int_int tptp.abs_abs_int M) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 tptp.pi)) (not (tptp.hBOOL (tptp.hAPP_real_bool _let_63 tptp.zero_zero_real))) (tptp.hBOOL (tptp.hAPP_real_bool _let_62 tptp.pi)) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X_1) tptp.one_one_int)) (= (tptp.hAPP_int_int tptp.abs_abs_int X_1) tptp.one_one_int))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.abs_abs_int X))) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_int_nat tptp.nat_1 _let_1)) _let_1))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.ln X)) X)))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)) (= (= (tptp.hAPP_real_real tptp.ln X_1) (tptp.hAPP_real_real tptp.ln Y_2)) (= X_1 Y_2)))))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.ln X_1)) (tptp.hAPP_real_real tptp.ln Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2))))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Y) X)) (= (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.abs_abs_int X)) (tptp.hAPP_int_int tptp.abs_abs_int Y))))) (= (tptp.hAPP_real_real tptp.ln tptp.one_one_real) tptp.zero_zero_real) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (= (tptp.hAPP_real_real tptp.ln X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))) (forall ((Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.abs_abs_int Z_2)) tptp.one_one_int)) (= Z_2 tptp.zero_zero_int))) (forall ((D_3 tptp.int) (I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_3) I)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.abs_abs_int D_3)) (tptp.hAPP_int_int tptp.abs_abs_int I)))))) (forall ((X tptp.int) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.abs_abs_int X)) N)))) (forall ((W tptp.int) (Z_1 tptp.int)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int W) Z_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int W))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Z_1))))) (forall ((Z_2 tptp.int)) (= (= (tptp.hAPP_int_int tptp.abs_abs_int Z_2) tptp.one_one_int) (or (= Z_2 tptp.one_one_int) (= Z_2 (tptp.hAPP_int_int tptp.number_number_of_int tptp.min))))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln X_1)) (tptp.hAPP_real_real tptp.ln Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.ln X))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.ln X))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.ln X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X_1)))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (= (= (tptp.hAPP_real_real tptp.ln X_1) tptp.zero_zero_real) (= X_1 tptp.one_one_real)))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.ln X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.ln X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.ln X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) tptp.one_one_real))))) (forall ((X_1 tptp.int) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.abs_abs_int X_1)) N_1))) (or (not (= X_1 tptp.zero_zero_int)) (= N_1 tptp.zero_zero_nat)))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.abs_abs_int X)) _let_1)))) (forall ((N_1 tptp.int) (Ma tptp.int)) (=> (not (= Ma tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ma) N_1)) Ma)) (= (tptp.hAPP_int_int tptp.abs_abs_int N_1) tptp.one_one_int)))) (forall ((Z_2 tptp.int) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Z_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Z_2))) Ma)))) (forall ((Ma tptp.nat) (Z_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) Z_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Ma) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Z_2)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.ln X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.ln X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X_1))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.ln X)) (tptp.hAPP_real_real tptp.ln Y))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))) X)))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.ln X)) (tptp.hAPP_real_real tptp.ln Y))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))) X)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) _let_1) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B) _let_1)) (= (tptp.hAPP_int_int tptp.abs_abs_int A) (tptp.hAPP_int_int tptp.abs_abs_int B))))) (forall ((A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.abs_abs_int A_3)) _let_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_12) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool _let_63 _let_36)) (not (= _let_14 _let_12)) (forall ((A_3 tptp.int)) (=> (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.one_one_int) (= (tptp.hAPP_int_int tptp.abs_abs_int A_3) tptp.one_one_int))) (forall ((X tptp.int) (Z_1 tptp.int) (D_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int _let_1 Z_1))) tptp.one_one_int)) D_3))) Z_1))))) (forall ((Z_1 tptp.int) (X tptp.int) (D_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Z_1))) tptp.one_one_int)) D_3)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_14) _let_12)) (not (= _let_14 tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_14) _let_12)) (tptp.hBOOL (tptp.hAPP_real_bool _let_24 _let_14)) (tptp.hBOOL (tptp.hAPP_real_bool _let_62 _let_14)) (forall ((Y tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.arctan Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (= (tptp.hAPP_real_real tptp.arctan tptp.one_one_real) _let_37) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (exists ((N_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Y_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N_2) X_1))))) X_1)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) X)) (exists ((N_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N_2) X))))) X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) _let_2))) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)))))))))) (forall ((K_1 tptp.int) (F tptp.fun_nat_int) (N_1 tptp.nat)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) tptp.one_one_nat))) (tptp.hAPP_nat_int F I_2)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) (tptp.hAPP_nat_int F N_1))) (exists ((I_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) N_1)) (= (tptp.hAPP_nat_int F I_2) K_1))))))) (forall ((K_1 tptp.int) (F tptp.fun_nat_int) (N_1 tptp.nat)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) N_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) tptp.one_one_nat))) (tptp.hAPP_nat_int F I_2)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F tptp.zero_zero_nat)) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) (tptp.hAPP_nat_int F N_1))) (exists ((I_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) N_1)) (= (tptp.hAPP_nat_int F I_2) K_1))))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sqrt X)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.arctan X)))) (forall ((U_1 tptp.real) (X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real U_1) U_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) X)))) (forall ((X_1 tptp.real) (A tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) (tptp.hAPP_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X_1 A))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2) tptp.zero_zero_real) (= Y_2 (tptp.hAPP_real_real tptp.uminus_uminus_real X_1)))) (forall ((X_1 tptp.real) (R_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) R_2)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real R_2)) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) R_2))))) (forall ((R_3 tptp.real) (S_1 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real R_3) S_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real R_3) (tptp.hAPP_real_real tptp.uminus_uminus_real S_1)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real tptp.uminus_uminus_real Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real tptp.uminus_uminus_real Y))) (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Y) (tptp.hAPP_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.hAPP_complex_real tptp.norm_norm_complex X))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) _let_1)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real X_1)) Y_2)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_2) (tptp.hAPP_real_real tptp.uminus_uminus_real X_1))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_2) (tptp.hAPP_real_real tptp.uminus_uminus_real X_1))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real X_1)) Y_2)))) (forall ((A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.abs_abs_real A_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real A_3))) (=> (not _let_2) (= _let_1 A_3)))))) (forall ((R_3 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.abs_abs_real R_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real R_3))) (=> (not _let_2) (= _let_1 R_3)))))) (forall ((X tptp.real) (Y tptp.real) (L_2 tptp.real) (M tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real M))) (let ((_let_2 (tptp.hAPP_real_real tptp.uminus_uminus_real L_2))) (let ((_let_3 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_3 Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_2) _let_1)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real _let_3 _let_2))) (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Y) _let_1))))))))) (forall ((U_1 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real U_1) _let_1))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) X))) (tptp.hAPP_real_real tptp.uminus_uminus_real X)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.ln _let_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) _let_1)))))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_59)) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_14)) tptp.zero_zero_real)) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_real_real tptp.arctan Y))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) _let_1)))))) (forall ((Y tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_real_real tptp.arctan Y)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) _let_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))))) (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) X))))))))) (forall ((K_1 tptp.int) (F tptp.fun_nat_int) (N_1 tptp.nat) (Ma tptp.nat)) (=> (forall ((I_2 tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) tptp.one_one_nat))) (tptp.hAPP_nat_int F I_2)))) tptp.one_one_int)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int F Ma)) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) (tptp.hAPP_nat_int F N_1))) (exists ((I_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) I_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) N_1)) (= (tptp.hAPP_nat_int F I_2) K_1)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_real_real tptp.arcsin Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_real_real tptp.arcsin Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_real_real tptp.arcsin Y)))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.arcsin Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N)))) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))) (= (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.pls) tptp.pls) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.uminus_uminus_int K_2)))) (= (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z_1)) W) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) W)))) (forall ((W tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.number_number_of_int W)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.uminus_uminus_int W)))) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z_1)) (tptp.hAPP_int_int tptp.uminus_uminus_int W)))) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z_1)) Z_1)) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int Ma))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ma))))) (forall ((D tptp.int) (Ta tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int tptp.uminus_uminus_int D)) Ta)))) (forall ((D tptp.int) (Ta tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ta)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int Ta)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) B_2))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) B_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2)))) (forall ((X tptp.int) (M tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.div_mod_int X) M))) M) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int X)) M))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_int_int tptp.uminus_uminus_int X_1))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X) Y) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X) (tptp.hAPP_complex_complex tptp.uminus473333897omplex Y)))) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z_1)) Z_1) tptp.zero_zero_int)) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (and (= N_1 tptp.zero_zero_nat) (= Ma tptp.zero_zero_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))))) (= tptp.min (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.one_one_int)) (forall ((K_2 tptp.int) (L_2 tptp.int)) (=> (not (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int K_2)) L_2) tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int (tptp.div_mod_int K_2) L_2) tptp.zero_zero_int)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (let ((_let_1 (tptp.div_mod_int K_2))) (=> (not (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int L_2)) tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int _let_1 L_2) tptp.zero_zero_int))))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.min) K_2) (tptp.hAPP_int_int tptp.uminus_uminus_int K_2))) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_1) W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) (tptp.hAPP_int_int tptp.uminus_uminus_int W)))) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) (tptp.hAPP_int_int tptp.uminus_uminus_int W)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_1) W))) (= (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.min) _let_1) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)))) (and (= N_1 tptp.zero_zero_nat) (= Ma tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) tptp.zero_zero_int))) (forall ((N tptp.nat)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) tptp.zero_zero_nat)) (forall ((I tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.abs_abs_int I))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int I))) (=> (not _let_2) (= _let_1 I)))))) (forall ((V_2 tptp.int) (W tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_int tptp.number_number_of_int W)) (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V_2) (tptp.hAPP_int_int tptp.uminus_uminus_int W))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.div_mod_int A_3))) (let ((_let_2 (tptp.hAPP_int_int _let_1 B_2))) (let ((_let_3 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) B_2))))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) B_2))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B_2) _let_1)))))))) (forall ((A_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) (tptp.hAPP_int_int tptp.number_number_of_int tptp.min)) (tptp.hAPP_int_int tptp.uminus_uminus_int A_3))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N)))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N)))) tptp.zero_zero_int))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N))))))) (forall ((A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) _let_1) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) _let_1))))) (forall ((Z_4 tptp.int) (Z_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.uminus_uminus_int Z_1))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.uminus_uminus_int Z_4)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3))) (let ((_let_2 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int _let_1 B_2)))) (let ((_let_3 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))) (let ((_let_4 (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) tptp.zero_zero_int))) (=> (not (= B_2 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2)))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) B_2))) (let ((_let_3 (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) tptp.zero_zero_int))) (=> (not (= B_2 tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_1) tptp.one_one_int))))))))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) _let_1)))))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) _let_1))))))) (forall ((A tptp.int) (B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_b1463609396nt_int tptp.if_int (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int R_2) tptp.zero_zero_int)))) (let ((_let_2 (tptp.hAPP_int_int tptp.uminus_uminus_int Q_1))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A B) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_1) R_2))) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel (tptp.hAPP_int_int tptp.uminus_uminus_int A) B) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int _let_1 _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int _let_1 tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int B) R_2))))))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) tptp.zero_zero_int)) (exists ((N_2 tptp.nat)) (= X (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N_2))))))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sgn_sgn_real X)) tptp.pi)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hAPP_real_real tptp.arctan X))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.arcsin X)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln X)) X)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.cos X))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.cos X)) tptp.one_one_real))) (= (tptp.hAPP_real_real tptp.cos tptp.zero_zero_real) tptp.one_one_real) (forall ((X tptp.real)) (not (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.arctan X)) tptp.zero_zero_real))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sgn_sgn_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) (tptp.hAPP_real_real tptp.abs_abs_real X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.cos Y))))))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_real_real tptp.cos X)))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real tptp.cos X))) tptp.one_one_real))) (= (tptp.hAPP_real_real tptp.cos tptp.pi) _let_34) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.pi)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.cos X)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real tptp.sgn_sgn_real X) tptp.one_one_real))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.cos Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.cos Y)) (tptp.hAPP_real_real tptp.cos X))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.sgn_sgn_real X) (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.sgn_sgn_real X))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)))) (let ((_let_3 (= X tptp.zero_zero_real))) (and (=> _let_3 (= _let_1 tptp.zero_zero_real)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.one_one_real)))))))))) (forall ((A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.sgn_sgn_real A_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)))) (let ((_let_3 (= A_3 tptp.zero_zero_real))) (and (=> _let_3 (= _let_1 tptp.zero_zero_real)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.one_one_real)))))))))) (not (= _let_61 tptp.zero_zero_real)) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.cos Y)) (tptp.hAPP_real_real tptp.cos X))))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_61) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_61) tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.cos _let_14) tptp.zero_zero_real) (= (tptp.hAPP_real_real tptp.cos _let_59) tptp.one_one_real) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP_real_real tptp.cos X))) (= (tptp.hAPP_real_real tptp.cos _let_57) _let_28) (= (tptp.hAPP_real_real tptp.cos _let_58) _let_56) (= (tptp.hAPP_real_real tptp.cos _let_37) _let_54) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_1) X))) tptp.one_one_real)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.cos X))))))) (= (tptp.hAPP_real_real tptp.cos _let_52) tptp.zero_zero_real) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.cos X))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.cos X))))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) tptp.pi)) (= (tptp.hAPP_real_real tptp.cos X_2) Y) (forall ((Y_1 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_1) tptp.pi)) (= (tptp.hAPP_real_real tptp.cos Y_1) Y)) (= Y_1 X_2)))))))) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real tptp.cos X_2) tptp.zero_zero_real) (forall ((Y_1 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_1) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real tptp.cos Y_1) tptp.zero_zero_real)) (= Y_1 X_2))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_real_real tptp.tan X))) (let ((_let_3 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)))) (let ((_let_4 (tptp.hAPP_real_real _let_3 X))) (=> (not (= (tptp.hAPP_real_real tptp.cos X) tptp.zero_zero_real)) (=> (not (= (tptp.hAPP_real_real tptp.cos _let_4) tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.tan _let_4) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real _let_3 _let_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_2) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)))))))))))) (forall ((X_4 tptp.real) (Y_4 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X_4) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_4) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_4) _let_1)))))) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.arccos _let_2)) _let_2)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.tan X)))) (= (tptp.hAPP_real_real tptp.tan tptp.zero_zero_real) tptp.zero_zero_real) (forall ((Y tptp.real)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real tptp.arctan Y)) Y)) (= (tptp.hAPP_real_real tptp.tan tptp.pi) tptp.zero_zero_real) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.pi)) (tptp.hAPP_real_real tptp.tan X))) (forall ((X tptp.real) (N tptp.int)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real N)) tptp.pi))) (tptp.hAPP_real_real tptp.tan X))) (forall ((I tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.sgn_sgn_int I))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) I)))) (let ((_let_3 (= I tptp.zero_zero_int))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.one_one_int)))))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.pi)) (= (tptp.hAPP_real_real tptp.arccos (tptp.hAPP_real_real tptp.cos X)) X)))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.arccos Y)) Y))) (= (tptp.hAPP_real_real tptp.tan _let_57) _let_55) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.arccos Y)))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real tptp.arccos Y)) Y)))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.arccos Y)) tptp.pi))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)) X)) (= (tptp.hAPP_real_real tptp.arccos (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP_real_real tptp.tan X))) (= (tptp.hAPP_real_real tptp.tan _let_37) tptp.one_one_real) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.tan Y))) (let ((_let_2 (tptp.hAPP_real_real tptp.tan X))) (let ((_let_3 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y))) (=> (not (= (tptp.hAPP_real_real tptp.cos X) tptp.zero_zero_real)) (=> (not (= (tptp.hAPP_real_real tptp.cos Y) tptp.zero_zero_real)) (=> (not (= (tptp.hAPP_real_real tptp.cos _let_3) tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.tan _let_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_2) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.cos Y))) (let ((_let_2 (tptp.hAPP_real_real tptp.cos X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.tan X)) (tptp.hAPP_real_real tptp.tan Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.tan X))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arccos Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.tan Y)) (tptp.hAPP_real_real tptp.tan X)))))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_2))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_3 Y_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 _let_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_3 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) _let_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.tan Y_2)) (tptp.hAPP_real_real tptp.tan X_1)))))))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arccos Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) tptp.pi))))))) (forall ((Y tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_real_real tptp.tan Y)) (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) Y)))) (= (tptp.hAPP_real_real tptp.tan _let_58) (tptp.hAPP_real_real _let_27 _let_55)) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.tan X)) tptp.zero_zero_real))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arctan Y))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) _let_2)) (= (tptp.hAPP_real_real tptp.tan _let_1) Y))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_1)) (= (tptp.hAPP_real_real tptp.arctan (tptp.hAPP_real_real tptp.tan X)) X))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arccos Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.hAPP_real_real tptp.cos _let_1) Y)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (exists ((Z tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) Z)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Z) _let_1)) (= (tptp.hAPP_real_real tptp.tan Z) X)))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP_real_real tptp.tan X_2) Y))))) (forall ((Y tptp.real)) (exists ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) _let_1)) (= (tptp.hAPP_real_real tptp.tan X_2) Y) (forall ((Y_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_1) _let_1)) (= (tptp.hAPP_real_real tptp.tan Y_1) Y)) (= Y_1 X_2)))))))) (forall ((Y tptp.real)) (exists ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) _let_1)) (= (tptp.hAPP_real_real tptp.tan X_2) Y))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) (tptp.hAPP_real_real tptp.tan X_2))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_1) X))) (let ((_let_3 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) _let_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_3)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) _let_3)) (= (tptp.hAPP_real_real tptp.tan X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sin _let_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.cos _let_2)) tptp.one_one_real))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.pi) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) M))))) (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) tptp.zero_zero_real))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real tptp.arccos X)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.real_nat N)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X)))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat X))) (= (tptp.hAPP_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (= (tptp.hAPP_nat_real tptp.real_nat N_1) (tptp.hAPP_nat_real tptp.real_nat Ma)) (= N_1 Ma))) (= (tptp.hAPP_real_real tptp.sin tptp.zero_zero_real) tptp.zero_zero_real) (forall ((N tptp.nat)) (= (tptp.natfloor (tptp.hAPP_nat_real tptp.real_nat N)) N)) (forall ((N tptp.nat)) (= (tptp.natceiling (tptp.hAPP_nat_real tptp.real_nat N)) N)) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.pi) (tptp.hAPP_nat_real tptp.real_nat N))) tptp.zero_zero_real)) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.pi)) tptp.zero_zero_real)) _let_60 _let_60 (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sin X)) tptp.one_one_real))) (forall ((N_1 tptp.nat)) (= (= (tptp.hAPP_nat_real tptp.real_nat N_1) tptp.zero_zero_real) (= N_1 tptp.zero_zero_nat))) (= (tptp.hAPP_nat_real tptp.real_nat tptp.zero_zero_nat) tptp.zero_zero_real) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.zero_zero_real)))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real tptp.real_nat Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma)))) (= (tptp.hAPP_real_real tptp.sin tptp.pi) tptp.zero_zero_real) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real tptp.real_nat Ma))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) Ma)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat M)) (tptp.hAPP_nat_real tptp.real_nat N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat M)) (tptp.hAPP_nat_real tptp.real_nat N)))) (= (tptp.hAPP_nat_real tptp.real_nat tptp.one_one_nat) tptp.one_one_real) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real tptp.real_nat M)) N) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_nat_real tptp.real_nat M)) N))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_nat_real tptp.real_nat (tptp.natceiling X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sin X))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.pi)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sin X))))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat N_1)) tptp.zero_zero_real)) (= N_1 tptp.zero_zero_nat))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_real_real tptp.sin X)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N))))) (forall ((X tptp.real)) (=> (= (tptp.hAPP_real_real tptp.cos X) tptp.one_one_real) (= (tptp.hAPP_real_real tptp.sin X) tptp.zero_zero_real))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real tptp.sin X))) tptp.one_one_real))) (= (tptp.hAPP_nat_real tptp.real_nat _let_43) tptp.one_one_real) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.cos Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.sin Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos Y)) (tptp.hAPP_real_real tptp.sin X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin Y)) (tptp.hAPP_real_real tptp.cos X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.cos Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.sin Y))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.one_one_real))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.pi) X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.pi)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real tptp.real_nat M)) (tptp.hAPP_nat_real tptp.real_nat N))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real tptp.real_nat X))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.tan X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.cos X)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat (tptp.natfloor X))) X)))) (forall ((X tptp.nat) (A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat X)) A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) (tptp.natfloor A_3))))) (forall ((X tptp.real) (A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_nat_real tptp.real_nat A_3))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natceiling X)) A_3)))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_real tptp.real_nat N))) tptp.pi)) tptp.zero_zero_real)) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.natfloor X))) (=> (= X (tptp.hAPP_nat_real tptp.real_nat _let_1)) (= (tptp.natfloor (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat _let_1) N))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.real_nat N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.sin X))) (let ((_let_2 (tptp.hAPP_real_real tptp.cos X))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) _let_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((X tptp.real)) (=> (= (tptp.hAPP_real_real tptp.sin X) tptp.zero_zero_real) (= (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real tptp.cos X)) tptp.one_one_real))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos Y)) (tptp.hAPP_real_real tptp.cos X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin Y)) (tptp.hAPP_real_real tptp.sin X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.cos Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.sin Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X)) (tptp.hAPP_real_real tptp.cos Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.sin Y))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat N_1)) tptp.one_one_real)) (tptp.hAPP_nat_real tptp.real_nat Ma))))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat Ma)) tptp.one_one_real))))) (forall ((A tptp.nat) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) (tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat A)) X_1))))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.pi)) tptp.zero_zero_real)) (forall ((A tptp.nat) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.natceiling X_1)) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.hAPP_nat_real tptp.real_nat A)))))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat (tptp.natfloor X))) tptp.one_one_real)))) (forall ((X tptp.real) (N tptp.nat)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.pi))) (tptp.hAPP_real_real tptp.tan X))) (forall ((A_3 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) X)) (= (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.natfloor X)) A_3))))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) tptp.one_one_real)) (tptp.hAPP_nat_real tptp.real_nat (tptp.natfloor X))))) (forall ((A_3 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat A_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) X)) (= (tptp.natceiling (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.natceiling X)) A_3))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X))) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat M)) tptp.pi)) _let_1))))))) (forall ((N tptp.nat) (D_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) D_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_3) N)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) D_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real tptp.real_nat D_3)))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_real_real tptp.ln X))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_nat_real tptp.real_nat N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.natfloor X)) N))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real tptp.real_nat X))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) X)))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int V_2))))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_real tptp.number267125858f_real V_2))))))) (forall ((N tptp.nat) (X tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real tptp.real_nat X))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) X)))) tptp.one_one_real))) (forall ((A_3 tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_nat_real tptp.real_nat A_3))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natfloor X)) A_3)))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real tptp.arcsin Y)) Y)))) (forall ((Z_1 tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natfloor Z_1)) tptp.one_one_nat)) N)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Z_1) (tptp.hAPP_nat_real tptp.real_nat N))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.natfloor X) N))))) (forall ((A_3 tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.natceiling (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_nat_real tptp.real_nat A_3))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.natceiling X)) A_3)))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X))) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat M)) tptp.pi)) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sin X))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) N)))) tptp.pi)) (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) N)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.sin X))) (tptp.hAPP_real_real tptp.cos X))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) X)) tptp.one_one_real)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) tptp.one_one_real)) N))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.cos Y))) (let ((_let_2 (tptp.hAPP_real_real tptp.cos X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.tan X)) (tptp.hAPP_real_real tptp.tan Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.nat) (D_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) D_3)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat X)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) D_3))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat X) D_3))) _let_1)))))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) tptp.pi)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) N))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real tptp.pi) (tptp.hAPP_nat_real tptp.real_nat N))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) N))) (= (tptp.hAPP_real_real tptp.sin _let_59) tptp.zero_zero_real) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP_real_real tptp.sin X))) (= (tptp.hAPP_real_real tptp.sin _let_14) tptp.one_one_real) (= (tptp.hAPP_real_real tptp.sin _let_58) _let_28) (= (tptp.hAPP_real_real tptp.sin _let_57) _let_56) (= (tptp.hAPP_real_real tptp.sin _let_37) _let_54) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) N))))) (forall ((Y tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.natfloor (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) (tptp.hAPP_nat_real tptp.real_nat Y))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.natfloor X)) Y))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real tptp.real_nat N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.natceiling X) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real tptp.sin X))))))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real tptp.cos A_3))) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real tptp.sin A_3))) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real R_3) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sin X)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.cos X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.cos X)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sin X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sin X)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.cos X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.cos X)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sin X)) _let_1))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.sin Y)) (tptp.hAPP_real_real tptp.sin X)))))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.cos X) (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X)))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sin X) (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X)))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_nat_real tptp.real_nat N))) tptp.pi)) tptp.one_one_real)) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.sin X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.cos X)) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.sin X)) _let_2)))))) (= (tptp.hAPP_real_real tptp.sin _let_52) _let_47) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X)) (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) _let_1)) (= (tptp.hAPP_real_real tptp.arcsin (tptp.hAPP_real_real tptp.sin X)) X))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real tptp.sin Y))) (let ((_let_3 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.sin X)))) (let ((_let_4 (tptp.hAPP_real_real tptp.cos Y))) (let ((_let_5 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X)))) (let ((_let_6 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) Y))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.sin _let_6)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_3 _let_4)) (tptp.hAPP_real_real _let_5 _let_2)))) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.cos _let_6)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_5 _let_4)) (tptp.hAPP_real_real _let_3 _let_2)))) _let_1)) tptp.zero_zero_real)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real tptp.uminus_uminus_real X))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real tptp.sin _let_2)) (tptp.hAPP_real_real tptp.sin X))) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.cos _let_2)) (tptp.hAPP_real_real tptp.cos X))) _let_1)) tptp.zero_zero_real)))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real tptp.arccos Y)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arcsin Y))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.hAPP_real_real tptp.sin _let_1) Y)))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.arcsin Y))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) _let_2)) (= (tptp.hAPP_real_real tptp.sin _let_1) Y))))))) (forall ((X_4 tptp.real) (Y_4 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X_4) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_4) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y_4) _let_1)))))) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real tptp.arccos _let_2)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_2) _let_1))))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) _let_1)) (= (tptp.hAPP_real_real tptp.sin X_2) Y) (forall ((Y_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_1) _let_1)) (= (tptp.hAPP_real_real tptp.sin Y_1) Y)) (= Y_1 X_2)))))))))) (forall ((R_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R_3)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_2) tptp.one_one_nat))) R_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_nat_real tptp.real_nat N_2))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) Y)) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N_2))) Y)))))))) (forall ((R_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R_3)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat N_2)) R_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N_2)))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (forall ((Y_1 tptp.real)) (exists ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) X))))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) N)) tptp.zero_zero_real))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.sin X_1) tptp.zero_zero_real) (or (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2)) (= X_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2)) (= X_1 (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.cos X_1) tptp.zero_zero_real) (or (exists ((N_2 tptp.nat)) (and (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2))) (= X_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (exists ((N_2 tptp.nat)) (and (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2))) (= X_1 (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1)))) (not (= (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat Ma))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1))))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_1) Y_2))) (or (and _let_2 _let_1) (and (not _let_2) (not _let_1))))))) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat tptp.zero_zero_nat)) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat tptp.suc X_1))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1))))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat tptp.one_one_nat))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat Y_2))))) (forall ((N tptp.nat)) (not (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)) tptp.zero_zero_real))) (forall ((N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat Y_2)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X_1) Y_2))) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_2)) (and _let_2 _let_1) (and (not _let_2) (not _let_1))))))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1))) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N))))) (forall ((X_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1))) (exists ((Y_1 tptp.nat)) (= X_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) Y_1)))))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (exists ((Y_1 tptp.nat)) (= X_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) Y_1))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc X)) _let_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) _let_1)))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.suc X)) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) _let_1))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X) (tptp.hAPP_nat_nat tptp.suc _let_1)) _let_1)))) (forall ((X tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) tptp.zero_zero_nat))) (forall ((X_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X_1) (tptp.hAPP_nat_nat tptp.suc _let_1)) _let_1)))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat X_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) tptp.zero_zero_nat))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) Y_2))) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Y_2))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M))) (let ((_let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) _let_1)) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_2) (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)))))))) (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) tptp.one_one_nat))))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X))) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) _let_1))) X)))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) _let_1)) X)))) (forall ((X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.even_odd_even_int X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_int_nat tptp.nat_1 X_1)))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_1)))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) (exists ((M_1 tptp.nat)) (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M_1))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.div_mod_nat N_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((N_1 tptp.nat)) (= (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1))) (exists ((M_1 tptp.nat)) (= N_1 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) M_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) _let_1))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real (tptp.hAPP_b646336293l_real tptp.if_real (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1))))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real) N_1)) tptp.zero_zero_real)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) _let_1) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat N) _let_1)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 _let_1))) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_2))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 _let_1))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))))))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1))) tptp.one_one_nat) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.hAPP_real_real tptp.sin X) tptp.zero_zero_real) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2)) (= X (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.hAPP_real_real tptp.cos X) tptp.zero_zero_real) (exists ((N_2 tptp.nat)) (and (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_2))) (= X (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))))) (forall ((N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (exists ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1))) X_2)) tptp.one_one_nat)))))) (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real tptp.sin_coeff X_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_2)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat X_2) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat X_2))))))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N)) (exists ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat N) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 _let_1))) X_2)))))) (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real tptp.cos_coeff X_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat X_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X_2) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat X_2))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_1))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 (tptp.hAPP_nat_nat tptp.fact_fact_nat N))) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))))))) (forall ((N tptp.nat)) (not (= (tptp.hAPP_nat_nat tptp.fact_fact_nat N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat M)) (tptp.hAPP_nat_nat tptp.fact_fact_nat N))))) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat tptp.zero_zero_nat) _let_43) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_43) _let_43) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat M)) (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))))) (forall ((X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc X))) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat tptp.fact_fact_nat X))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)) (tptp.hAPP_nat_nat tptp.fact_fact_nat M))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat))) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat tptp.fact_fact_nat N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)) (tptp.hAPP_nat_nat tptp.fact_fact_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.fact_fact_nat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (let ((_let_4 (tptp.hAPP_r474017924t_real tptp.power_power_real X))) (let ((_let_5 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) _let_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_5)))) (tptp.hAPP_nat_real _let_4 _let_5))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real _let_4 _let_3)) _let_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) _let_2)) N)))))))))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.exp_real X)) (tptp.hAPP_real_real tptp.exp_real Y))))) (forall ((Y tptp.real) (X tptp.real)) (=> (= (tptp.hAPP_real_real tptp.exp_real Y) X) (= (tptp.hAPP_real_real tptp.ln X) Y))) (forall ((U_1 tptp.real) (X tptp.real)) (=> (= (tptp.hAPP_real_real tptp.exp_real U_1) X) (= (tptp.hAPP_real_real tptp.ln X) U_1))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real tptp.exp_real X)) X)) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real X_1)) (tptp.hAPP_real_real tptp.exp_real Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.exp_real X)) (tptp.hAPP_real_real tptp.exp_real Y))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.exp_real X_1)) (tptp.hAPP_real_real tptp.exp_real Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)))) (= (tptp.hAPP_real_real tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_real tptp.exp_real X_1) (tptp.hAPP_real_real tptp.exp_real Y_2)) (= X_1 Y_2))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.exp_real X))) (= (tptp.hAPP_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real tptp.inverse_inverse_real X)) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.sqrt X)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) (tptp.hAPP_real_real tptp.inverse_inverse_real Y)))) (forall ((R tptp.real) (S_4 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real R) S_4) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R) (tptp.hAPP_real_real tptp.inverse_inverse_real S_4)))) (forall ((X tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.exp_real X)) tptp.zero_zero_real)))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.exp_real X_1) tptp.one_one_real) (= X_1 tptp.zero_zero_real))) (forall ((Y tptp.real) (U_1 tptp.real) (X1_1 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X1_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X1_1) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) U_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.inverse_inverse_real X)) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.inverse_inverse_real X1_1)) U_1)))))))) (forall ((Y tptp.real) (U_1 tptp.real) (X1_1 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X1_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X1_1) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) U_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) (tptp.hAPP_real_real tptp.inverse_inverse_real X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real U_1) (tptp.hAPP_real_real tptp.inverse_inverse_real X1_1))))))))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.inverse_inverse_real X)) X) tptp.one_one_real))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.hAPP_real_real tptp.exp_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.zero_zero_real)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.hAPP_real_real tptp.exp_real X))))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.exp_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)))) (forall ((X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) (tptp.hAPP_real_real tptp.exp_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)))) (forall ((X tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.hAPP_real_real tptp.exp_real X)))) (forall ((N tptp.nat) (X tptp.real)) (= (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) X)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.exp_real X)) N))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_real_real tptp.ln X_1)) X_1) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_real_real tptp.ln X)) X))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.sqrt X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_1) X) (tptp.hAPP_real_real tptp.inverse_inverse_real _let_1))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real tptp.inverse_inverse_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.ln X))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.hAPP_real_real tptp.exp_real X))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real tptp.one_one_real)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.ln Y)) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.ln X)) X)))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.sqrt X))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real tptp.inverse_inverse_real X)))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.exp_real X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real tptp.cos X))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.tan X)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.inverse_inverse_real _let_2)) _let_1)))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) Y)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y) tptp.one_one_real))) (= (tptp.hAPP_real_real tptp.exp_real X_2) Y))))) (forall ((X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N_2)))) X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.log _let_1) X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real tptp.exp_real tptp.one_one_real))) (tptp.hAPP_real_real tptp.ln _let_1))) (tptp.hAPP_real_real tptp.ln X)))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.arccos X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.sin X_1) (tptp.hAPP_real_real tptp.cos X_1)))) (forall ((A_3 tptp.real)) (= (tptp.hAPP_real_real (tptp.log A_3) tptp.one_one_real) tptp.zero_zero_real)) (forall ((A_3 tptp.real) (X tptp.real)) (= (tptp.hAPP_real_real (tptp.log A_3) X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.ln X)) (tptp.hAPP_real_real tptp.ln A_3)))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.cos X_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X_1))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.ln X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real X_1))))) (forall ((A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (=> (not (= A_3 tptp.one_one_real)) (= (tptp.hAPP_real_real (tptp.log A_3) A_3) tptp.one_one_real)))) (forall ((Y_2 tptp.real) (X_1 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.log A))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 Y_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2))))))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real tptp.ln X) (tptp.hAPP_real_real (tptp.log (tptp.hAPP_real_real tptp.exp_real tptp.one_one_real)) X))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.ln X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) X_1))))) (forall ((Y_2 tptp.real) (X_1 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.log A))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 Y_2)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2))))))))) (forall ((B_2 tptp.real) (N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.log B_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_real_real _let_1 X)))))) (forall ((Y tptp.real) (X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.log A_3))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 A_3)) (=> (not (= A_3 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 Y)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))))))) (forall ((Y tptp.real) (X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.log A_3))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 A_3)) (=> (not (= A_3 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 Y)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))))))) (forall ((X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.log A_3))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 A_3)) (=> (not (= A_3 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.inverse_inverse_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real _let_1 X))))))))) (forall ((X tptp.real) (B_2 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_3)) (=> (not (= A_3 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2)) (=> (not (= B_2 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (= (tptp.hAPP_real_real (tptp.log A_3) X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.ln B_2)) (tptp.hAPP_real_real tptp.ln A_3))) (tptp.hAPP_real_real (tptp.log B_2) X)))))))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.sqrt X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.sqrt X_1))) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.cos X_1))) (=> (not (= _let_1 tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.tan X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.arctan X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))))) (forall ((D_1 tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.sqrt X_1)))) (=> (not (= X_1 tptp.zero_zero_real)) (=> (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (= D_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_2) _let_1))) (=> (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)) (= D_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)) _let_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.sqrt X_1) D_1)))))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real tptp.arcsin X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real tptp.one_one_real) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.log (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real _let_1 X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.exp_real tptp.one_one_real))) (tptp.hAPP_real_real tptp.ln X)))))) (forall ((V tptp.fun_real_real) (K_1 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (not (= A B)) (=> (forall ((X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real V X_2) K_1))) (= (tptp.hAPP_real_real V (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A) B)) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real V A)) (tptp.hAPP_real_real V B))) _let_1)))))) (forall ((D tptp.real) (F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) Y_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real F X_1)) (tptp.hAPP_real_real F Y_1))))) (= L tptp.zero_zero_real))))) (forall ((D tptp.real) (F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) Y_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real F Y_1)) (tptp.hAPP_real_real F X_1))))) (= L tptp.zero_zero_real))))) (forall ((D tptp.real) (F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) Y_1))) D)) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real F Y_1)))) (= L tptp.zero_zero_real))))) (forall ((F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((H_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H_1) D_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) H_1))) (tptp.hAPP_real_real F X_1))))))))))) (forall ((F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((H_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H_1) D_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F X_1)) (tptp.hAPP_real_real F (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) H_1)))))))))))) (forall ((F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((H_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H_1) D_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) H_1))) (tptp.hAPP_real_real F X_1))))))))))) (forall ((F tptp.fun_real_real) (X_1 tptp.real) (L tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_1) L)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((H_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H_1) D_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F X_1)) (tptp.hAPP_real_real F (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) H_1)))))))))))) (forall ((F tptp.fun_real_real) (K_1 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (forall ((X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) K_1))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real F B)) (tptp.hAPP_real_real F A))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) K_1)))) (forall ((F tptp.fun_real_real) (K_1 tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (forall ((X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) K_1))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real F B)) (tptp.hAPP_real_real F A)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) K_1))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real _let_1 X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_nat_real tptp.real_nat N_1))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))))))))))) (forall ((D_1 tptp.real) (X_1 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (let ((_let_2 (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D_1 _let_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (not (= X_1 tptp.zero_zero_real)) (=> (=> _let_4 (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) _let_3)) (=> (=> _let_4 (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)) (= D_1 (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real _let_1 X_1) D_1)))))))))))) (forall ((N tptp.nat)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) X) X)) (forall ((X_1 tptp.real) (Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (= (tptp.hAPP_real_real _let_1 X_1) (tptp.hAPP_real_real _let_1 Y_2)) (= X_1 Y_2))))) (forall ((X tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root M))) (let ((_let_2 (tptp.hAPP_n546711566l_real tptp.root N))) (let ((_let_3 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_3 N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real _let_2 X)) (tptp.hAPP_real_real _let_2 (tptp.hAPP_real_real _let_1 X))))))))) (forall ((Y tptp.real) (X tptp.real) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) N) X) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X) Y)))) (forall ((X tptp.real) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)) N) X))) (forall ((X tptp.real) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N))) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) X))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y))))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1) tptp.zero_zero_real) (= X_1 tptp.zero_zero_real)))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_real_real _let_1 Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y))))))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))) (forall ((X tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) X) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root M) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X))))))) (forall ((X tptp.real) (K_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) K_2)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_1 X)) K_2))))) (forall ((N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) tptp.one_one_real) tptp.one_one_real))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1) tptp.one_one_real) (= X_1 tptp.one_one_real)))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real _let_1 X)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.abs_abs_real X)) (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real _let_1 X)))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.inverse_inverse_real X)) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real _let_1 X)))))) (forall ((Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.zero_zero_real))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X))))))) (forall ((Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real))))) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X))))))) (forall ((Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.one_one_real))))) (forall ((X tptp.real) (N_5 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_5) X)) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X))))))) (forall ((Y_2 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) Y_2))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y_2)))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real))))) (forall ((X tptp.real) (N_5 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_5) X)) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X))))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root _let_1) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) X)))) (forall ((X_4 tptp.real) (N_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_6)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_6) X_4)))))) (forall ((Y tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y)))))))) (forall ((Y tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (let ((_let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_2 Y)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y))))))))) (forall ((X tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) X) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root M) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)))))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) X)))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)) N) X)))) (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) N) X) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X) Y))))) (forall ((X tptp.real) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)) N) X)))) (forall ((X tptp.real) (N_5 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_5) X)))))))) (forall ((X tptp.real) (N_5 tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N_5)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N) X)) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_5) X)))))))) (= tptp.sqrt (tptp.hAPP_n546711566l_real tptp.root _let_3)) (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.inverse_inverse_real X)) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real _let_1 X))))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat N_1))) (=> (not (= X_1 tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real _let_1 X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))))))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n546711566l_real tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real _let_1 X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real _let_1 X_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))))))))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (exists ((X_2 tptp.real)) (= (tptp.hAPP_real_real tptp.exp_real X_2) Y)))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.abs_abs_int K_2))) (let ((_let_2 (tptp.pdivmod K_2 L_2))) (let ((_let_3 (= L_2 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) _let_1))) (=> (not _let_3) (= _let_2 (tptp.posDivAlg _let_1 (tptp.hAPP_int_int tptp.abs_abs_int L_2))))))))) (forall ((F tptp.fun_real_real) (F_1 tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) (tptp.hAPP_real_real F_1 X_2))))) (exists ((Z tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) Z)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Z) B)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real F B)) (tptp.hAPP_real_real F A)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) (tptp.hAPP_real_real F_1 Z)))))))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.abs_abs_int L_2))) (let ((_let_2 (tptp.hAPP_int_int tptp.abs_abs_int K_2))) (= (tptp.pdivmod K_2 L_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_2) _let_1)) (tptp.hAPP_int_int (tptp.div_mod_int _let_2) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (exists ((R_1 tptp.real) (A_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_1))) (and (= X (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.cos A_2))) (= Y (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.sin A_2)))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (exists ((R_1 tptp.real) (A_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_1))) (and (= X (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.cos A_2))) (= Y (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.sin A_2)))))))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (let ((_let_1 (tptp.div_mod_int K_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.z3mod K_2) L_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) L_2)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_int_int _let_1 L_2))) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int L_2))))))))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.div_div_int K_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.z3div K_2) L_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) L_2)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_int_int _let_1 L_2))) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int L_2)))))))))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (F tptp.fun_real_real)) (=> (forall ((X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) tptp.zero_zero_real))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real F Y_2)))) (forall ((X tptp.real)) (exists ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_nat_real tptp.real_nat N_2))))) (forall ((K_2 tptp.nat) (L_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_2) L_2)) (exists ((N_2 tptp.nat)) (= L_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_2) N_2))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1)))))) (forall ((P_1 tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 tptp.zero_zero_nat))) (=> (exists ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X1))) (exists ((N_2 tptp.nat)) (and (not (tptp.hBOOL (tptp.hAPP_nat_bool P_1 N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 (tptp.hAPP_nat_nat tptp.suc N_2)))))))) (forall ((Real1_2 tptp.real) (Real2_2 tptp.real) (Real1_1 tptp.real) (Real2_1 tptp.real)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 Real1_2) Real2_2) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 Real1_1) Real2_1)) (and (= Real1_2 Real1_1) (= Real2_2 Real2_1)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A) B) tptp.zero_zero_complex) (and (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (= tptp.zero_zero_complex (tptp.hAPP_real_complex _let_50 tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real) (W_1 tptp.int)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A) B) (tptp.hAPP_int_complex tptp.number528085621omplex W_1)) (and (= A (tptp.hAPP_int_real tptp.number267125858f_real W_1)) (= B tptp.zero_zero_real)))) (= tptp.one_one_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.one_one_real) tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))) (forall ((A_3 tptp.real) (B_2 tptp.real) (C_1 tptp.real) (D_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 C_1) D_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) C_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real B_2) D_3)))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex tptp.uminus473333897omplex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.uminus_uminus_real A_3)) (tptp.hAPP_real_real tptp.uminus_uminus_real B_2)))) (forall ((A_3 tptp.real) (B_2 tptp.real) (C_1 tptp.real) (D_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 C_1) D_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_3) C_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_2) D_3)))) (forall ((A_3 tptp.real) (B_2 tptp.real) (C_1 tptp.real) (D_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real B_2))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 C_1) D_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_2 C_1)) (tptp.hAPP_real_real _let_1 D_3))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_2 D_3)) (tptp.hAPP_real_real _let_1 C_1))))))) (forall ((A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.cos A_3)) (tptp.hAPP_real_real tptp.sin A_3))) tptp.one_one_real)) (forall ((A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real A_3) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real B_2) _let_1)))) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real A_3) _let_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real B_2)) _let_2)))))) (forall ((Real1 tptp.real) (Real2 tptp.real)) (= (tptp.complex_size (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 Real1) Real2)) tptp.zero_zero_nat)) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (= (tptp.hAPP_real_real tptp.cos (tptp.arg (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real) Y))) tptp.zero_zero_real))) (forall ((Y tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.cos (tptp.arg (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real) Y))) tptp.zero_zero_real))) (forall ((Real1 tptp.real) (Real2 tptp.real)) (= (tptp.hAPP_complex_nat tptp.size_size_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 Real1) Real2)) tptp.zero_zero_nat)) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex X) Y) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X) (tptp.hAPP_complex_complex tptp.invers1449016382omplex Y)))) (forall ((Y tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (tptp.hAPP_real_real tptp.cos (tptp.arg (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real) Y))) tptp.zero_zero_real))) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex tptp.ii) _let_3) _let_49) (not (= tptp.ii tptp.zero_zero_complex)) (not (= tptp.ii tptp.one_one_complex)) (forall ((W tptp.int)) (not (= tptp.ii (tptp.hAPP_int_complex tptp.number528085621omplex W)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.ii))) (= (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex _let_1 X)) (tptp.hAPP_complex_complex tptp.uminus473333897omplex X)))) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex tptp.ii) _let_44) (= tptp.ii (tptp.hAPP_real_complex _let_50 tptp.one_one_real)) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X_1) Y_2) tptp.ii) (and (= X_1 tptp.zero_zero_real) (= Y_2 tptp.one_one_real)))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) tptp.ii) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.uminus_uminus_real B_2)) A_3))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.ii) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.uminus_uminus_real B_2)) A_3))) (= _let_48 _let_49) (= _let_48 _let_46) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real Y) _let_1)))) (let ((_let_3 (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.ii))) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.of_real_complex X)) (tptp.hAPP_complex_complex _let_3 (tptp.of_real_complex Y)))) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.of_real_complex (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) _let_2))) (tptp.hAPP_complex_complex _let_3 (tptp.of_real_complex (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real Y) _let_2))))))))) (forall ((X_1 tptp.real) (Y_2 tptp.real) (Xa_1 tptp.real)) (= (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X_1) Y_2) (tptp.of_real_complex Xa_1)) (and (= X_1 Xa_1) (= Y_2 tptp.zero_zero_real)))) (forall ((R_3 tptp.real)) (= (tptp.of_real_complex R_3) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 R_3) tptp.zero_zero_real))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_complex tptp.sgn_sgn_complex Z_1) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex Z_1) (tptp.of_real_complex (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1))))) (forall ((X tptp.real) (Y tptp.real) (R_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) R_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) R_3)))) (forall ((R_3 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real _let_1 X)) (tptp.hAPP_real_real _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real) (R_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) R_3)) Y))) (forall ((R_3 tptp.real) (X tptp.real) (Y tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real R_3) X)) Y))) (= _let_48 (tptp.of_real_complex _let_34)) (forall ((R_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_3)) tptp.ii) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real) R_3))) (forall ((R_3 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex tptp.ii) (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 tptp.zero_zero_real) R_3))) (= (tptp.of_real_complex _let_47) _let_46) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_3)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.cos A_3)) (tptp.hAPP_real_real tptp.sin A_3)))) (tptp.hAPP_real_real tptp.abs_abs_real R_3))) (= (tptp.expi (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex _let_45) (tptp.of_real_complex tptp.pi))) tptp.ii)) tptp.one_one_complex) (forall ((A_3 tptp.complex) (B_2 tptp.complex)) (= (tptp.expi (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex A_3) B_2)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.expi A_3)) (tptp.expi B_2)))) (= (tptp.expi tptp.zero_zero_complex) tptp.one_one_complex) (forall ((Z_1 tptp.complex)) (exists ((R_1 tptp.real) (A_2 tptp.real)) (= Z_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_1)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.cos A_2)) (tptp.hAPP_real_real tptp.sin A_2)))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (exists ((Y_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Y_1)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F A)) (tptp.hAPP_real_real F B)))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (exists ((Y_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_1) tptp.zero_zero_real)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F B)) (tptp.hAPP_real_real F A)))))) (forall ((I_1 tptp.int) (P_1 tptp.fun_int_bool) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_1)))))) (forall ((P_1 tptp.fun_int_bool) (P1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D)))))) (=> (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Z)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P1 X_2)))))) (=> (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P1 X1))) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1)))))))) (forall ((P_1 tptp.fun_int_bool) (P_2 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D)))))) (=> (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) X_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))))) (=> (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X1))) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))))))) (forall ((D_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.coprime D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2))))) (forall ((D_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.coprime D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3))))) (forall ((B_2 tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.coprime D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))))))) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.coprime D))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A) B))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime N_1) N_1)) (= N_1 tptp.one_one_nat))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) tptp.one_one_nat))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime tptp.one_one_nat) A_3))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A) B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime B) A)))) (forall ((E_1 tptp.nat) (B_2 tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_3) A_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat E_1) B_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime D_3) E_1)))))) (forall ((N tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_2) N))))) (forall ((N tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.coprime D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)))))) (forall ((N tptp.nat)) (= (tptp.archim1246769320r_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (forall ((X tptp.real)) (= (tptp.natfloor X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.archim1246769320r_real X)))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) A_3))) (forall ((A_3 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((D tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime D) tptp.zero_zero_nat)) (= D tptp.one_one_nat))) (forall ((D tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime tptp.zero_zero_nat) D)) (= D tptp.one_one_nat))) (forall ((N tptp.nat) (M tptp.nat) (R_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) R_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) R_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) R_3)))))) (forall ((D_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime D_3) A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A) B)) (forall ((D_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_2))) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B))) (= D_2 tptp.one_one_nat)))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) N))) (forall ((A tptp.nat) (N_1 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B) _let_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A) B))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N)))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real tptp.real_nat N)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N)))) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.archim1246769320r_real X)) N)))) (forall ((N tptp.nat)) (= (tptp.archim1246769320r_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_nat_real tptp.real_nat N))) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (forall ((B_2 tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.archim1246769320r_real A_3)) (tptp.archim1246769320r_real B_2))) (tptp.archim1246769320r_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3) B_2)))))))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real tptp.real_nat N)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N)))) (= (tptp.hAPP_int_nat tptp.nat_1 (tptp.archim1246769320r_real X)) N)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A) B)) (exists ((X_2 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B))) (or (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 X_2)) (tptp.hAPP_nat_nat _let_2 Y_1)) tptp.one_one_nat) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_2 X_2)) (tptp.hAPP_nat_nat _let_1 Y_1)) tptp.one_one_nat))))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (=> (not (= B_2 tptp.one_one_nat)) (exists ((X_2 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) X_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2) Y_1)) tptp.one_one_nat)))))) (forall ((V_2 tptp.int)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) tptp.one_one_nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int V_2) tptp.pls)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.pred V_2)))))))) (forall ((X tptp.int)) (= (tptp.hAPP_int_int tptp.succ (tptp.hAPP_int_int tptp.pred X)) X)) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.pred (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit0 K_2))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.pred (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.pred K_2)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) L)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.pred K_1)) L)))) (= (tptp.hAPP_int_int tptp.pred tptp.pls) tptp.min) (= (tptp.hAPP_int_int tptp.pred tptp.min) (tptp.hAPP_int_int tptp.bit0 tptp.min)) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.pred K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_2) tptp.one_one_int))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.bit1 K_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.pred (tptp.hAPP_int_int tptp.uminus_uminus_int K_2))))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_2) tptp.min) (tptp.hAPP_int_int tptp.pred K_2))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.min) K_2) (tptp.hAPP_int_int tptp.pred K_2))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.bit0 K_2)) (tptp.hAPP_int_int tptp.bit1 L_2)) (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.pred K_2)) L_2)))) (forall ((V tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (= (tptp.hAPP_int_nat tptp.number_number_of_nat V) tptp.zero_zero_nat))) (forall ((M tptp.nat) (V_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.pls) V_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_int_nat tptp.number_number_of_nat V_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.pred V_2)))))) (forall ((Z_1 tptp.complex)) (exists ((A_2 tptp.complex) (R_1 tptp.real)) (= Z_1 (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_1)) (tptp.expi A_2))))) (forall ((X_3 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.resSet Ma) X_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int X_3))))) (forall ((Ma tptp.int) (X_3 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.resSet Ma) X_3)) (forall ((Y1 tptp.int) (Y2 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y1) X_3)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y2) X_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong Y1) Y2) Ma))) (= Y1 Y2))))) (forall ((P_5 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.resSet P_5) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5)))) (forall ((Nat tptp.nat)) (= (tptp.hAPP_nat_nat tptp.nat_size (tptp.hAPP_nat_nat tptp.suc Nat)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.nat_size Nat)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Nat tptp.nat)) (= (tptp.hAPP_nat_nat tptp.size_size_nat (tptp.hAPP_nat_nat tptp.suc Nat)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat tptp.size_size_nat Nat)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.code_c271388182l_size tptp.zero_z126310315umeral) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat tptp.size_size_nat N) N)) (= (tptp.hAPP_nat_nat tptp.size_size_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.hAPP_nat_nat tptp.nat_size tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((Code_numeral_1 tptp.code_code_numeral)) (= (tptp.code_c271388182l_size (tptp.code_S1047413653umeral Code_numeral_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.code_c271388182l_size Code_numeral_1)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex tptp.invers1449016382omplex X)) (tptp.hAPP_complex_complex tptp.invers1449016382omplex (tptp.hAPP_complex_complex tptp.cnj X)))) (forall ((Z_2 tptp.complex)) (= (= (tptp.hAPP_complex_complex tptp.cnj Z_2) tptp.zero_zero_complex) (= Z_2 tptp.zero_zero_complex))) (= (tptp.hAPP_complex_complex tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.number528085621omplex W))) (= (tptp.hAPP_complex_complex tptp.cnj _let_1) _let_1))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X) Y)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_complex_complex tptp.cnj Y)))) (= (tptp.hAPP_complex_complex tptp.cnj tptp.one_one_complex) tptp.one_one_complex) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex tptp.uminus473333897omplex X)) (tptp.hAPP_complex_complex tptp.uminus473333897omplex (tptp.hAPP_complex_complex tptp.cnj X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X) Y)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_complex_complex tptp.cnj Y)))) (forall ((X_1 tptp.complex) (Y_2 tptp.complex)) (= (= (tptp.hAPP_complex_complex tptp.cnj X_1) (tptp.hAPP_complex_complex tptp.cnj Y_2)) (= X_1 Y_2))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex tptp.cnj Z_1)) Z_1)) (forall ((Code_numeral_5 tptp.code_code_numeral) (Code_numeral_4 tptp.code_code_numeral)) (= (= (tptp.code_S1047413653umeral Code_numeral_5) (tptp.code_S1047413653umeral Code_numeral_4)) (= Code_numeral_5 Code_numeral_4))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N))) (= (tptp.hAPP_complex_complex tptp.cnj _let_1) _let_1))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex tptp.cnj Z_1)) (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X) Y)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_complex_complex tptp.cnj Y)))) (forall ((X tptp.complex) (N tptp.nat)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex X) N)) (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.hAPP_complex_complex tptp.cnj X)) N))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex X) Y)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_complex_complex tptp.cnj Y)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.of_real_complex X))) (= (tptp.hAPP_complex_complex tptp.cnj _let_1) _let_1))) (forall ((Code_numeral_3 tptp.code_code_numeral)) (not (= (tptp.code_S1047413653umeral Code_numeral_3) tptp.zero_z126310315umeral))) (forall ((Code_numeral_2 tptp.code_code_numeral)) (not (= tptp.zero_z126310315umeral (tptp.code_S1047413653umeral Code_numeral_2)))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r265291036omplex tptp.complex_1 A_3))) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_real_complex _let_1 B_2)) (tptp.hAPP_real_complex _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real B_2))))) (= (tptp.hAPP_complex_complex tptp.cnj tptp.ii) _let_44) (forall ((N tptp.code_code_numeral)) (= (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.minus_1690775515umeral (tptp.code_S1047413653umeral N)) tptp.one_on1645066479umeral) N)) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex tptp.cnj X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex tptp.cnj X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex tptp.cnj X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4))))) (forall ((Code_numeral_1 tptp.code_code_numeral)) (= (tptp.hAPP_C2129356693al_nat tptp.size_s945831648umeral (tptp.code_S1047413653umeral Code_numeral_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_C2129356693al_nat tptp.size_s945831648umeral Code_numeral_1)) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_real tptp.im Z_1)))) tptp.ii))) (forall ((Y tptp.code_code_numeral)) (=> (not (= Y tptp.zero_z126310315umeral)) (not (forall ((Code_numeral tptp.code_code_numeral)) (not (= Y (tptp.code_S1047413653umeral Code_numeral))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) Y)) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.im X)))) (forall ((Z_1 tptp.real)) (= (tptp.hAPP_complex_real tptp.im (tptp.of_real_complex Z_1)) tptp.zero_zero_real)) (= (tptp.hAPP_complex_real tptp.im tptp.ii) tptp.one_one_real) (= (tptp.hAPP_complex_real tptp.im tptp.zero_zero_complex) tptp.zero_zero_real) (= (tptp.hAPP_complex_real tptp.im tptp.one_one_complex) tptp.zero_zero_real) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_complex_real tptp.im X)) (tptp.hAPP_complex_real tptp.im Y)))) (forall ((V_2 tptp.int)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_int_complex tptp.number528085621omplex V_2)) tptp.zero_zero_real)) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex tptp.uminus473333897omplex X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.im X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_complex_real tptp.im X)) (tptp.hAPP_complex_real tptp.im Y)))) (forall ((N tptp.nat)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N)) tptp.zero_zero_real)) (forall ((X tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_complex_real tptp.im X))) (tptp.hAPP_complex_real tptp.norm_norm_complex X)))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1))) tptp.zero_zero_real)) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex tptp.sgn_sgn_complex Z_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_complex_real tptp.im Z_1)) (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1)))) (= (tptp.hAPP_C2129356693al_nat tptp.size_s945831648umeral tptp.zero_z126310315umeral) tptp.zero_zero_nat) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.im X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.im X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.im X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_complex_real tptp.im X))) (let ((_let_3 (tptp.hAPP_complex_real tptp.re X))) (let ((_let_4 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_3) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_2) _let_1)))) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex X) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_3) _let_4)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)) _let_4)))))))) (forall ((Z_1 tptp.complex)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1)) (tptp.of_real_complex (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.re Z_1)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.im Z_1)) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_complex_real tptp.im X))) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex tptp.invers1449016382omplex X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.re X)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_2) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 X) Y)) X)) (forall ((Z_1 tptp.real)) (= (tptp.hAPP_complex_real tptp.re (tptp.of_real_complex Z_1)) Z_1)) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex tptp.cnj X)) (tptp.hAPP_complex_real tptp.re X))) (forall ((X_1 tptp.complex) (Y_2 tptp.complex)) (= (= X_1 Y_2) (and (= (tptp.hAPP_complex_real tptp.re X_1) (tptp.hAPP_complex_real tptp.re Y_2)) (= (tptp.hAPP_complex_real tptp.im X_1) (tptp.hAPP_complex_real tptp.im Y_2))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.hAPP_complex_real tptp.re X) (tptp.hAPP_complex_real tptp.re Y)) (=> (= (tptp.hAPP_complex_real tptp.im X) (tptp.hAPP_complex_real tptp.im Y)) (= X Y)))) (forall ((X tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.norm_norm_complex X)))) (= (tptp.hAPP_complex_real tptp.re tptp.ii) tptp.zero_zero_real) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_complex_real tptp.re Z_1)) (tptp.hAPP_complex_real tptp.im Z_1)) Z_1)) (= (tptp.hAPP_complex_real tptp.re tptp.zero_zero_complex) tptp.zero_zero_real) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.re Y)))) (= (tptp.hAPP_complex_real tptp.re tptp.one_one_complex) tptp.one_one_real) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex tptp.uminus473333897omplex X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.re X)))) (forall ((V_2 tptp.int)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_int_complex tptp.number528085621omplex V_2)) (tptp.hAPP_int_real tptp.number267125858f_real V_2))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.re Y)))) (forall ((N tptp.nat)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_nat_complex tptp.semiri2020571505omplex N)) (tptp.hAPP_nat_real tptp.semiri132038758t_real N))) (forall ((X tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_complex_real tptp.re X))) (tptp.hAPP_complex_real tptp.norm_norm_complex X)))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex tptp.sgn_sgn_complex Z_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_complex_real tptp.re Z_1)) (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.im Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.im X)) (tptp.hAPP_complex_real tptp.re Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.re Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.im X)) (tptp.hAPP_complex_real tptp.im Y))))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_complex tptp.cnj Z_1) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_complex_real tptp.re Z_1)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.im Z_1))))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1)))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex X) Y) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_complex_real tptp.re X)) (tptp.hAPP_complex_real tptp.re Y))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_complex_real tptp.im X)) (tptp.hAPP_complex_real tptp.im Y))))) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_complex tptp.uminus473333897omplex X) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.re X))) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_complex_real tptp.im X))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.hAPP_complex_real tptp.re Y))) (let ((_let_2 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.im X)))) (let ((_let_3 (tptp.hAPP_complex_real tptp.im Y))) (let ((_let_4 (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.re X)))) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex X) Y) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real _let_4 _let_1)) (tptp.hAPP_real_real _let_2 _let_3))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real _let_4 _let_3)) (tptp.hAPP_real_real _let_2 _let_1))))))))) (forall ((Z_1 tptp.complex)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.plus_plus_complex Z_1) (tptp.hAPP_complex_complex tptp.cnj Z_1)) (tptp.of_real_complex (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_complex_real tptp.re Z_1))))) (forall ((Z_1 tptp.complex)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_complex_real tptp.norm_norm_complex Z_1) (tptp.hAPP_real_real tptp.sqrt (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.re Z_1)) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.im Z_1)) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_complex_real tptp.re X))) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex tptp.invers1449016382omplex X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_2) _let_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_complex_real tptp.im X)) _let_1))))))) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.re X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) K_4)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.re X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4)))))) (exists ((K_4 tptp.real)) (forall ((X_2 tptp.complex)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.norm_norm_real (tptp.hAPP_complex_real tptp.re X_2))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_complex_real tptp.norm_norm_complex X_2)) K_4))))) (forall ((Z_1 tptp.complex)) (= (tptp.expi Z_1) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_complex_real tptp.re Z_1)))) (tptp.cis (tptp.hAPP_complex_real tptp.im Z_1))))) (forall ((N tptp.nat) (A_3 tptp.real)) (= (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) A_3)) (tptp.hAPP_complex_real tptp.im (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.cis A_3)) N)))) (forall ((N tptp.nat) (A_3 tptp.real)) (= (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) A_3)) (tptp.hAPP_complex_real tptp.re (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.cis A_3)) N)))) (forall ((A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.re (tptp.cis A_3)) (tptp.hAPP_real_real tptp.cos A_3))) (forall ((A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.im (tptp.cis A_3)) (tptp.hAPP_real_real tptp.sin A_3))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.cis A_3)) (tptp.cis B_2)) (tptp.cis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) B_2)))) (= (tptp.cis tptp.zero_zero_real) tptp.one_one_complex) (forall ((A_3 tptp.real)) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex (tptp.cis A_3)) (tptp.cis (tptp.hAPP_real_real tptp.uminus_uminus_real A_3)))) (forall ((A_3 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex (tptp.cis A_3)) (tptp.cis B_2)) (tptp.cis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_3) B_2)))) (forall ((A_3 tptp.real)) (= (tptp.cis A_3) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real tptp.cos A_3)) (tptp.hAPP_real_real tptp.sin A_3)))) (forall ((A_3 tptp.real) (N tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.cis A_3)) N) (tptp.cis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) A_3)))) (forall ((N tptp.nat) (A_3 tptp.real)) (= (tptp.cis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc N))) A_3)) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.cis A_3)) (tptp.cis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) A_3))))) (forall ((X tptp.nat)) (= (tptp.bezw X tptp.zero_zero_nat) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (forall ((Y tptp.nat) (X tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z_1)))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z_1)))))) (forall ((Y tptp.nat) (X tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z_1)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z_1)))))) (forall ((M tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int B_2))) (let ((_let_2 (tptp.hAPP_int_int tptp.uminus_uminus_int A_3))) (let ((_let_3 (tptp.divmod_int A_3 B_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)))) (let ((_let_5 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_int_bool _let_5 A_3)))) (let ((_let_7 (= A_3 tptp.zero_zero_int))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP_int_bool _let_5 B_2)))) (and (=> _let_6 (and (=> _let_8 (= _let_3 (tptp.posDivAlg A_3 B_2))) (=> (not _let_8) (and (=> _let_7 (= _let_3 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.zero_zero_int))) (=> (not _let_7) (= _let_3 (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.negDivAlg _let_2 _let_1)))))))) (=> (not _let_6) (and (=> _let_4 (= _let_3 (tptp.negDivAlg A_3 B_2))) (=> (not _let_4) (= _let_3 (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.posDivAlg _let_2 _let_1)))))))))))))))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime tptp.zero_zero_nat))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime tptp.one_one_nat))) (forall ((Q_2 tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime Q_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) Q_2)) (= P_3 Q_2))))) (forall ((Q_2 tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime Q_2)) (=> (not (= P_3 Q_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime P_3) Q_2)))))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime _let_43))) (forall ((P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) P_3)))) (forall ((A tptp.nat) (B tptp.nat) (P_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_5))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_5)) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A) B))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B))))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2))))))) (forall ((M tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))))) (forall ((P_3 tptp.nat) (Q_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_3) Q_2))) (or (= P_3 tptp.one_one_nat) (= Q_2 tptp.one_one_nat)))) (forall ((X tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) _let_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) N)) _let_1)))))) (forall ((X tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)))))) (forall ((A_3 tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)))))) (forall ((P_5 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_5) N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_5)) (= N_1 tptp.one_one_nat)))) (forall ((P_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2))))))) (forall ((N tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime P_3) N))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A) B)) (forall ((P_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_4))) (not (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)))))))) (forall ((A_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime A_3)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime (tptp.hAPP_nat_int tptp.semiri1621563631at_int A_3))))) (forall ((P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) P_3)))) (forall ((P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (not (= N tptp.zero_zero_nat)) (=> (= N (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_3) M)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))))) (forall ((P_5 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_5)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) P_5)) (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M_1) P_5)) (or (= M_1 tptp.one_one_nat) (= M_1 P_5))))))) (forall ((D tptp.nat) (K_1 tptp.nat) (P_5 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_5)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_5) K_1))) (exists ((I_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_2) K_1)) (= D (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_5) I_2))))))) (forall ((N tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) N)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3))))))) (forall ((X tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime X) P_3)))))) (forall ((N tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (or (= N tptp.one_one_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime P_3) N))))) (forall ((Q_2 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_2))) (= (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.hAPP_i1524277240nt_int _let_1 R_3)) (tptp.hAPP_i1524277240nt_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int R_3))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (Qr_1 tptp.product_prod_int_int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) Qr_1)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.hAPP_P1975530577nt_int tptp.negateSnd Qr_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime _let_3)) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (not (= B_2 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.divmod_int_rel A_3 B_2) (tptp.divmod_int A_3 B_2))))) (forall ((M tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((N tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat) (P_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) N)))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)))))))) (forall ((P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_3)))) (forall ((P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (or (= P_3 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.even_odd_even_nat P_3)))))) (forall ((P_3 tptp.int) (Q_2 tptp.int)) (= (tptp.divmod_int P_3 Q_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int P_3) Q_2)) (tptp.hAPP_int_int (tptp.div_mod_int P_3) Q_2)))) (forall ((N tptp.code_code_numeral) (M tptp.code_code_numeral)) (= (tptp.code_d418564891umeral N M) (tptp.hAPP_C2132160860umeral (tptp.hAPP_C1614127039umeral tptp.produc2136830103umeral (tptp.hAPP_C498520661umeral (tptp.hAPP_C1594335432umeral tptp.div_di1218280263umeral N) M)) (tptp.hAPP_C498520661umeral (tptp.div_mo1740067990umeral N) M)))) (forall ((M tptp.int) (R_3 tptp.int) (S_1 tptp.int) (T_1 tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.xzgcd M N) (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int R_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int S_1) T_1))) (= R_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_1) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T_1) N)))))) (forall ((M tptp.int) (N tptp.int) (R_5 tptp.int) (S_3 tptp.int) (S_1 tptp.int) (T_2 tptp.int) (T_1 tptp.int) (R_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int R_5) R_3)))) (let ((_let_2 (tptp.xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int R_3) tptp.zero_zero_int)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int R_5) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int S_3) T_2)))) (=> (not _let_3) (= _let_2 (tptp.xzgcda M N R_3 (tptp.hAPP_int_int (tptp.div_mod_int R_5) R_3) S_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int S_3) (tptp.hAPP_int_int _let_1 S_1)) T_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int T_2) (tptp.hAPP_int_int _let_1 T_1)))))))))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.xzgcd M N) (tptp.xzgcda M N M N tptp.one_one_int tptp.zero_zero_int tptp.zero_zero_int tptp.one_one_int))) (forall ((M tptp.int) (N tptp.int) (R_5 tptp.int) (S_3 tptp.int) (S_1 tptp.int) (T_2 tptp.int) (T_1 tptp.int) (Rn tptp.int) (Sn_1 tptp.int) (Tn_1 tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) R_3)) (=> (= (tptp.xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1) (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int Rn) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Sn_1) Tn_1))) (=> (= R_5 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_3) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T_2) N))) (=> (= R_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_1) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T_1) N))) (= Rn (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Sn_1) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Tn_1) N)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime X) Y))) (exists ((P_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_4))) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y))))))) (forall ((X tptp.nat) (K_2 tptp.nat) (N tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (not (= N tptp.zero_zero_nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) K_2)) (exists ((I_2 tptp.nat)) (= X (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) I_2))))))) (forall ((N tptp.nat)) (=> (not (= N tptp.one_one_nat)) (exists ((P_4 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_4) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.divmod_nat M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat _let_1) N))) (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_1) N))))))) (forall ((A_3 tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) A_3))) (exists ((X_2 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) X_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat P_3) Y_1)) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime N)))) (exists ((M_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) N)) (= N (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_1) K))))))) (forall ((M tptp.nat)) (= (tptp.divmod_nat M tptp.zero_zero_nat) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= (tptp.divmod_nat M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.divmod_nat M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N)))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat) (Q_2 tptp.nat) (R_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 R_3))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel B_2 C_1) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Q_2) R_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_1)) (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel (tptp.hAPP_nat_nat _let_1 B_2) C_1) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Q_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat _let_2) C_1))) (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_2) C_1))))))))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat) (Q_2 tptp.nat) (R_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel A_3 B_2) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Q_2) R_3))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 B_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 C_1)) (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel A_3 (tptp.hAPP_nat_nat _let_1 C_1)) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat Q_2) C_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.div_mod_nat Q_2) C_1))) R_3)))))))))) (forall ((B_2 tptp.nat) (Bq tptp.nat) (Br tptp.nat) (A_3 tptp.nat) (C_1 tptp.nat) (Aq tptp.nat) (Ar tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ar) Br))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel A_3 C_1) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Aq) Ar))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel B_2 C_1) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Bq) Br))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) C_1)) (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_3) B_2) C_1) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Aq) Bq)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat _let_1) C_1))) (tptp.hAPP_nat_nat (tptp.div_mod_nat _let_1) C_1))))))))) (forall ((Qr_2 tptp.product_prod_nat_nat) (M tptp.nat) (N tptp.nat) (Qr_1 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.divmod_nat_rel M N))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool _let_1 Qr_1)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool _let_1 Qr_2)) (= Qr_1 Qr_2))))) (forall ((M tptp.nat) (N tptp.nat) (Qr_1 tptp.product_prod_nat_nat)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) Qr_1)) (= (tptp.divmod_nat M N) Qr_1))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) (tptp.divmod_nat M N)))) (forall ((M tptp.nat) (N tptp.nat) (Q_2 tptp.nat) (R_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Q_2) R_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N) Q_2))) (forall ((M tptp.nat) (N tptp.nat) (Q_2 tptp.nat) (R_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Q_2) R_3))) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) R_3))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N)) (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (not (forall ((Q_4 tptp.nat) (R_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel M N) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat Q_4) R_1))))))) (forall ((N tptp.nat)) (exists ((P_4 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) P_4))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int tptp.one_one_int) _let_1) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.negDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.one_one_int) (tptp.hAPP_int_int tptp.uminus_uminus_int _let_1)))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.divmod_int A_3 B_2)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.negDivAlg A_3 B_2)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.posDivAlg A_3 B_2)))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int tptp.one_one_int) _let_1) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.posDivAlg tptp.one_one_int _let_1)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.negDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.posDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int _let_1))) (let ((_let_3 (tptp.bezw X Y))) (let ((_let_4 (= Y tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= _let_3 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) Y))))))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int _let_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.bezw X Y) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat X) Y)))))))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.one_one_int) _let_1) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.negDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int tptp.one_one_int) (tptp.hAPP_int_int tptp.uminus_uminus_int _let_1)))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.divmod_int A_3 B_2)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.negDivAlg A_3 B_2)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) B_2)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.posDivAlg A_3 B_2)))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int W))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (= (tptp.hAPP_int_int (tptp.div_mod_int tptp.one_one_int) _let_1) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.posDivAlg tptp.one_one_int _let_1)))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.negDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A_3) tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_2) tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.div_mod_int A_3) B_2) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int (tptp.hAPP_P1975530577nt_int tptp.negateSnd (tptp.posDivAlg (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat M) N) (tptp.hAPP_P1654798560at_nat tptp.product_fst_nat_nat (tptp.divmod_nat M N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.div_mod_nat M) N) (tptp.hAPP_P1654798560at_nat tptp.product_snd_nat_nat (tptp.divmod_nat M N)))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (Qr tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.hAPP_P1654798560at_nat tptp.product_snd_nat_nat Qr))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (let ((_let_3 (= N_1 tptp.zero_zero_nat))) (let ((_let_4 (tptp.hAPP_P1654798560at_nat tptp.product_fst_nat_nat Qr))) (= (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.divmod_nat_rel Ma N_1) Qr)) (and (= Ma (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_4) N_1)) _let_1)) (=> _let_3 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_3) (and (=> _let_2 (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat _let_1) N_1)))) (=> (not _let_2) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) _let_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat _let_1) tptp.zero_zero_nat))))))))))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (N_1 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_P731461727l_real tptp.produc556554744l_real _let_1)) (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B) A)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_1)))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_2))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real _let_1)) (tptp.hAPP_P731461727l_real tptp.produc556554744l_real _let_1))))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real)) (= (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) tptp.zero_zero_nat) (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A) B))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.bolzano_bisect P_1 A B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real (tptp.hAPP_n332733730l_real _let_1 N_2))) (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real (tptp.hAPP_n332733730l_real _let_1 (tptp.hAPP_nat_nat tptp.suc N_2))))))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.bolzano_bisect P_1 A B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_P731461727l_real tptp.produc556554744l_real (tptp.hAPP_n332733730l_real _let_1 (tptp.hAPP_nat_nat tptp.suc N_2)))) (tptp.hAPP_P731461727l_real tptp.produc556554744l_real (tptp.hAPP_n332733730l_real _let_1 N_2)))))))) (forall ((N_1 tptp.nat) (A tptp.real) (B tptp.real) (P_1 tptp.fun_Pr1127657839l_bool)) (let ((_let_1 (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_1))) (=> (forall ((A_2 tptp.real) (B_4 tptp.real) (C_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2))) (=> (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 B_4))) (=> (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real B_4) C_3))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_4)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_4) C_3)) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 C_3))))))))) (=> (not (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A) B)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (not (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real _let_1)) (tptp.hAPP_P731461727l_real tptp.produc556554744l_real _let_1)))))))))) (forall ((A tptp.real) (B tptp.real) (P_1 tptp.fun_Pr1127657839l_bool)) (=> (forall ((A_2 tptp.real) (B_4 tptp.real) (C_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2))) (=> (and (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 B_4))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real B_4) C_3))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_4) C_3))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 C_3)))))) (=> (not (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A) B)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_2))) (not (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real _let_1)) (tptp.hAPP_P731461727l_real tptp.produc556554744l_real _let_1))))))))))) (= tptp.one_on1684967323de_int (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int _let_1)) (forall ((K_2 tptp.quickcheck_code_int)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int _let_1))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int _let_1)) (tptp.quickcheck_int_of (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int K_2) _let_2))))) (let ((_let_4 (tptp.quickcheck_int_of K_2))) (let ((_let_5 (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int K_2) _let_2) tptp.zero_z891286103de_int))) (let ((_let_6 (= K_2 tptp.zero_z891286103de_int))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_3) tptp.one_one_int))))))))))))) (forall ((R_3 tptp.real) (A_3 tptp.real) (N tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_c1088319240omplex tptp.power_power_complex (tptp.rcis R_3 A_3)) N) (tptp.rcis (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real R_3) N) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N)) A_3)))) (forall ((N_1 tptp.quickcheck_code_int) (Ma tptp.quickcheck_code_int)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le258702272de_int N_1) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.quickcheck_int_of N_1)) (tptp.quickcheck_int_of Ma))))) (forall ((N_1 tptp.quickcheck_code_int) (Ma tptp.quickcheck_code_int)) (= (tptp.hBOOL (tptp.hAPP_Q2096512830t_bool (tptp.hAPP_Q1010094925t_bool tptp.ord_le1860547276de_int N_1) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.quickcheck_int_of N_1)) (tptp.quickcheck_int_of Ma))))) (forall ((X_1 tptp.quickcheck_code_int) (Y_2 tptp.quickcheck_code_int)) (= (= (tptp.quickcheck_int_of X_1) (tptp.quickcheck_int_of Y_2)) (= X_1 Y_2))) (forall ((K_1 tptp.quickcheck_code_int) (L tptp.quickcheck_code_int)) (= (= (tptp.quickcheck_int_of K_1) (tptp.quickcheck_int_of L)) (= K_1 L))) (forall ((K_2 tptp.int)) (= (tptp.quickcheck_int_of (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int K_2)) (tptp.hAPP_int_int tptp.number_number_of_int K_2))) (= tptp.zero_z891286103de_int (tptp.hAPP_i1732201573de_int tptp.number1226105091de_int tptp.pls)) (forall ((R_3 tptp.real)) (= (tptp.rcis R_3 tptp.zero_zero_real) (tptp.of_real_complex R_3))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.rcis R_3 A_3)) (tptp.hAPP_real_real tptp.abs_abs_real R_3))) (forall ((A_3 tptp.real)) (= (tptp.cis A_3) (tptp.rcis tptp.one_one_real A_3))) (forall ((A_3 tptp.real)) (= (tptp.rcis tptp.zero_zero_real A_3) tptp.zero_zero_complex)) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.re (tptp.rcis R_3 A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3) (tptp.hAPP_real_real tptp.cos A_3)))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_complex_real tptp.im (tptp.rcis R_3 A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3) (tptp.hAPP_real_real tptp.sin A_3)))) (forall ((R1 tptp.real) (A_3 tptp.real) (R2 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.rcis R1 A_3)) (tptp.rcis R2 B_2)) (tptp.rcis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R1) R2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) B_2)))) (forall ((R1 tptp.real) (A_3 tptp.real) (R2 tptp.real) (B_2 tptp.real)) (= (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.invers1025623611omplex (tptp.rcis R1 A_3)) (tptp.rcis R2 B_2)) (tptp.rcis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real R1) R2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_3) B_2)))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.rcis R_3 A_3) (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.times_times_complex (tptp.of_real_complex R_3)) (tptp.cis A_3)))) (forall ((R_3 tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_complex_complex tptp.invers1449016382omplex (tptp.rcis R_3 A_3)) (tptp.rcis (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) R_3) (tptp.hAPP_real_real tptp.uminus_uminus_real A_3)))) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.quickc495462417de_int N M) (tptp.hAPP_Q1256397320de_int (tptp.hAPP_Q952608535de_int tptp.produc1318306967de_int (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int N) M)) (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int N) M)))) (forall ((I tptp.quickcheck_code_int)) (= (tptp.quickcheck_nat_of I) (tptp.hAPP_int_nat tptp.nat_1 (tptp.quickcheck_int_of I)))) (forall ((P_1 tptp.fun_int_bool) (A0 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.accp_int tptp.quickc1265749348ro_rel) A0)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.accp_int tptp.quickc1265749348ro_rel) I_2)) (=> (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) tptp.zero_zero_int))) (=> (not (= I_2 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 A0))))) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.fact_fact_int X))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_int_nat tptp.nat_1 X))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.fact_fact_int M)) (tptp.hAPP_int_int tptp.fact_fact_int N))))) (= (tptp.hAPP_int_int tptp.fact_fact_int tptp.one_one_int) tptp.one_one_int) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.fact_fact_int M)) (tptp.hAPP_int_int tptp.fact_fact_int N)))))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int M) tptp.zero_zero_int)) (= (tptp.hAPP_int_int tptp.fact_fact_int M) tptp.zero_zero_int))) (= (tptp.hAPP_int_int tptp.fact_fact_int tptp.zero_zero_int) tptp.one_one_int) (forall ((X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int tptp.fact_fact_int X)))))) (forall ((N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N)) (not (= (tptp.hAPP_int_int tptp.fact_fact_int N) tptp.zero_zero_int)))) (forall ((M tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.fact_fact_int M)))) (forall ((X tptp.nat)) (= (tptp.hAPP_int_int tptp.fact_fact_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.fact_fact_nat X)))) (forall ((N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.fact_fact_int N))))) (forall ((N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.hAPP_int_int tptp.fact_fact_int N))))) (forall ((M tptp.int) (K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.fact_fact_int M)) (tptp.hAPP_int_int tptp.fact_fact_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) K_2)))))) (forall ((N tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.one_one_int) M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) (tptp.hAPP_int_int tptp.fact_fact_int N)))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.fact_fact_int X))))) (forall ((M tptp.int) (K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.fact_fact_int M)) (tptp.hAPP_int_int tptp.fact_fact_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) tptp.one_one_int)) K_2))))))) (forall ((N tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N)) (= (tptp.hAPP_int_int tptp.fact_fact_int _let_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_1) (tptp.hAPP_int_int tptp.fact_fact_int N)))))) (forall ((N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (= (tptp.hAPP_int_int tptp.fact_fact_int N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N) (tptp.hAPP_int_int tptp.fact_fact_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int N) tptp.one_one_int)))))) (forall ((I tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) I)) (= (tptp.hAPP_list_int_nat tptp.size_size_list_int (tptp.quickc666637781d_zero I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_int_nat tptp.nat_1 I))) tptp.one_one_nat)))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) P_5)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) P_5)) (tptp.hAPP_int_nat tptp.nat_1 A))))) (forall ((A tptp.real) (B tptp.real) (P_1 tptp.fun_Pr1127657839l_bool)) (=> (forall ((A_2 tptp.real) (B_4 tptp.real) (C_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2))) (=> (and (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 B_4))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real B_4) C_3))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_4) C_3))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 C_3)))))) (=> (forall ((X_2 tptp.real)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((A_2 tptp.real) (B_4 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_4) A_2)) D_2))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2) B_4)))))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A) B))))))) (forall ((Ma tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma)))))) (forall ((B tptp.int) (A tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.int) (Ma tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma)))) (forall ((B tptp.int) (A tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)))) (forall ((P_1 tptp.fun_Pr1127657839l_bool)) (=> (and (forall ((A_2 tptp.real) (B_4 tptp.real) (C_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2))) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real B_4) C_3)) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 B_4))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real B_4) C_3)))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real _let_1 C_3)))))) (forall ((X_2 tptp.real)) (exists ((D_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D_2)) (forall ((A_2 tptp.real) (B_4 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real B_4) A_2)) D_2))) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2) B_4))))))))) (forall ((A_2 tptp.real) (B_4 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_2) B_4)) (tptp.hBOOL (tptp.hAPP_P1333854989l_bool P_1 (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real tptp.produc865579683l_real A_2) B_4))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.bezw X Y))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int _let_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int X))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int _let_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y))) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y))))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) N))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) M))) (forall ((M tptp.nat) (N tptp.nat) (K_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) N)))) (forall ((N tptp.nat) (M tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2) tptp.one_one_nat) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_2) M)) tptp.one_one_nat))) (forall ((A_3 tptp.nat) (N tptp.nat) (B_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat B_2) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) N))) (forall ((A_3 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) A_3) A_3)) (forall ((X tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) X) X)) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat B_2) A_3))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) X))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 B_2))) (= (tptp.hAPP_nat_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 Y))) (= (tptp.hAPP_nat_nat _let_1 _let_2) _let_2)))) (forall ((B_2 tptp.nat) (A_3 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat B_2))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 C_1)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 C_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_1)))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (C_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat _let_1 B_2)) C_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat B_2) C_1))))) (forall ((X tptp.nat) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat _let_1 Y)) Z_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) Z_1))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) X)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 B_2)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) X)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)))))))) (forall ((B_2 tptp.nat) (A_3 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) X)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 A_3)))) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat _let_1) X)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 _let_1)))))))) (forall ((X tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)))))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N))))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M))))) (forall ((B_2 tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat) (C_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) C_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat C_1) D_3)))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) Z_1))))))) (forall ((B_2 tptp.nat) (X tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))))))) (forall ((N tptp.nat) (K_2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N))))))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat Y) X)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X) Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) X))) (forall ((A_3 tptp.nat) (B_2 tptp.nat) (X tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat B_2) X)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) X)))) (forall ((B_2 tptp.nat) (A_3 tptp.nat) (X tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat A_3) X)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) X)))) (forall ((B tptp.nat) (D tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D))) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B)) (forall ((E tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat E))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 D)))))) (= D (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y_2) Z_2))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_2)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_2)))))) (forall ((K_1 tptp.nat) (Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X_1) Y_2)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X_1) Y_2) X_1))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)) X))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.hAPP_nat_nat _let_1 N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N))) (forall ((K_2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((X tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat tptp.one_one_nat) X) tptp.one_one_nat)) (forall ((M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)) (forall ((X tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) tptp.one_one_nat) tptp.one_one_nat)) (forall ((X tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)) (forall ((X tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Ma) N_1) tptp.zero_zero_nat) (and (= Ma tptp.zero_zero_nat) (= N_1 tptp.zero_zero_nat)))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X_1) Y_2) tptp.zero_zero_nat) (and (= X_1 tptp.zero_zero_nat) (= Y_2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) _let_1) _let_1))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Ma) N_1))) (or (not (= Ma tptp.zero_zero_nat)) (not (= N_1 tptp.zero_zero_nat))))) (forall ((B_2 tptp.nat) (A_3 tptp.nat)) (=> (not (= A_3 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) A_3)))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (=> (not (= B_2 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)) B_2)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat tptp.suc N)) N) tptp.one_one_nat)) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) M)) N)) (tptp.hAPP_nat_nat _let_1 N)))) (forall ((X tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat X))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2) tptp.one_one_nat) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_2)) (= X tptp.one_one_nat)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) tptp.one_one_nat) (forall ((D_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_2))) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B))) (= D_2 tptp.one_one_nat)))))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) tptp.one_one_nat)) N) tptp.one_one_nat)) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat D))) (= (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.one_one_nat) (and (= (tptp.hAPP_nat_nat _let_1 A) tptp.one_one_nat) (= (tptp.hAPP_nat_nat _let_1 B) tptp.one_one_nat))))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat K_2) N) tptp.one_one_nat) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K_2) M)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((B_2 tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat D_3))) (=> (= (tptp.hAPP_nat_nat _let_1 A_3) tptp.one_one_nat) (=> (= (tptp.hAPP_nat_nat _let_1 B_2) tptp.one_one_nat) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2)) tptp.one_one_nat))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat) (D tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A) D) tptp.one_one_nat) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat B) C) tptp.one_one_nat) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B) D)) (and (= A B) (= C D)))))) (forall ((D_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat D_3))) (=> (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2)) tptp.one_one_nat) (= (tptp.hAPP_nat_nat _let_1 A_3) tptp.one_one_nat)))) (forall ((D_3 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat D_3))) (=> (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2)) tptp.one_one_nat) (= (tptp.hAPP_nat_nat _let_1 B_2) tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y))) (let ((_let_2 (= Y tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat Y) (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y))))) (forall ((N tptp.nat) (D_3 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat D_3))) (=> (= (tptp.hAPP_nat_nat _let_1 A_3) tptp.one_one_nat) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat A_3) N)) tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.archim856651990g_real (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (forall ((X tptp.real)) (= (tptp.natceiling X) (tptp.hAPP_int_nat tptp.nat_1 (tptp.archim856651990g_real X)))) (forall ((B_5 tptp.nat) (A_5 tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (=> (not (= _let_1 tptp.zero_zero_nat)) (=> (= A_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_5) _let_1)) (=> (= B_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_5) _let_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_5) B_5) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) tptp.one_one_nat)) N) tptp.one_one_nat))) (forall ((N tptp.nat) (M tptp.nat) (R_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat M) R_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat N) R_3)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M) N) tptp.one_one_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) R_3)))))) (forall ((Ma tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_1))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat K_1) N_1) tptp.one_one_nat) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ma) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Ma)))))) (forall ((M tptp.nat) (K_2 tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat K_2))) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat K_2) N) tptp.one_one_nat) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N))) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M)))))) (forall ((B_2 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (=> (or (not (= A_3 tptp.zero_zero_nat)) (not (= B_2 tptp.zero_zero_nat))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat A_3) _let_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat B_2) _let_1)) tptp.one_one_nat)))) (forall ((X tptp.nat) (Y tptp.nat) (M tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.div_mod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)) M) tptp.one_one_nat) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) M) tptp.one_one_nat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A) B) tptp.one_one_nat) (forall ((D_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat D_2))) (= (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B))) (= D_2 (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((A_3 tptp.nat) (B_2 tptp.nat)) (=> (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2) tptp.zero_zero_nat)) (exists ((A_4 tptp.nat) (B_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2))) (and (= A_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_4) _let_1)) (= B_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_3) _let_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_4) B_3) tptp.one_one_nat)))))) (forall ((B_2 tptp.nat) (A_3 tptp.nat)) (=> (not (= A_3 tptp.zero_zero_nat)) (exists ((X_2 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) X_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_2) Y_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat A_3) B_2)))))) (forall ((X_3 tptp.fun_nat_real)) (= (tptp.hBOOL (tptp.cauchy_real X_3)) (forall ((J_1 tptp.nat)) (exists ((M_3 tptp.nat)) (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) M_1)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real X_3 M_1)) (tptp.hAPP_nat_real X_3 N_2)))) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.suc J_1))))))))))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.archim856651990g_real X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int)))))) (forall ((A_3 tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.ln X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)) A_3)))))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int X_1)) (tptp.hAPP_int_real tptp.real_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_1) Y_2)))) (forall ((X tptp.real) (A_3 tptp.real)) (not (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3) tptp.zero_zero_real))) (forall ((A_3 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr tptp.one_one_real) A_3) tptp.one_one_real)) (forall ((N tptp.int)) (= (tptp.archim1246769320r_real (tptp.hAPP_int_real tptp.real_int N)) N)) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real X_1)) X_1) (exists ((N_2 tptp.int)) (= X_1 (tptp.hAPP_int_real tptp.real_int N_2))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real _let_1 A_3)) B_2) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3) B_2))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real _let_1 A_3)) B_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real _let_1 B_2)) A_3)))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (= (tptp.hAPP_int_real tptp.real_int X_1) (tptp.hAPP_int_real tptp.real_int Y_2)) (= X_1 Y_2))) (= (tptp.hAPP_int_real tptp.real_int tptp.zero_zero_int) tptp.zero_zero_real) (forall ((X_1 tptp.int)) (= (= (tptp.hAPP_int_real tptp.real_int X_1) tptp.zero_zero_real) (= X_1 tptp.zero_zero_int))) (forall ((X_1 tptp.int) (Y_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int X_1)) (tptp.hAPP_int_real tptp.real_int Y_2))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_2)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.real_int X)) (tptp.hAPP_int_real tptp.real_int Y)))) (forall ((X tptp.int) (N tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.real_int X)) N) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)))) (forall ((X tptp.int) (N tptp.nat)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.real_int X)) N))) (forall ((N tptp.nat)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_real tptp.real_nat N))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int X)) (tptp.hAPP_int_real tptp.real_int Y)))) (forall ((V_2 tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int tptp.number_number_of_int V_2)) (tptp.hAPP_int_real tptp.number267125858f_real V_2))) (= (tptp.hAPP_int_real tptp.real_int tptp.one_one_int) tptp.one_one_real) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.real_int X)) (tptp.hAPP_int_real tptp.real_int Y)))) (forall ((N tptp.int)) (= (tptp.archim856651990g_real (tptp.hAPP_int_real tptp.real_int N)) N)) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_int_real tptp.real_int (tptp.archim856651990g_real X_1)) X_1) (exists ((N_2 tptp.int)) (= X_1 (tptp.hAPP_int_real tptp.real_int N_2))))) (forall ((X tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int tptp.uminus_uminus_int X)) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_int_real tptp.real_int X)))) (forall ((X tptp.int)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int tptp.abs_abs_int X)) (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_int_real tptp.real_int X)))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real R_3))) R_3))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real R_3) (tptp.hAPP_int_real tptp.real_int (tptp.archim856651990g_real R_3))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) Y)))) (forall ((X tptp.real) (A_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)))) (forall ((Y tptp.real) (X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr Y) A_3)))))))) (forall ((Y tptp.real) (X tptp.real) (A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr Y) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3))))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2))))))) (forall ((X tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) tptp.zero_zero_real) tptp.one_one_real)) (forall ((A tptp.real) (B tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2))))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A_3) B_2)))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real A_3) B_2)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2))))) (forall ((X tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2)) (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real A_3) B_2))))) (forall ((X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real A_3)) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_real_real _let_1 A_3))))) (forall ((N tptp.int) (X tptp.int)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N) X))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int N)) (tptp.hAPP_int_real tptp.real_int X))))) (forall ((X_1 tptp.real) (A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.archim1246769320r_real X_1)) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) (tptp.hAPP_int_real tptp.real_int A))))) (forall ((A_3 tptp.int) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int A_3)) X)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) (tptp.archim1246769320r_real X))))) (forall ((A_3 tptp.int) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_3) (tptp.archim1246769320r_real X))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int A_3)) X)))) (forall ((A tptp.int) (X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) (tptp.archim1246769320r_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int A)) X_1)))) (forall ((X tptp.real) (A_3 tptp.int)) (= (tptp.archim1246769320r_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_int_real tptp.real_int A_3))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.archim1246769320r_real X)) A_3))) (forall ((A tptp.int) (X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.archim856651990g_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int A)) X_1)))) (forall ((X_1 tptp.real) (A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.archim856651990g_real X_1)) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.hAPP_int_real tptp.real_int A))))) (forall ((X tptp.real) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_int_real tptp.real_int A_3))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.archim856651990g_real X)) A_3)))) (forall ((X tptp.real) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.archim856651990g_real X)) A_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) (tptp.hAPP_int_real tptp.real_int A_3))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.archim1246769320r_real X))) (=> (= X (tptp.hAPP_int_real tptp.real_int _let_1)) (= (tptp.archim1246769320r_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int _let_1) N))))) (forall ((X tptp.real) (A_3 tptp.int)) (= (tptp.archim1246769320r_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) (tptp.hAPP_int_real tptp.real_int A_3))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.archim1246769320r_real X)) A_3))) (forall ((X tptp.real) (A_3 tptp.int)) (= (tptp.archim856651990g_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_int_real tptp.real_int A_3))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.archim856651990g_real X)) A_3))) (forall ((N tptp.int)) (= (tptp.archim1246769320r_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_int_real tptp.real_int N))) (tptp.hAPP_int_int tptp.uminus_uminus_int N))) (forall ((X tptp.real) (A_3 tptp.int)) (= (tptp.archim856651990g_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) (tptp.hAPP_int_real tptp.real_int A_3))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.archim856651990g_real X)) A_3))) (forall ((Y tptp.real) (X tptp.real) (A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr Y) A_3))))))) (forall ((A_3 tptp.real) (Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real X) Y)) A_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr Y) A_3))))))) (forall ((A_3 tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A_3)) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3))))))) (forall ((A tptp.real) (B tptp.real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X_1)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real _let_1 A)) (tptp.hAPP_real_real _let_1 B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)))))) (forall ((X_1 tptp.real)) (= (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X_1) tptp.one_one_real) X_1) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)))) (forall ((A_3 tptp.real) (Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real X) Y)) A_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr Y) A_3))))))) (forall ((X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.powr X))) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_real_real _let_1 A_3))))) (forall ((X tptp.real) (A_3 tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) A_3) (tptp.hAPP_real_real tptp.exp_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3) (tptp.hAPP_real_real tptp.ln X))))) (forall ((N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int N_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int N_1) tptp.zero_zero_int)))) (forall ((N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_int_real tptp.real_int N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N_1)))) (forall ((N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_int_real tptp.real_int N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N_1)))) (forall ((N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int N_1)) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) tptp.zero_zero_int)))) (forall ((Ma tptp.int) (N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int Ma)) (tptp.hAPP_int_real tptp.number267125858f_real N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Ma) (tptp.hAPP_int_int tptp.number_number_of_int N_1))))) (forall ((N_1 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real N_1)) (tptp.hAPP_int_real tptp.real_int Ma))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int N_1)) Ma)))) (forall ((Ma tptp.int) (N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int Ma)) (tptp.hAPP_int_real tptp.number267125858f_real N_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ma) (tptp.hAPP_int_int tptp.number_number_of_int N_1))))) (forall ((N_1 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.number267125858f_real N_1)) (tptp.hAPP_int_real tptp.real_int Ma))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int N_1)) Ma)))) (forall ((N_1 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int N_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int N_1)) tptp.one_one_real)) (tptp.hAPP_int_real tptp.real_int Ma))))) (forall ((N tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int N)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int X)) tptp.one_one_real))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N) X)))) (forall ((N_1 tptp.int) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int N_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.real_int N_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int Ma)) tptp.one_one_real))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_real tptp.real_int X)))) (forall ((N tptp.int) (D_3 tptp.int)) (=> (not (= D_3 tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_3) N)) (= (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N) D_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int N)) (tptp.hAPP_int_real tptp.real_int D_3)))))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real R_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real R_3))) tptp.one_one_real)))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real R_3))) tptp.one_one_real)))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.archim1246769320r_real X) N))))) (forall ((X tptp.real) (I tptp.int)) (= (tptp.hAPP_real_real tptp.tan (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.real_int I)) tptp.pi))) (tptp.hAPP_real_real tptp.tan X))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real R_3) tptp.one_one_real)) (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real R_3))))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real R_3) tptp.one_one_real)) (tptp.hAPP_int_real tptp.real_int (tptp.archim1246769320r_real R_3))))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int (tptp.archim856651990g_real R_3))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real R_3) tptp.one_one_real)))) (forall ((R_3 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.real_int (tptp.archim856651990g_real R_3))) tptp.one_one_real)) R_3))) (forall ((N tptp.nat) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) (tptp.hAPP_nat_real tptp.real_nat N)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N)))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 Y)) (= (tptp.hAPP_real_real tptp.ln (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) (tptp.hAPP_real_real tptp.ln X))))))) (forall ((X tptp.real) (A_3 tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 A_3)) (=> (not (= A_3 tptp.one_one_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr A_3) (tptp.hAPP_real_real (tptp.log A_3) X)) X)))))) (forall ((Y tptp.real) (A_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (=> (not (= A_3 tptp.one_one_real)) (= (tptp.hAPP_real_real (tptp.log A_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr A_3) Y)) Y)))) (forall ((N tptp.int) (M tptp.int) (R_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int M)) R_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int N)) tptp.one_one_real))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M) N))))) (forall ((N tptp.int) (X tptp.int)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int N)) (tptp.hAPP_int_real tptp.real_int X))) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N) X)))))) (forall ((N tptp.int) (X tptp.int)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int N)) (tptp.hAPP_int_real tptp.real_int X))) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int N) X)))) tptp.one_one_real))) (forall ((X tptp.int) (D_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int D_3))) (=> (not (= D_3 tptp.zero_zero_int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int X)) _let_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) D_3))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.div_mod_int X) D_3))) _let_1)))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.archim1246769320r_real X) N))))) (forall ((A tptp.int) (X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.archim1246769320r_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int A)) tptp.one_one_real)) X_1)))) (forall ((X_1 tptp.real) (A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.archim1246769320r_real X_1)) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_int_real tptp.real_int A)) tptp.one_one_real))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real _let_1) tptp.one_one_real)) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X) _let_1)) (= (tptp.archim856651990g_real X) N))))) (forall ((X_1 tptp.real) (A tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.archim856651990g_real X_1)) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.real_int A)) tptp.one_one_real))))) (forall ((A tptp.int) (X_1 tptp.real)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) (tptp.archim856651990g_real X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_int_real tptp.real_int A)) tptp.one_one_real)) X_1)))) (forall ((B_2 tptp.real) (Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.log B_2))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) Y)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real Y) (tptp.hAPP_real_real _let_1 X))))))) (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (tptp.hAPP_int_real tptp.real_int N))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.archim856651990g_real X) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int)))))) (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X) N))) (let ((_let_2 (= X tptp.zero_zero_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr X) (tptp.hAPP_nat_real tptp.real_nat N)))))))))) (forall ((A_3 tptp.real) (X tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) A_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr (tptp.hAPP_real_real tptp.ln X)) A_3)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.powr A_3) A_3)) X)))))) (forall ((R_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R_3)) (exists ((N_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int N_2)) R_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N_2) tptp.one_one_int)))))))) (forall ((R_3 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) tptp.zero_zero_real)) (exists ((N_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int N_2)) R_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N_2) tptp.one_one_int)))))))) (forall ((R_3 tptp.real)) (exists ((N_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_int_real tptp.real_int N_2)) R_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_3) (tptp.hAPP_int_real tptp.real_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N_2) tptp.one_one_int))))))) (forall ((C_1 tptp.nat) (N tptp.nat) (A_3 tptp.nat) (B_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.coprime A_3) B_2)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_3) B_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat C_1) N)) (exists ((R_1 tptp.nat) (S_2 tptp.nat)) (and (= A_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat R_1) N)) (= B_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat S_2) N))))))) (forall ((X tptp.nat) (Y tptp.nat) (K_2 tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_3)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3) K_2)) (exists ((I_2 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat P_3))) (and (= X (tptp.hAPP_nat_nat _let_1 I_2)) (= Y (tptp.hAPP_nat_nat _let_1 J_1)))))))) (forall ((X tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd X) M) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) (tptp.hAPP_int_nat tptp.phi M))) tptp.one_one_int) M))))) (forall ((I tptp.int) (J_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2)) I))) (forall ((I tptp.int) (J_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2)) J_2))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_2) N) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) M)) N) (tptp.hAPP_int_int (tptp.legacy_zgcd M) N)))) (forall ((N tptp.int) (K_2 tptp.int) (M tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_2) M) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd N) M) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) N)) M) tptp.one_one_int)))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) N) (tptp.hAPP_int_int (tptp.legacy_zgcd N) (tptp.hAPP_int_int (tptp.div_mod_int M) N)))) (forall ((M tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) tptp.one_one_int) tptp.one_one_int)) (forall ((M tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd tptp.one_one_int) M) tptp.one_one_int)) (forall ((I_1 tptp.int) (J tptp.int)) (= (= (tptp.hAPP_int_int (tptp.legacy_zgcd I_1) J) tptp.zero_zero_int) (and (= I_1 tptp.zero_zero_int) (= J tptp.zero_zero_int)))) (forall ((K_1 tptp.int) (Ma tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.legacy_zgcd Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)))))) (forall ((N tptp.int) (K_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.legacy_zgcd M) N))))))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.legacy_zgcd K_2))) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int _let_1 M)) N) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.legacy_zgcd M) N))))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.legacy_zgcd K_2))) (let ((_let_2 (tptp.legacy_zgcd M))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 N)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 N)))))) (forall ((I tptp.int) (J_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2) (tptp.hAPP_int_int (tptp.legacy_zgcd J_2) I))) (forall ((A_3 tptp.int) (B_2 tptp.int) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2)) N) (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) N)))) (forall ((I tptp.int) (J_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int tptp.uminus_uminus_int I)) J_2) (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2))) (forall ((I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.legacy_zgcd I))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int J_2)) (tptp.hAPP_int_int _let_1 J_2)))) (forall ((M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) M) M))) (forall ((I tptp.int) (J_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2)))) (forall ((X tptp.int) (Y tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.legacy_zgcd X) Y)))) (forall ((M tptp.int) (N tptp.int) (K_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int N) K_2))) N) (tptp.hAPP_int_int (tptp.legacy_zgcd M) N))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.abs_abs_int K_2)) (tptp.hAPP_int_int (tptp.legacy_zgcd M) N))))) (forall ((N tptp.nat) (A_3 tptp.int) (B_2 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) B_2) tptp.one_one_int))) (forall ((N tptp.nat) (A_3 tptp.int) (B_2 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) N)) tptp.one_one_int))) (forall ((M tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd tptp.zero_zero_int) M) (tptp.hAPP_int_int tptp.abs_abs_int M))) (forall ((M tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) tptp.zero_zero_int) (tptp.hAPP_int_int tptp.abs_abs_int M))) (forall ((M tptp.int) (N tptp.int) (K_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.legacy_zgcd M) N)) (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) M)) N)))) (forall ((N tptp.int) (K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) N)) K_2))) (forall ((M tptp.int) (N tptp.int) (K_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.legacy_zgcd M) N)) (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N)))))) (forall ((N tptp.int) (K_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_2)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) N)) K_2) K_2))) (forall ((N_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Ma) N_1)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd N_1) Ma) Ma)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2))) (=> (or (not (= A_3 tptp.zero_zero_int)) (not (= B_2 tptp.zero_zero_int))) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) _let_1)) tptp.one_one_int)))) (forall ((M tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) N) (tptp.hAPP_int_int (tptp.legacy_zgcd N) (tptp.hAPP_int_int (tptp.div_mod_int M) N))))) (forall ((N tptp.int) (A_3 tptp.int) (B_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) N) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N)))))))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_2) N) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) M)) N)) (tptp.hAPP_int_int (tptp.legacy_zgcd M) N))))) (forall ((M tptp.int) (N tptp.int) (K_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd N) K_2) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((K_2 tptp.int) (I tptp.int) (J_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int I))) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd I) J_2) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) J_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K_2)))))) (forall ((Ma tptp.int)) (= (= (tptp.hAPP_int_int (tptp.legacy_zgcd tptp.zero_zero_int) Ma) tptp.one_one_int) (= (tptp.hAPP_int_int tptp.abs_abs_int Ma) tptp.one_one_int))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_1) L) (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_b1463609396nt_int tptp.if_int (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int L) tptp.zero_zero_int)) K_1) (tptp.hAPP_int_int (tptp.legacy_zgcd L) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.abs_abs_int K_1)) (tptp.hAPP_int_int tptp.abs_abs_int L))))))) (forall ((N tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_3) N))) (= (tptp.hAPP_int_int (tptp.legacy_zgcd N) P_3) tptp.one_one_int)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.hAPP_int_int (tptp.legacy_zgcd A) B) tptp.one_one_int) (not (exists ((P_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int P_4))) (and (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_4)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)))))))) (forall ((B_2 tptp.int) (A_3 tptp.int) (M tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) M) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A_3) B_2) M)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd B_2) M) tptp.one_one_int))))) (forall ((N tptp.int) (P_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int N) P_3)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd N) P_3) tptp.one_one_int))))) (forall ((A tptp.int) (B tptp.int) (K_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_1) Ma) tptp.one_one_int) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) K_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) K_1)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)))))) (forall ((A tptp.int) (B tptp.int) (K_1 tptp.int) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd K_1) Ma) tptp.one_one_int) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int _let_1 A)) (tptp.hAPP_int_int _let_1 B)) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma))))))) (forall ((M tptp.int) (N tptp.int) (K_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd N) K_2) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M))))))) (forall ((A tptp.int) (B tptp.int) (Ma tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd B) Ma) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int C) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A) B) tptp.one_one_int) (exists ((K tptp.int)) (= A (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int K) (tptp.hAPP_int_nat tptp.nat_1 X_1)))))))))) (forall ((Ma tptp.int) (K_1 tptp.int) (N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N_1)) (= (= (tptp.hAPP_int_int (tptp.legacy_zgcd Ma) N_1) K_1) (exists ((S_2 tptp.int) (T tptp.int)) (= (tptp.xzgcd Ma N_1) (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int K_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int S_2) T))))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int) (N tptp.nat)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int C_1) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2) tptp.one_one_int) (exists ((K tptp.int)) (= (tptp.hAPP_int_int tptp.abs_abs_int A_3) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int K) N))))))) (forall ((M tptp.int) (N tptp.int) (R_5 tptp.int) (R_3 tptp.int) (S_3 tptp.int) (S_1 tptp.int) (T_2 tptp.int) (T_1 tptp.int) (K_2 tptp.int)) (=> (exists ((Sn tptp.int) (Tn tptp.int)) (= (tptp.xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1) (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int K_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Sn) Tn)))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) R_3)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd R_5) R_3) K_2)))) (forall ((B_2 tptp.int) (A_3 tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) N) tptp.one_one_int) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) X_2)) B_2) N)) (forall ((Y_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y_1) N)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) Y_1)) B_2) N))) (= Y_1 X_2)))))))) (forall ((A_3 tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) N) tptp.one_one_int) (exists ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) X_2)) tptp.one_one_int) N)))))) (forall ((M tptp.int) (N tptp.int) (S_3 tptp.int) (S_1 tptp.int) (T_2 tptp.int) (T_1 tptp.int) (R_5 tptp.int) (R_3 tptp.int) (K_2 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd R_5) R_3) K_2) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) R_3)) (exists ((Sn tptp.int) (Tn tptp.int)) (= (tptp.xzgcda M N R_5 R_3 S_3 S_1 T_2 T_1) (tptp.hAPP_P408881810nt_int (tptp.hAPP_i1730167831nt_int tptp.produc282740534nt_int K_2) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Sn) Tn))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B)) C) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int D) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) tptp.zOdd)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A) B) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd B) C) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd C) A) tptp.one_one_int) (exists ((K tptp.int) (L_1 tptp.int) (M_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.nat_1 X_1))) (and (= A (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int K) _let_1)) (= B (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int L_1) _let_1)) (= C (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int M_1) _let_1))))))))))))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd M) N) K_2) (exists ((S_2 tptp.int) (T tptp.int)) (= K_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int S_2) M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int T) N))))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int) (D_3 tptp.int) (N tptp.nat)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) C_1) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int D_3) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.one_one_nat) N)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd B_2) C_1) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd C_1) A_3) tptp.one_one_int) (exists ((K tptp.int) (L_1 tptp.int) (M_1 tptp.int)) (and (= (tptp.hAPP_int_int tptp.abs_abs_int A_3) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int K) N)) (= (tptp.hAPP_int_int tptp.abs_abs_int B_2) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int L_1) N)) (= (tptp.hAPP_int_int tptp.abs_abs_int C_1) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int M_1) N)))))))))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (or (not (= A_3 tptp.zero_zero_int)) (not (= B_2 tptp.zero_zero_int))) (exists ((C_3 tptp.int) (D_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.legacy_zgcd A_3) B_2)))) (and (= A_3 (tptp.hAPP_int_int _let_1 C_3)) (= B_2 (tptp.hAPP_int_int _let_1 D_2)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd C_3) D_2) tptp.one_one_int)))))) (forall ((Sa tptp.nat) (Ta tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Sa) Ta)) (tptp.hBOOL (tptp.hAPP_f115998247l_bool (tptp.hAPP_P1876494581l_bool tptp.member180897546at_nat (tptp.hAPP_P369611207at_nat (tptp.hAPP_P402336767at_nat tptp.produc494345619at_nat (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat A) Sa)) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat B) Ta))) tptp.pair_less))))) (forall ((Sa tptp.nat) (Ta tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (tptp.hBOOL (tptp.hAPP_f115998247l_bool (tptp.hAPP_P1876494581l_bool tptp.member180897546at_nat (tptp.hAPP_P369611207at_nat (tptp.hAPP_P402336767at_nat tptp.produc494345619at_nat (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat A) Sa)) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat B) Ta))) tptp.pair_less)))) (forall ((Sa tptp.nat) (Ta tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Sa) Ta)) (tptp.hBOOL (tptp.hAPP_f115998247l_bool (tptp.hAPP_P1876494581l_bool tptp.member180897546at_nat (tptp.hAPP_P369611207at_nat (tptp.hAPP_P402336767at_nat tptp.produc494345619at_nat (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat A) Sa)) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat B) Ta))) tptp.pair_leq))))) (forall ((Sa tptp.nat) (Ta tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A) B)) (tptp.hBOOL (tptp.hAPP_f115998247l_bool (tptp.hAPP_P1876494581l_bool tptp.member180897546at_nat (tptp.hAPP_P369611207at_nat (tptp.hAPP_P402336767at_nat tptp.produc494345619at_nat (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat A) Sa)) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat B) Ta))) tptp.pair_leq)))) (forall ((Y tptp.real) (X tptp.real)) (exists ((R_1 tptp.real) (A_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_1))) (and (= X (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.cos A_2))) (= Y (tptp.hAPP_real_real _let_1 (tptp.hAPP_real_real tptp.sin A_2))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real (tptp.dist_dist_real X) Y) (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.hAPP_complex_real (tptp.dist_dist_complex X) Y) (tptp.hAPP_complex_real tptp.norm_norm_complex (tptp.hAPP_complex_complex (tptp.hAPP_c172932010omplex tptp.minus_minus_complex X) Y)))) (forall ((Z_1 tptp.int)) (=> (forall ((N_2 tptp.nat)) (not (= Z_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))) (not (forall ((N_2 tptp.nat)) (not (= Z_1 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N_2))))))))) (forall ((Z_2 tptp.int) (P_1 tptp.fun_int_bool)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat tptp.suc N_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 Z_2))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (exists ((Y_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_1) tptp.zero_zero_real)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real F B)) (tptp.hAPP_real_real F A)))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (exists ((Y_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y_1)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real F A)) (tptp.hAPP_real_real F B)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat) (P_1 tptp.fun_nat_fun_nat_bool)) (=> (forall ((M_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 M_1) tptp.zero_zero_nat))) (=> (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 N_2) (tptp.hAPP_nat_nat (tptp.div_mod_nat M_1) N_2))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 M_1) N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 Ma) N_1))))) (forall ((N tptp.nat) (P_3 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) P_3)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_3) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.dvd_dvd_nat P_3) (tptp.hAPP_nat_nat tptp.fact N)))))) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.div_mo231679042de_int N) M) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.hAPP_int_int (tptp.div_mod_int (tptp.quickcheck_int_of N)) (tptp.quickcheck_int_of M))))) (forall ((N_1 tptp.int) (Ma tptp.int)) (= (= (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int N_1) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int Ma)) (= N_1 Ma))) (forall ((X tptp.quickcheck_code_int)) (= (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.quickcheck_int_of X)) X)) (forall ((K_2 tptp.quickcheck_code_int)) (= (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.quickcheck_int_of K_2)) K_2)) (forall ((N tptp.int)) (= (tptp.quickcheck_int_of (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int N)) N)) (= tptp.number1226105091de_int tptp.quickcheck_of_int) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.fact M)) (tptp.hAPP_nat_nat tptp.fact N))))) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.times_123202395de_int N) M) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.quickcheck_int_of N)) (tptp.quickcheck_int_of M))))) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.plus_p1446045655de_int N) M) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.quickcheck_int_of N)) (tptp.quickcheck_int_of M))))) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.minus_534354567de_int N) M) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.quickcheck_int_of N)) (tptp.quickcheck_int_of M))))) (= tptp.zero_z891286103de_int (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int tptp.zero_zero_int)) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.fact N)))) (= (tptp.hAPP_nat_nat tptp.fact tptp.zero_zero_nat) tptp.one_one_nat) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N))) (= (tptp.hAPP_nat_nat tptp.fact _let_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.hAPP_nat_nat tptp.fact N))))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.hAPP_nat_nat tptp.fact N)))) (= tptp.one_on1684967323de_int (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int tptp.one_one_int)) (forall ((N tptp.quickcheck_code_int) (M tptp.quickcheck_code_int)) (= (tptp.hAPP_Q1762011733de_int (tptp.hAPP_Q1729056540de_int tptp.div_di1430059507de_int N) M) (tptp.hAPP_i1732201573de_int tptp.quickcheck_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.quickcheck_int_of N)) (tptp.quickcheck_int_of M))))) (forall ((N tptp.nat)) (exists ((P_4 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool tptp.prime P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) P_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat P_4) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.fact N))))))) (forall ((F tptp.fun_nat_nat)) (=> (forall ((I_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat tptp.suc I_2))) (tptp.hAPP_nat_nat F I_2)))) (exists ((I_2 tptp.nat)) (forall ((K tptp.nat)) (= (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_2) K)) (tptp.hAPP_nat_nat F I_2)))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (A0 tptp.int) (A1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.norm_frac_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.norm_frac_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_2) B_4))) (=> (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_4) tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 (tptp.hAPP_int_int tptp.uminus_uminus_int A_2)) (tptp.hAPP_int_int tptp.uminus_uminus_int B_4)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A_2) B_4))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (A0 tptp.int) (A1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.upto_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((I_2 tptp.int) (J_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.upto_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int I_2) J_1))) (=> (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) J_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)) J_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 I_2) J_1))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((P_1 tptp.fun_int_fun_int_bool) (A0 tptp.int) (A1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.lazy_small_lazy_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((D_2 tptp.int) (I_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool P_1 D_2))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.lazy_small_lazy_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int D_2) I_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int D_2) I_2))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 I_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P_1 A0) A1))))) (forall ((Ma tptp.int)) (= (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma) (tptp.hAPP_i1948725293t_bool (tptp.bnorRset (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ma) tptp.one_one_int)) Ma))) _let_42 _let_42 (forall ((Z_1 tptp.int)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_int_complex tptp.ring_11397209091omplex Z_1)) tptp.zero_zero_real)) (forall ((Z_1 tptp.int)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_int_complex tptp.ring_11397209091omplex Z_1)) (tptp.hAPP_int_real tptp.ring_1_of_int_real Z_1))) (forall ((Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_complex tptp.ring_11397209091omplex Z_1))) (= (tptp.hAPP_complex_complex tptp.cnj _let_1) _let_1))) (forall ((N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (= (tptp.hAPP_int_int tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((X tptp.int)) (= (tptp.hAPP_int_real tptp.number267125858f_real X) (tptp.hAPP_int_real tptp.ring_1_of_int_real X))) (forall ((W tptp.int)) (= (tptp.hAPP_int_int tptp.number_number_of_int W) (tptp.hAPP_int_int tptp.ring_1_of_int_int W))) (forall ((W tptp.int)) (= (tptp.hAPP_int_complex tptp.number528085621omplex W) (tptp.hAPP_int_complex tptp.ring_11397209091omplex W))) (forall ((Ma tptp.int)) (= (tptp.hAPP_int_nat tptp.phi Ma) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma)))) (forall ((A tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd A) Ma) tptp.one_one_int) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) X_2) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma))) (forall ((Y_1 tptp.int)) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) Y_1) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_1) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma)))) (= Y_1 X_2)))))))) (forall ((X_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd X_1) Ma) tptp.one_one_int) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.noXRRset Ma) X_1)) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma)))))) (forall ((X_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd X_1) Ma) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset (tptp.hAPP_i1948725293t_bool (tptp.noXRRset Ma) X_1)) Ma))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd A) Ma) tptp.one_one_int)))) (forall ((A tptp.int) (B tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) B) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int B) A_1)) (= A B))))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.rRset2norRR A_1 Ma) A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) _let_1) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int _let_1) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma))))))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.rRset2norRR A_1 Ma) A)) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma))))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) (tptp.hAPP_int_int (tptp.rRset2norRR A_1 Ma) A)) Ma)))))) (forall ((A_1 tptp.fun_int_bool) (Ma tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (and (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool A_1) (tptp.rsetR Ma))) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A_1) (tptp.hAPP_int_nat tptp.phi Ma))))) (forall ((A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool A_1) (tptp.rsetR Ma))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_1)))) (forall ((A tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) Ma)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma)) (tptp.rsetR Ma))))) (forall ((A_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (= (tptp.image_int_int (tptp.rRset2norRR A_1 Ma) A_1) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.int_lcm X) Y) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.nat_lcm (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int X))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Y)))))) (forall ((F tptp.fun_int_int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (let ((_let_1 (tptp.resSet Ma))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A_1)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A_1)) (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) A_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.hAPP_int_int F X_2)) (tptp.hAPP_int_int F Xa)) Ma)) (= X_2 Xa)))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.image_int_int F A_1)))))))) (forall ((A_1 tptp.fun_nat_bool) (B_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) B_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A_1)) (tptp.image_nat_int tptp.semiri1621563631at_int B_1))))) (forall ((A_1 tptp.fun_nat_bool) (B_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A_1) B_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A_1)) (tptp.image_nat_int tptp.semiri1621563631at_int B_1))))) (forall ((A_1 tptp.fun_nat_bool) (B_1 tptp.fun_nat_bool)) (= (= A_1 B_1) (= (tptp.image_nat_int tptp.semiri1621563631at_int A_1) (tptp.image_nat_int tptp.semiri1621563631at_int B_1)))) (forall ((X_1 tptp.nat) (A_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.image_nat_int tptp.semiri1621563631at_int A_1))))) (forall ((A_1 tptp.fun_nat_bool)) (= (tptp.image_int_nat tptp.nat_1 (tptp.image_nat_int tptp.semiri1621563631at_int A_1)) A_1)) (forall ((A_1 tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_nat_int tptp.semiri1621563631at_int A_1)))) (forall ((A_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int tptp.semiri1621563631at_int A_1))))) (forall ((A tptp.int) (P_5 tptp.int)) (= (tptp.setS A P_5) (tptp.image_275383677t_bool (tptp.multInvPair A P_5) (tptp.hAPP_i1948725293t_bool tptp.sRStar P_5)))) (forall ((S tptp.fun_nat_bool)) (= (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S))) (forall ((M_1 tptp.nat)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat N_2) S))))))) (forall ((S tptp.fun_nat_bool)) (= (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S))) (forall ((M_1 tptp.nat)) (exists ((N_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat N_2) S))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.nat_lcm X) Y) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)) (tptp.hAPP_nat_nat (tptp.nat_gcd X) Y)))) (forall ((B_1 tptp.fun_int_bool) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set B_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool A_1) B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool (tptp.image_int_nat tptp.nat_1 A_1)) (tptp.image_int_nat tptp.nat_1 B_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y) (tptp.hAPP_nat_nat (tptp.nat_gcd X) Y))) (forall ((X_1 tptp.int) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1))))) (forall ((S tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set S)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) S)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)))))) (forall ((C_2 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set (tptp.image_nat_int tptp.semiri1621563631at_int C_2)))) (forall ((B_1 tptp.fun_int_bool) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set B_1)) (= (= A_1 B_1) (= (tptp.image_int_nat tptp.nat_1 A_1) (tptp.image_int_nat tptp.nat_1 B_1)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.nat_gcd X) Y))) (let ((_let_2 (= Y tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.nat_gcd Y) (tptp.hAPP_nat_nat (tptp.div_mod_nat X) Y)))))))) (forall ((A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (= (tptp.image_nat_int tptp.semiri1621563631at_int (tptp.image_int_nat tptp.nat_1 A_1)) A_1))) (forall ((A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_int_nat tptp.nat_1 A_1)))))) (forall ((A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int A_1) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.image_int_nat tptp.nat_1 A_1))))) (forall ((B_1 tptp.fun_int_bool) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set B_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_1) B_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_int_nat tptp.nat_1 A_1)) (tptp.image_int_nat tptp.nat_1 B_1))))))) (forall ((X_1 tptp.nat) (Y_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.nat_gcd X_1) Y_2))) (let ((_let_2 (= Y_2 tptp.zero_zero_nat))) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.accp_P490777396at_nat tptp.nat_gcd_rel) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat X_1) Y_2))) (and (=> _let_2 (= _let_1 X_1)) (=> (not _let_2) (= _let_1 (tptp.hAPP_nat_nat (tptp.nat_gcd Y_2) (tptp.hAPP_nat_nat (tptp.div_mod_nat X_1) Y_2))))))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.int_gcd X) Y) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.nat_gcd (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int X))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Y)))))) (forall ((P_1 tptp.fun_nat_fun_nat_bool) (A0 tptp.nat) (A1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.accp_P490777396at_nat tptp.nat_gcd_rel) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat A0) A1))) (=> (forall ((X_2 tptp.nat) (Y_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_P1555980039t_bool (tptp.accp_P490777396at_nat tptp.nat_gcd_rel) (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat X_2) Y_1))) (=> (=> (not (= Y_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 Y_1) (tptp.hAPP_nat_nat (tptp.div_mod_nat X_2) Y_1)))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 X_2) Y_1))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P_1 A0) A1))))) (forall ((N_4 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_4)) (exists ((M_1 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) M_1))))))) (forall ((N_4 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_4)) (exists ((M_1 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) M_1))))))) (forall ((N_1 tptp.nat) (N_4 tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_4)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) N_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_4)))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.ord_gr1297742076an_int L) U)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int U) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int L) tptp.one_one_int))))) (forall ((L tptp.int) (U tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_gr1297742076an_int L) U)))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) tptp.field_1210416355s_real)) (not (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (not (= N_2 tptp.zero_zero_nat)) (=> (= (tptp.hAPP_real_real tptp.abs_abs_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real tptp.real_nat M_1)) (tptp.hAPP_nat_real tptp.real_nat N_2))) (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat M_1) N_2) tptp.one_one_nat)))))))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr660468384an_nat L) U)))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real (tptp.hAPP_nat_real tptp.real_nat N_1)) tptp.field_1210416355s_real))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr660468384an_nat L) U)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat U) (tptp.hAPP_nat_nat tptp.suc L)))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) tptp.field_1210416355s_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Y_2))))))) (forall ((F tptp.fun_real_real) (Y_2 tptp.real) (X_1 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real A) B))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real Y_2) _let_1)) (=> (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real A) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) tptp.zero_zero_real)))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real F Y_2)))))))) (forall ((K_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool tptp.iszero_rat (tptp.hAPP_int_rat tptp.number_number_of_rat K_1))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.iszero_int (tptp.hAPP_int_int tptp.number_number_of_int K_1))))) (forall ((X_1 tptp.real) (Y_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) Y_2)) (exists ((X_2 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) tptp.field_1210416355s_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) Y_2)))))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_2) X_1)) (= (tptp.comple124823625p_real (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real Y_2) X_1)) X_1))) (forall ((X_1 tptp.real) (X_3 tptp.fun_real_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) X_3)) (=> (exists ((Z tptp.real)) (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) X_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Z))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.comple124823625p_real X_3)))))) (forall ((Z_2 tptp.real) (X_1 tptp.real) (X_3 tptp.fun_real_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) X_3)) (=> (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) X_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Z_2)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.comple124823625p_real X_3)))))) (forall ((K_2 tptp.int)) (= (tptp.frct (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int K_2)) tptp.one_one_int)) (tptp.hAPP_int_rat tptp.number_number_of_rat K_2))) (forall ((K_2 tptp.int)) (= (tptp.frct (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int K_2) tptp.zero_zero_int)) tptp.zero_zero_rat)) (forall ((K_2 tptp.int)) (= (tptp.frct (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K_2)) tptp.zero_zero_rat)) (= (tptp.frct _let_41) tptp.one_one_rat) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.frct (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int K_2)) (tptp.hAPP_int_int tptp.number_number_of_int L_2))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)) (tptp.hAPP_int_rat tptp.number_number_of_rat L_2)))) (forall ((K_2 tptp.int)) (= (tptp.frct (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int K_2))) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)))) (forall ((Z_2 tptp.real) (X_3 tptp.fun_real_bool)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real Z_2) X_3)) (=> (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) X_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Z_2)))) (= (tptp.comple124823625p_real X_3) Z_2)))) (forall ((Z_2 tptp.real) (Y_2 tptp.real) (X_1 tptp.real) (X_3 tptp.fun_real_bool)) (let ((_let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_2))) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_1) X_3)) (=> (tptp.hBOOL (tptp.hAPP_real_bool _let_1 X_1)) (=> (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) X_3)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) Z_2)))) (tptp.hBOOL (tptp.hAPP_real_bool _let_1 (tptp.comple124823625p_real X_3)))))))) (forall ((Q_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_rat tptp.abs_abs_rat Q_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Q_2) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_rat_rat tptp.uminus_uminus_rat Q_2))) (=> (not _let_2) (= _let_1 Q_2)))))) (forall ((Q_2 tptp.rat)) (let ((_let_1 (tptp.hAPP_rat_rat tptp.sgn_sgn_rat Q_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) Q_2)))) (let ((_let_3 (= Q_2 tptp.zero_zero_rat))) (and (=> _let_3 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.hAPP_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))))))))) (forall ((Q_2 tptp.rat) (R_3 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat Q_2) R_3) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat Q_2) (tptp.hAPP_rat_rat tptp.inverse_inverse_rat R_3)))) (forall ((P_3 tptp.int) (Q_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Q_2) tptp.zero_zero_int)) (= (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.uminus_uminus_int P_3)) (tptp.hAPP_int_int tptp.uminus_uminus_int Q_2)))))) (forall ((P_3 tptp.rat)) (= (tptp.quotient_of (tptp.hAPP_rat_rat tptp.sgn_sgn_rat P_3)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.sgn_sgn_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int (tptp.quotient_of P_3)))) tptp.one_one_int))) (forall ((A_3 tptp.rat) (B_2 tptp.rat)) (=> (= (tptp.quotient_of A_3) (tptp.quotient_of B_2)) (= A_3 B_2))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.quotient_of A) (tptp.quotient_of B)) (= A B))) (forall ((Q_2 tptp.rat) (R_3 tptp.rat)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat Q_2) R_3) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat Q_2) (tptp.hAPP_rat_rat tptp.uminus_uminus_rat R_3)))) (forall ((Z_2 tptp.rat) (W_1 tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat Z_2) W_1)) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat Z_2) W_1)) (not (= Z_2 W_1))))) (forall ((R_3 tptp.rat) (P_3 tptp.int) (Q_2 tptp.int)) (=> (= (tptp.quotient_of R_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Q_2)))) (= (tptp.quotient_of tptp.one_one_rat) _let_41) (forall ((R_3 tptp.product_prod_int_int) (P_3 tptp.int) (Q_2 tptp.int)) (=> (= (tptp.normalize R_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Q_2)))) (forall ((P_3 tptp.int)) (= (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) tptp.zero_zero_int)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((P_3 tptp.int) (R_3 tptp.int) (S_1 tptp.int) (Q_2 tptp.int)) (=> (not (= Q_2 tptp.zero_zero_int)) (=> (not (= S_1 tptp.zero_zero_int)) (=> (= (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int R_3) S_1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int P_3) S_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int R_3) Q_2)))))) (= (tptp.quotient_of tptp.zero_zero_rat) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((K_2 tptp.int)) (= (tptp.quotient_of (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int tptp.number_number_of_int K_2)) tptp.one_one_int))) (forall ((R_3 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) R_3)) (not (forall ((S_2 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) S_2)) (forall ((T tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) T)) (not (= R_3 (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat S_2) T)))))))))) (forall ((X_1 tptp.product_prod_int_int) (Y_2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int X_1))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int Y_2))) (= (tptp.hBOOL (tptp.hAPP_f526364711l_bool (tptp.hAPP_P1062890741l_bool tptp.member2143287562nt_int (tptp.hAPP_P230595783nt_int (tptp.hAPP_P941956607nt_int tptp.produc883642259nt_int X_1) Y_2)) tptp.ratrel)) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int X_1)) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int Y_2)) _let_1))))))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract tptp.one_one_int) (tptp.hAPP_int_int tptp.number_number_of_int K_2)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat tptp.one_one_rat) (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)))) (forall ((R_3 tptp.int) (S_1 tptp.int)) (= (tptp.ratreal (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat (tptp.hAPP_int_rat tptp.number_number_of_rat R_3)) (tptp.hAPP_int_rat tptp.number_number_of_rat S_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.number267125858f_real R_3)) (tptp.hAPP_int_real tptp.number267125858f_real S_1)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (P_3 tptp.int) (Q_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2))) (=> (= (tptp.quotient_of _let_1) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract P_3) Q_2) _let_1)))) (forall ((A_3 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) tptp.zero_zero_int) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract tptp.zero_zero_int) tptp.one_one_int))) (= tptp.one_one_rat _let_40) (= _let_40 tptp.one_one_rat) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract tptp.zero_zero_int) K_2) tptp.zero_zero_rat)) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract K_2) tptp.zero_zero_int) tptp.zero_zero_rat)) (forall ((A_3 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_rat tptp.fract tptp.zero_zero_int))) (= (tptp.hAPP_int_rat _let_1 A_3) (tptp.hAPP_int_rat _let_1 C_1)))) (forall ((K_2 tptp.nat)) (= (tptp.hAPP_nat_rat tptp.semiri151668891at_rat K_2) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_2)) tptp.one_one_int))) (forall ((K_2 tptp.nat)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_nat_int tptp.semiri1621563631at_int K_2)) tptp.one_one_int) (tptp.hAPP_nat_rat tptp.semiri151668891at_rat K_2))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat tptp.ring_1_of_int_rat K_2) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract K_2) tptp.one_one_int))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract K_2) tptp.one_one_int) (tptp.hAPP_int_rat tptp.ring_1_of_int_rat K_2))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract K_2) L_2) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat (tptp.hAPP_int_rat tptp.ring_1_of_int_rat K_2)) (tptp.hAPP_int_rat tptp.ring_1_of_int_rat L_2)))) (forall ((W tptp.int)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat W) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract W) tptp.one_one_int))) (forall ((X tptp.rat)) (= (tptp.archim1246769320r_real (tptp.ratreal X)) (tptp.archim791455193or_rat X))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.archim791455193or_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_rat_rat tptp.inverse_inverse_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract B_2) A_3))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int C_1))) (=> (not (= C_1 tptp.zero_zero_int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int _let_1 A_3)) (tptp.hAPP_int_int _let_1 B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2))))) (forall ((A tptp.int) (C tptp.int) (D tptp.int) (B tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C) D)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) D) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C) B)))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int) (D_3 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C_1) D_3)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) D_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) C_1)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_rat_rat tptp.uminus_uminus_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.uminus_uminus_int A_3)) B_2))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int) (D_3 tptp.int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C_1) D_3)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) C_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) D_3)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_rat_rat tptp.abs_abs_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.abs_abs_int A_3)) (tptp.hAPP_int_int tptp.abs_abs_int B_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int) (P_3 tptp.int) (Q_2 tptp.int)) (=> (= (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_3) B_2)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract P_3) Q_2) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)))) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.ratreal X_1)) (tptp.ratreal Y_2))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_1) Y_2)))) (= _let_39 tptp.zero_zero_real) (= tptp.zero_zero_real _let_39) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_real tptp.number267125858f_real K_2) (tptp.ratreal (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)))) (forall ((K_2 tptp.int)) (= (tptp.ratreal (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)) (tptp.hAPP_int_real tptp.number267125858f_real K_2))) (= _let_38 tptp.one_one_real) (= tptp.one_one_real _let_38) (forall ((X_1 tptp.rat) (Y_2 tptp.rat)) (= (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.ratreal X_1)) (tptp.ratreal Y_2))) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat X_1) Y_2)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.ratreal X)) (tptp.ratreal Y)) (tptp.ratreal (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.ratreal X)) (tptp.ratreal Y)) (tptp.ratreal (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat X) Y)))) (forall ((X tptp.rat)) (= (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.ratreal X)) (tptp.ratreal (tptp.hAPP_rat_rat tptp.uminus_uminus_rat X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.ratreal X)) (tptp.ratreal Y)) (tptp.ratreal (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.ratreal X)) (tptp.ratreal Y)) (tptp.ratreal (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.times_times_rat X) Y)))) (forall ((X tptp.rat)) (= (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.ratreal X)) (tptp.ratreal (tptp.hAPP_rat_rat tptp.inverse_inverse_rat X)))) (= tptp.zero_zero_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract tptp.zero_zero_int) tptp.one_one_int)) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat tptp.number_number_of_rat K_2) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.number_number_of_int K_2)) tptp.one_one_int))) (forall ((K_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.number_number_of_int K_2)) tptp.one_one_int) (tptp.hAPP_int_rat tptp.number_number_of_rat K_2))) (forall ((K_2 tptp.int) (L_2 tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int tptp.number_number_of_int K_2)) (tptp.hAPP_int_int tptp.number_number_of_int L_2)) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.inverse_divide_rat (tptp.hAPP_int_rat tptp.number_number_of_rat K_2)) (tptp.hAPP_int_rat tptp.number_number_of_rat L_2)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.quotient_of (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.normalize (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A_3) B_2)))) (forall ((P_3 tptp.product_prod_int_int)) (= (tptp.frct P_3) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int P_3)) (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int P_3)))) (forall ((A tptp.int) (C tptp.int) (D tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) D)) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C) B)) _let_1)))))))) (forall ((R_3 tptp.int) (S_1 tptp.int)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.ratreal (tptp.hAPP_int_rat tptp.number_number_of_rat R_3))) (tptp.ratreal (tptp.hAPP_int_rat tptp.number_number_of_rat S_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_int_real tptp.number267125858f_real R_3)) (tptp.hAPP_int_real tptp.number267125858f_real S_1)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_rat_rat tptp.sgn_sgn_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat tptp.ring_1_of_int_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.sgn_sgn_int A_3)) (tptp.hAPP_int_int tptp.sgn_sgn_int B_2))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)))))) (forall ((A tptp.int) (C tptp.int) (D tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C) D))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) D)) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C) B)) _let_1)))))))) (forall ((A_3 tptp.int) (C_1 tptp.int) (D_3 tptp.int) (B_2 tptp.int)) (=> (not (= B_2 tptp.zero_zero_int)) (=> (not (= D_3 tptp.zero_zero_int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C_1) D_3)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) D_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C_1) B_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) D_3)))))) (forall ((A_3 tptp.int) (C_1 tptp.int) (D_3 tptp.int) (B_2 tptp.int)) (=> (not (= B_2 tptp.zero_zero_int)) (=> (not (= D_3 tptp.zero_zero_int)) (= (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.minus_minus_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract C_1) D_3)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) D_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int C_1) B_2))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_2) D_3)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) A))))) (forall ((M tptp.int) (N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) N)) N) (tptp.hAPP_rat_rat (tptp.hAPP_rat_fun_rat_rat tptp.plus_plus_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract M) N)) tptp.one_one_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) tptp.zero_zero_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) B_2))) (let ((_let_2 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat tptp.ring_1_of_int_rat _let_1)) _let_2)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat _let_2) (tptp.hAPP_int_rat tptp.ring_1_of_int_rat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_eq_rat (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A) B)) tptp.one_one_rat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A) B))))) (forall ((Q_1 tptp.rat) (P_1 tptp.fun_rat_bool)) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_4)) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_2) B_4))))) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 Q_1)))) (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) Q_1))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int R_2) B))) (= (tptp.hAPP_P1975530577nt_int (tptp.adjust B) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int Q_1) R_2)) (tptp.hAPP_P1975530577nt_int (tptp.hAPP_P1145851913nt_int (tptp.hAPP_b40753821nt_int tptp.if_Pro1731782967nt_int (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_2)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) _let_2)) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int _let_1) R_2)))))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) K_1))))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K_1))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.nat_tr160667106at_int tptp.semiri1621563631at_int) (tptp.cOMBK_bool_nat tptp.fTrue))) (forall ((P_1 tptp.fun_int_bool)) (= (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) P_1)) (tptp.image_nat_int tptp.semiri1621563631at_int (tptp.collect_nat (tptp.hAPP_f1154658180t_bool (tptp.hAPP_f1361476881t_bool tptp.cOMBB_int_bool_nat P_1) tptp.semiri1621563631at_int))))) (forall ((N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N_1)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) N_1))))) N_1))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) _let_1)) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) N_1)))) (tptp.hAPP_int_nat tptp.nat_1 N_1))))) (forall ((N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N_1)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) N_1)))) (tptp.hAPP_int_nat tptp.nat_1 N_1)))) (forall ((N_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) N_1)))))) (forall ((N_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) N_1)))))) (forall ((K_1 tptp.real) (Xa_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.cos) (tptp.hAPP_r1250527377l_real (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real tptp.plus_plus_real) K_1)) Xa_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Xa_1) K_1)))))) (forall ((X_2 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc X_2)))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X_1)) (tptp.hAPP_real_real tptp.sin X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real) tptp.sin)) tptp.sin) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1))))) (forall ((K_1 tptp.real) (Xa_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.sin) (tptp.hAPP_r1250527377l_real (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real tptp.plus_plus_real) K_1)) Xa_1) (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real Xa_1) K_1))))) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) X_1))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) N_1))) (tptp.hAPP_nat_nat tptp.suc N_1))) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) X_1))) (tptp.hAPP_nat_nat tptp.suc X_1))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W))) (= (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 W)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((P_1 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) P_1))))) (forall ((P_1 tptp.fun_nat_bool)) (= (tptp.collect_nat P_1) (tptp.image_int_nat tptp.nat_1 (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_f1448486952t_bool (tptp.hAPP_f696844121t_bool tptp.cOMBB_nat_bool_int P_1) tptp.nat_1)))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.bseq_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)))))) (forall ((N_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) N_1)))))) (forall ((Z_2 tptp.int) (Z_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_2) Z_3))) (let ((_let_2 (tptp.hAPP_int_nat tptp.nat_1 Z_2))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_int_nat tptp.nat_1 Z_3)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg Z_3)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat (tptp.hAPP_int_bool tptp.nat_neg _let_1)) tptp.zero_zero_nat) (tptp.hAPP_int_nat tptp.nat_1 _let_1)))))))))) (forall ((I_1 tptp.int)) (=> (not (= I_1 tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.dvd_dvd_int) I_1)))))) (forall ((Ma tptp.nat)) (=> (not (= Ma tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.dvd_dvd_nat) Ma)))))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat tptp.prime)))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.cauchy_complex X_3)) (tptp.hBOOL (tptp.cauchy_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat tptp.cnj) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.cauchy_complex X_3)) (tptp.hBOOL (tptp.cauchy_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.im) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.cauchy_complex X_3)) (tptp.hBOOL (tptp.cauchy_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.re) X_3))))) (forall ((N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real (tptp.hAPP_nat_real tptp.real_nat N_1)) tptp.ring_1_Ints_real))) (forall ((X_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real (tptp.hAPP_int_real tptp.real_int X_1)) tptp.ring_1_Ints_real))) (forall ((G tptp.fun_real_real) (X_1 tptp.real) (Ma tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real G X_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.cos) G) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real G X_1)))) Ma))))) (forall ((G tptp.fun_real_real) (X_1 tptp.real) (Ma tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real G X_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.sin) G) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real G X_1))) Ma))))) (forall ((X_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) X_1))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) N_1))) N_1)) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) X_1))) X_1)) (forall ((P_1 tptp.fun_nat_bool) (I_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) P_1)) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I_1)))))) (forall ((Z_1 tptp.int) (W tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int Z_1))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W)))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 W))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_2) _let_2))))) (forall ((I_1 tptp.nat) (M_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (let ((_let_2 (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_2))) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool (tptp.hAPP_f66927821l_bool (tptp.hAPP_f2037783381l_bool tptp.cOMBB_1146692694ol_nat tptp.member_nat) tptp.suc)) M_2))) (tptp.hAPP_n1699378549t_bool _let_1 I_1)))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_2))) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I_1)))))))))) (forall ((I_1 tptp.nat) (M_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_2)) (not (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_2))) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) (tptp.hAPP_nat_nat tptp.suc I_1))))) tptp.zero_zero_nat)))) (forall ((I_1 tptp.nat) (M_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat))) (let ((_let_2 (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat tptp.zero_zero_nat) M_2)) (= (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool (tptp.hAPP_f66927821l_bool (tptp.hAPP_f2037783381l_bool tptp.cOMBB_1146692694ol_nat tptp.member_nat) tptp.suc)) M_2))) (tptp.hAPP_n1699378549t_bool _let_1 I_1))))) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) M_2))) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat tptp.suc I_1)))))))))) (forall ((N_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) N_1)))))) (forall ((Ma tptp.int) (X_1 tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.noXRRset Ma) X_1) (tptp.image_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.times_times_int) X_1) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma)))) (forall ((N_1 tptp.nat) (G tptp.fun_real_real) (X_1 tptp.real) (Ma tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real G X_1) Ma)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) G)) N_1) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real G X_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) tptp.one_one_nat)))) Ma))))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) _let_1)) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) N_1)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat tptp.nat_1 N_1)) tptp.one_one_nat))))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) _let_1)) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) N_1))))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int N_1) tptp.one_one_int))))) (forall ((N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) _let_1)) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) N_1)))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_int_nat tptp.nat_1 N_1)) tptp.one_one_nat))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X_1))) (tptp.hAPP_real_real tptp.cos X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real) tptp.cos)) tptp.cos) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1))))) (forall ((N_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))))) (= (= (tptp.hAPP_nat_nat tptp.suc N_1) (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (and _let_2 (=> _let_2 (= (tptp.hAPP_int_nat tptp.nat_1 _let_1) N_1))))))) (forall ((V tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))))) (= (= (tptp.hAPP_int_nat tptp.number_number_of_nat V) (tptp.hAPP_nat_nat tptp.suc N_1)) (and _let_2 (=> _let_2 (= (tptp.hAPP_int_nat tptp.nat_1 _let_1) N_1))))))) (forall ((W tptp.int)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 W)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg (tptp.hAPP_int_int tptp.number_number_of_int W))))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real tptp.power_power_real) N_1) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real) tptp.cos)) tptp.cos) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 tptp.min))) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1))))) (forall ((V tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat tptp.suc N_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_int_nat tptp.nat_1 _let_1)) N_1)))))) (forall ((N_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat V))) (and _let_2 (=> _let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) (tptp.hAPP_int_nat tptp.nat_1 _let_1))))))))) (forall ((N_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat V))) (and _let_2 (=> _let_2 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) (tptp.hAPP_int_nat tptp.nat_1 _let_1))))))))) (forall ((V tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat tptp.suc N_1))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_neg _let_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat tptp.nat_1 _let_1)) N_1)))))) (forall ((X_3 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_int_int (tptp.standardRes Ma) X_3)) (tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) Ma))))))) (forall ((X_1 tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (let ((_let_1 (tptp.rsetR Ma))) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Ma)) (=> (= (tptp.hAPP_int_int (tptp.legacy_zgcd X_1) Ma) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool (tptp.image_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.times_times_int) X_1) A_1)) _let_1))))))) (forall ((Z_1 tptp.int) (W tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int Z_1))) (let ((_let_2 (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit1 W))))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.number_number_of_int W))))) (let ((_let_4 (tptp.hAPP_nat_int _let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat W)))) (and (=> _let_3 (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) _let_4)) _let_4))) (=> (not _let_3) (= _let_2 tptp.one_one_int)))))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real) tptp.sin)) tptp.sin) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1))))) (forall ((B tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.log B) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.ln B)) X_1)))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real) tptp.cos)) tptp.cos) X_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1)))))) (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.plus_plus_real) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_2 tptp.sin)) _let_1))) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_2 tptp.cos)) _let_1)) X_2) tptp.zero_zero_real))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) tptp.sin)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.cos X_1)) (tptp.hAPP_real_real tptp.sin X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) tptp.sin)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1))))) (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int V) (tptp.hAPP_int_int tptp.uminus_uminus_int V_1))))) (let ((_let_2 (tptp.hAPP_int_nat tptp.number_number_of_nat V))) (let ((_let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_int_nat tptp.number_number_of_nat V_1)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int V_1) tptp.pls)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat (tptp.hAPP_int_bool tptp.nat_neg _let_1)) tptp.zero_zero_nat) (tptp.hAPP_int_nat tptp.nat_1 _let_1)))))))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) tptp.cos)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 tptp.min))) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) tptp.cos)) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)) X_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) (tptp.hAPP_real_real tptp.cos X_1))) (tptp.hAPP_real_real tptp.sin X_1))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X_1))) (tptp.hAPP_real_real tptp.cos X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real) tptp.cos)) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real _let_1) _let_1))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.cos X_1))) (=> (not (= _let_1 tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.inverse_divide_real) tptp.sin)) tptp.cos) X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_1) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))))))) (forall ((Y_2 tptp.real) (X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_real_real tptp.sin Y_2))) (let ((_let_3 (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.times_times_real))) (let ((_let_4 (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real (tptp.hAPP_f556082547l_real _let_3 tptp.sin)))) (let ((_let_5 (tptp.hAPP_real_real tptp.cos Y_2))) (let ((_let_6 (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real (tptp.hAPP_f556082547l_real _let_3 tptp.cos)))) (let ((_let_7 (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.minus_minus_real))) (let ((_let_8 (tptp.hAPP_r1250527377l_real (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real tptp.plus_plus_real) Y_2))) (let ((_let_9 (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real))) (let ((_let_10 (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.plus_plus_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_10 (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_9 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_7 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.sin) _let_8))) (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_10 (tptp.hAPP_r1250527377l_real _let_4 _let_5))) (tptp.hAPP_r1250527377l_real _let_6 _let_2))))) _let_1))) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_9 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_7 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.cos) _let_8))) (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_7 (tptp.hAPP_r1250527377l_real _let_6 _let_5))) (tptp.hAPP_r1250527377l_real _let_4 _let_2))))) _let_1)) X_2) tptp.zero_zero_real))))))))))))) (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_int_real tptp.number267125858f_real _let_1)) (tptp.hAPP_real_real tptp.cos X_2))) (tptp.hAPP_real_real tptp.sin X_2)))) (let ((_let_3 (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1))) (let ((_let_4 (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.plus_plus_real) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_4 tptp.sin)) _let_3))) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_4 tptp.cos)) _let_3)) X_2) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real _let_2) _let_2)))))))) (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real tptp.power_power_real))) (let ((_let_3 (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.plus_plus_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_3 (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_2 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real _let_3 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.sin) tptp.uminus_uminus_real))) tptp.sin))) _let_1))) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real (tptp.hAPP_f1407095736t_real _let_2 (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.minus_minus_real) (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real tptp.cos) tptp.uminus_uminus_real))) tptp.cos))) _let_1)) X_2) tptp.zero_zero_real)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.int_gcd A) B))) (let ((_let_2 (tptp.norm_frac A B))) (let ((_let_3 (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B) tptp.zero_zero_int)))) (=> (tptp.hBOOL (tptp.hAPP_P603027463t_bool (tptp.accp_P2006205492nt_int tptp.norm_frac_rel) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int A) B))) (and (=> _let_4 (= _let_2 (tptp.norm_frac (tptp.hAPP_int_int tptp.uminus_uminus_int A) (tptp.hAPP_int_int tptp.uminus_uminus_int B)))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_3) (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B) _let_1))))))))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.monoseq_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) _let_1)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.monoseq_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.int_gcd A_3) B_2))) (let ((_let_2 (tptp.norm_frac A_3 B_2))) (let ((_let_3 (or (= A_3 tptp.zero_zero_int) (= B_2 tptp.zero_zero_int)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B_2) tptp.zero_zero_int)))) (and (=> _let_4 (= _let_2 (tptp.norm_frac (tptp.hAPP_int_int tptp.uminus_uminus_int A_3) (tptp.hAPP_int_int tptp.uminus_uminus_int B_2)))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_3) (= _let_2 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) _let_1)))))))))))) (forall ((Z_2 tptp.complex)) (let ((_let_1 (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj))) (let ((_let_2 (tptp.hAPP_complex_complex tptp.sgn_sgn_complex Z_2))) (= (tptp.arg Z_2) (tptp.hilbert_Eps_real (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_1 (tptp.hAPP_f1402056515l_bool (tptp.hAPP_f824790735l_bool tptp.cOMBB_real_bool_real (tptp.hAPP_r1134773055l_bool tptp.fequal_real (tptp.hAPP_complex_real tptp.re _let_2))) tptp.cos))) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_1 (tptp.hAPP_f1402056515l_bool (tptp.hAPP_f824790735l_bool tptp.cOMBB_real_bool_real (tptp.hAPP_r1134773055l_bool tptp.fequal_real (tptp.hAPP_complex_real tptp.im _let_2))) tptp.sin))) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real tptp.pi)))) (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool tptp.ord_less_eq_real) tptp.pi))))))))) (forall ((A tptp.int) (P_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int _let_1) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_5) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.comple219730294t_bool (tptp.setS A P_5)))) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int)) _let_1)))) P_5)))))))) (forall ((A tptp.int)) (= (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.hAPP_i1948725293t_bool tptp.d22set A)) (tptp.hAPP_int_int tptp.zfact A))) (forall ((A tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) Ma)) (= (tptp.hAPP_int_int (tptp.legacy_zgcd (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma))) Ma) tptp.one_one_int))) (forall ((A tptp.int) (Ma tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.bnorRset A) Ma))) (=> (not (= X_1 tptp.zero_zero_int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) Ma)) (= (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.image_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.times_times_int) X_1) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.big_co1548731110nt_int tptp.cOMBI_int _let_1)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X_1) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int _let_1)))))))) (forall ((X_1 tptp.fun_int_bool) (A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.quadRes P_5) A))) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_1) (tptp.setS A P_5))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.big_co1548731110nt_int tptp.cOMBI_int X_1)) A) P_5)))))))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.hAPP_i1948725293t_bool (tptp.wset A) P_5))) tptp.one_one_int) P_5)))))) (forall ((A tptp.int) (P_5 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong A) tptp.zero_zero_int) P_5))) (= (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.comple219730294t_bool (tptp.setS A P_5))) (tptp.hAPP_int_int tptp.zfact (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int P_5) tptp.one_one_int))))))) (forall ((F tptp.fun_int_int) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int F X_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.big_co1548731110nt_int F A_1)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (let ((_let_2 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) tptp.one_one_real)) (= (tptp.hAPP_real_real tptp.arctan X_1) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) _let_1)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (let ((_let_3 (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))))) (let ((_let_4 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) _let_1)) tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1122023986l_real (tptp.hAPP_f1786887945l_real tptp.cOMBB_1896127834l_real tptp.suminf_real) (tptp.hAPP_f1993765077t_real (tptp.hAPP_f895854793t_real tptp.cOMBB_1948233853l_real _let_3) (tptp.hAPP_f1993765077t_real (tptp.hAPP_f895854793t_real tptp.cOMBB_1948233853l_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) _let_4))))) (tptp.hAPP_f1501741374t_real (tptp.hAPP_f1135648319t_real tptp.cOMBC_1329014627t_real (tptp.hAPP_f1163894827t_real (tptp.hAPP_f1998755145t_real tptp.cOMBB_421464275l_real tptp.cOMBB_nat_real_nat) tptp.power_power_real)) _let_4)))) X_1) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real _let_3 (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))))))))))) (forall ((X_2 tptp.real)) (= (tptp.hAPP_real_real tptp.sin X_2) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.sin_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_2))))) (forall ((X_1 tptp.real)) (= (tptp.hAPP_real_real tptp.sin X_1) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.sin_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))))) (forall ((X_2 tptp.real)) (= (tptp.hAPP_real_real tptp.cos X_2) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.cos_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_2))))) (forall ((X_1 tptp.real)) (= (tptp.hAPP_real_real tptp.cos X_1) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.cos_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))))) (forall ((X_1 tptp.real)) (= (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_real_real tptp.sin X_1)) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.uminus_uminus_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.sin_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP_real_real tptp.exp_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real) X_1)) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.fact_fact_nat) _let_1))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))))))) (= _let_37 (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real _let_34))) tptp.one_one_real))) (tptp.hAPP_f1676298106t_real _let_17 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) _let_3))) tptp.one_one_nat))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (= (tptp.hAPP_real_real tptp.ln X_1) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) tptp.one_one_nat)))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) tptp.one_one_real))) tptp.suc)))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (let ((_let_2 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_2 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) _let_1)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))))))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.abs_abs_real) F))) (tptp.hBOOL (tptp.summable_real F)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_nat_real F N_2))) (tptp.hAPP_nat_real G N_2)))))) (=> (tptp.hBOOL (tptp.summable_real G)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.abs_abs_real) F)))))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.abs_abs_real) F))) (=> (tptp.hBOOL (tptp.summable_real _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_f352196356l_real tptp.suminf_real F))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1)))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.sin_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.cos_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))))) (forall ((P_5 tptp.rat)) (= (tptp.archim791455193or_rat P_5) (tptp.hAPP_P1175774780nt_int (tptp.produc1298267108nt_int tptp.div_div_int) (tptp.quotient_of P_5)))) (forall ((P_5 tptp.rat)) (= (tptp.quotient_of (tptp.hAPP_rat_rat tptp.uminus_uminus_rat P_5)) (tptp.hAPP_P1975530577nt_int (tptp.produc1518849193nt_int (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int) tptp.uminus_uminus_int)) (tptp.quotient_of P_5)))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))))) (forall ((P_5 tptp.rat)) (= (tptp.quotient_of (tptp.hAPP_rat_rat tptp.abs_abs_rat P_5)) (tptp.hAPP_P1975530577nt_int (tptp.produc1518849193nt_int (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int) tptp.abs_abs_int)) (tptp.quotient_of P_5)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj))) (let ((_let_2 (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B))) (= (tptp.divmod_int_rel A B) (tptp.produc93441119t_bool (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool (tptp.hAPP_f1545556668t_bool (tptp.hAPP_f85237525t_bool tptp.cOMBB_389152643ol_int tptp.cOMBS_int_bool_bool) (tptp.hAPP_f1344929775l_bool (tptp.hAPP_f1830214065l_bool tptp.cOMBB_793166024ol_int _let_1) (tptp.hAPP_f720654810t_bool (tptp.hAPP_f908327869t_bool tptp.cOMBB_1290694363ol_int (tptp.hAPP_f1512942609t_bool tptp.cOMBB_int_bool_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int A))) (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.plus_plus_int) (tptp.hAPP_int_fun_int_int tptp.times_times_int B)))))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.fimplies _let_2)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_int) B))))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot _let_2))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int B))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.ord_less_eq_int) tptp.zero_zero_int)))))))))) (= tptp.twoSqu2000912462sum2sq (tptp.produc1298267108nt_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f808647893nt_int tptp.cOMBC_736024425nt_int (tptp.hAPP_f836602773nt_int (tptp.hAPP_f888249301nt_int tptp.cOMBB_1875755114nt_int tptp.cOMBB_int_int_int) (tptp.hAPP_f1760145644nt_int _let_22 _let_33))) _let_33))) (forall ((P_5 tptp.rat)) (= (tptp.quotient_of (tptp.hAPP_rat_rat tptp.inverse_inverse_rat P_5)) (tptp.hAPP_P1975530577nt_int (tptp.produc1518849193nt_int (tptp.hAPP_f465821005nt_int (tptp.hAPP_f1081447804nt_int tptp.cOMBS_1470252563nt_int (tptp.hAPP_f400200275nt_int (tptp.hAPP_f1731308757nt_int tptp.cOMBB_735549356nt_int tptp.cOMBB_1389251822nt_int) (tptp.hAPP_P621635040nt_int (tptp.hAPP_f1582586579nt_int tptp.cOMBC_707974837nt_int (tptp.hAPP_f251264923nt_int (tptp.hAPP_f279307923nt_int tptp.cOMBB_662120866nt_int tptp.if_Pro1731782967nt_int) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) tptp.zero_zero_int))) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))) (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f434654626nt_int tptp.cOMBS_2011279539nt_int (tptp.hAPP_f2094497995nt_int (tptp.hAPP_f534361363nt_int tptp.cOMBB_1657320178nt_int tptp.cOMBC_1964283556nt_int) (tptp.hAPP_f2004554147nt_int (tptp.hAPP_f1228585167nt_int tptp.cOMBB_1102189010nt_int (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int)) (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.times_times_int) tptp.sgn_sgn_int)))) tptp.abs_abs_int))) (tptp.quotient_of P_5)))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.fact_fact_nat) _let_1))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1)))))) (forall ((B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int))) (let ((_let_3 (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.minus_minus_int) B))) (= (tptp.adjust B) (tptp.produc1518849193nt_int (tptp.hAPP_f465821005nt_int (tptp.hAPP_f1081447804nt_int tptp.cOMBS_1470252563nt_int (tptp.hAPP_f617310012nt_int (tptp.hAPP_f197974549nt_int tptp.cOMBB_638531587nt_int tptp.cOMBS_1891347093nt_int) (tptp.hAPP_f55007289nt_int (tptp.hAPP_f747475781nt_int tptp.cOMBB_222539774nt_int (tptp.hAPP_f1311564564nt_int tptp.cOMBS_1640193733nt_int (tptp.hAPP_f251264923nt_int (tptp.hAPP_f279307923nt_int tptp.cOMBB_662120866nt_int tptp.if_Pro1731782967nt_int) (tptp.hAPP_f429935748t_bool (tptp.hAPP_f1512942609t_bool tptp.cOMBB_int_bool_int (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int)) _let_3)))) (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f960630521nt_int tptp.cOMBC_1805044090nt_int (tptp.hAPP_f142232355nt_int (tptp.hAPP_f1377453843nt_int tptp.cOMBB_320287386nt_int tptp.cOMBB_1846624359nt_int) (tptp.hAPP_f1574055885nt_int _let_2 (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.plus_plus_int) _let_1)) tptp.one_one_int)))) _let_3)))) (tptp.hAPP_f1574055885nt_int _let_2 _let_1)))))))) (forall ((X0 tptp.real) (F tptp.fun_nat_real) (R_4 tptp.real)) (let ((_let_1 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (let ((_let_2 (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 F)))) (=> (forall ((X_2 tptp.real)) (let ((_let_1 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real (tptp.hAPP_real_real tptp.uminus_uminus_real R_4)) R_4))) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 F)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.suc)))) (tptp.hAPP_r474017924t_real tptp.power_power_real X_2))))))) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X0) (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real (tptp.hAPP_real_real tptp.uminus_uminus_real R_4)) R_4))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_4)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1122023986l_real (tptp.hAPP_f1786887945l_real tptp.cOMBB_1896127834l_real tptp.suminf_real) (tptp.hAPP_f1993765077t_real (tptp.hAPP_f895854793t_real tptp.cOMBB_1948233853l_real _let_2) (tptp.hAPP_f1501741374t_real (tptp.hAPP_f1135648319t_real tptp.cOMBC_1329014627t_real (tptp.hAPP_f1163894827t_real (tptp.hAPP_f1998755145t_real tptp.cOMBB_421464275l_real tptp.cOMBB_nat_real_nat) tptp.power_power_real)) tptp.suc))) X0) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_1 (tptp.hAPP_f1888375463t_real _let_2 (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.suc)))) (tptp.hAPP_r474017924t_real tptp.power_power_real X0))))))))))) (= tptp.frac (tptp.produc93441119t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_21 _let_32))) (tptp.hAPP_i345030060t_bool (tptp.hAPP_f791698359t_bool tptp.cOMBC_241247961t_bool (tptp.hAPP_f791698359t_bool (tptp.hAPP_f847817363t_bool tptp.cOMBB_562416518ol_int tptp.cOMBC_int_int_bool) (tptp.hAPP_f725770969t_bool (tptp.hAPP_f983569339t_bool tptp.cOMBB_550562460ol_int (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int tptp.fequal_int)) tptp.int_gcd))) tptp.one_one_int)))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_f213450978omplex tptp.suminf_complex X_3)) (tptp.hAPP_f213450978omplex tptp.suminf_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat tptp.cnj) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (tptp.hBOOL (tptp.summable_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat tptp.cnj) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.re) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.im) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_f213450978omplex tptp.suminf_complex X_3)) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.re) X_3))))) (forall ((X_3 tptp.fun_nat_complex)) (=> (tptp.hBOOL (tptp.summable_complex X_3)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_f213450978omplex tptp.suminf_complex X_3)) (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.im) X_3))))) (= tptp.ratrel (tptp.collec50511176nt_int (tptp.produc973645403t_bool (tptp.hAPP_f1781059817t_bool (tptp.hAPP_f125837377t_bool tptp.cOMBS_1610675060t_bool (tptp.hAPP_f1965248563t_bool (tptp.hAPP_f1273270095t_bool tptp.cOMBB_595786433nt_int tptp.cOMBB_1344650379nt_int) _let_31)) (tptp.hAPP_f1781059817t_bool (tptp.hAPP_f326728547t_bool tptp.cOMBB_2086486755nt_int (tptp.hAPP_f461489489t_bool tptp.cOMBS_400904860l_bool _let_31)) (tptp.hAPP_f1187443546t_bool (tptp.hAPP_f11709033t_bool tptp.cOMBS_1676841879t_bool (tptp.hAPP_f223623489t_bool (tptp.hAPP_f1815301987t_bool tptp.cOMBB_650041899nt_int tptp.cOMBS_480885903t_bool) (tptp.hAPP_f1198736473t_bool (tptp.hAPP_f2042071795t_bool tptp.cOMBB_773384995nt_int _let_30) (tptp.hAPP_f167782601nt_int (tptp.hAPP_f1769710159nt_int tptp.cOMBC_2037038898nt_int (tptp.hAPP_f301246617nt_int (tptp.hAPP_f1151807883nt_int tptp.cOMBB_563965291nt_int tptp.cOMBB_47643171nt_int) _let_29)) tptp.product_snd_int_int)))) (tptp.hAPP_f167782601nt_int (tptp.hAPP_f400538607nt_int tptp.cOMBB_866192175nt_int (tptp.hAPP_f578362681nt_int tptp.cOMBC_1417754532nt_int _let_29)) tptp.product_snd_int_int))))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.divmod_nat Ma N_1))) (let ((_let_2 (or (= N_1 tptp.zero_zero_nat) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Ma) N_1))))) (and (=> _let_2 (= _let_1 (tptp.hAPP_n1289843868at_nat (tptp.hAPP_n1865633855at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) Ma))) (=> (not _let_2) (= _let_1 (tptp.hAPP_P1586233937at_nat (tptp.produc1391996073at_nat (tptp.hAPP_f837737749at_nat (tptp.hAPP_f999082675at_nat tptp.cOMBB_348438404at_nat tptp.product_Pair_nat_nat) tptp.suc)) (tptp.divmod_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma) N_1) N_1)))))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real) (N_1 tptp.nat)) (let ((_let_1 (tptp.bolzano_bisect P_1 A B))) (let ((_let_2 (tptp.hAPP_r337325687l_real (tptp.hAPP_f1644353557l_real tptp.cOMBC_1508019322l_real (tptp.hAPP_f1644353557l_real (tptp.hAPP_f1874145443l_real tptp.cOMBB_1768400739l_real tptp.cOMBC_real_real_real) (tptp.hAPP_f1732848529l_real (tptp.hAPP_f1310479593l_real tptp.cOMBB_2092576745l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.inverse_divide_real)) tptp.plus_plus_real))) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.hAPP_f320596107l_real (tptp.hAPP_f850851693l_real tptp.cOMBS_193881978l_real (tptp.hAPP_f1119546819l_real (tptp.hAPP_f555557763l_real tptp.cOMBB_422423973l_real tptp.cOMBB_2107848501l_real) tptp.produc865579683l_real)) _let_2))) (= (tptp.hAPP_n332733730l_real _let_1 (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_P1860904029l_real (tptp.produc595218619l_real (tptp.hAPP_f2072293513l_real (tptp.hAPP_f1763467369l_real tptp.cOMBS_163651580l_real (tptp.hAPP_f1663701695l_real (tptp.hAPP_f774948957l_real tptp.cOMBB_3698607l_real tptp.cOMBS_902912708l_real) (tptp.hAPP_f324002831l_real (tptp.hAPP_f677014621l_real tptp.cOMBS_107495110l_real (tptp.hAPP_f1161935955l_real (tptp.hAPP_f328572565l_real tptp.cOMBB_520243667l_real tptp.cOMBS_794971624l_real) (tptp.hAPP_f517738447l_real (tptp.hAPP_f1879982819l_real tptp.cOMBB_731595089l_real (tptp.hAPP_f1076489843l_real tptp.cOMBB_415306361l_real tptp.if_Pro313124157l_real)) (tptp.hAPP_f1884005689l_bool (tptp.hAPP_f172451459l_bool tptp.cOMBB_421479067l_real (tptp.hAPP_f940061907l_bool tptp.cOMBB_1795223523l_real P_1)) _let_3)))) (tptp.hAPP_f1591894897l_real (tptp.hAPP_f644105375l_real tptp.cOMBC_467724138l_real (tptp.hAPP_f1108539711l_real (tptp.hAPP_f1109256153l_real tptp.cOMBB_44084907l_real tptp.cOMBS_511527878l_real) (tptp.hAPP_f823702159l_real (tptp.hAPP_f1040184293l_real tptp.cOMBB_557258983l_real (tptp.hAPP_f2114902373l_real tptp.cOMBB_237479429l_real tptp.produc865579683l_real)) _let_2))) tptp.cOMBI_real)))) _let_3)) (tptp.hAPP_n332733730l_real _let_1 N_1))))))) (forall ((A tptp.fun_nat_real) (R_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_2)) (=> (tptp.hBOOL (tptp.summable_real A)) (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_f352196356l_real tptp.suminf_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat A) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) N_2))))) R_2)))))))) (forall ((L tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.pdivmod K_1 L))) (let ((_let_2 (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int))) (let ((_let_3 (tptp.divmod_int K_1 L))) (let ((_let_4 (= L tptp.zero_zero_int))) (let ((_let_5 (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int))) (let ((_let_6 (= K_1 tptp.zero_zero_int))) (and (=> _let_6 (= _let_3 (tptp.hAPP_i1524277240nt_int _let_5 tptp.zero_zero_int))) (=> (not _let_6) (and (=> _let_4 (= _let_3 (tptp.hAPP_i1524277240nt_int _let_5 K_1))) (=> (not _let_4) (= _let_3 (tptp.hAPP_P1975530577nt_int (tptp.produc713050258nt_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.sgn_sgn_int L))) (tptp.hAPP_P1975530577nt_int (tptp.hAPP_P1145851913nt_int (tptp.hAPP_b40753821nt_int tptp.if_Pro1731782967nt_int (tptp.fdisj (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) K_1)) (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) tptp.zero_zero_int)))) _let_1) (tptp.hAPP_P1975530577nt_int (tptp.produc1518849193nt_int (tptp.hAPP_f465821005nt_int (tptp.hAPP_f1081447804nt_int tptp.cOMBS_1470252563nt_int (tptp.hAPP_f617310012nt_int (tptp.hAPP_f197974549nt_int tptp.cOMBB_638531587nt_int tptp.cOMBS_1891347093nt_int) (tptp.hAPP_f1148171384nt_int (tptp.hAPP_f334321603nt_int tptp.cOMBB_1484610687nt_int (tptp.hAPP_f1582586579nt_int tptp.cOMBC_707974837nt_int (tptp.hAPP_f251264923nt_int (tptp.hAPP_f279307923nt_int tptp.cOMBB_662120866nt_int tptp.if_Pro1731782967nt_int) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) tptp.zero_zero_int)))) (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f465821005nt_int tptp.cOMBC_1964283556nt_int (tptp.hAPP_f1574055885nt_int _let_2 tptp.uminus_uminus_int)) tptp.zero_zero_int)))) (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f960630521nt_int tptp.cOMBC_1805044090nt_int (tptp.hAPP_f142232355nt_int (tptp.hAPP_f1377453843nt_int tptp.cOMBB_320287386nt_int tptp.cOMBB_1846624359nt_int) (tptp.hAPP_f1574055885nt_int _let_2 (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.minus_minus_int) tptp.uminus_uminus_int)) tptp.one_one_int)))) (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.abs_abs_int L))))) _let_1))))))))))))))) (= tptp.negateSnd (tptp.produc713050258nt_int tptp.uminus_uminus_int)) (forall ((L tptp.int) (K_1 tptp.int)) (let ((_let_1 (tptp.pdivmod K_1 L))) (let ((_let_2 (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int tptp.product_Pair_int_int))) (let ((_let_3 (tptp.hAPP_int_int tptp.sgn_sgn_int L))) (let ((_let_4 (tptp.divmod_int K_1 L))) (let ((_let_5 (= L tptp.zero_zero_int))) (let ((_let_6 (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int))) (let ((_let_7 (= K_1 tptp.zero_zero_int))) (and (=> _let_7 (= _let_4 (tptp.hAPP_i1524277240nt_int _let_6 tptp.zero_zero_int))) (=> (not _let_7) (and (=> _let_5 (= _let_4 (tptp.hAPP_i1524277240nt_int _let_6 K_1))) (=> (not _let_5) (= _let_4 (tptp.hAPP_P1975530577nt_int (tptp.produc713050258nt_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_3)) (tptp.hAPP_P1975530577nt_int (tptp.hAPP_P1145851913nt_int (tptp.hAPP_b40753821nt_int tptp.if_Pro1731782967nt_int (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int (tptp.hAPP_int_int tptp.sgn_sgn_int K_1)) _let_3)) _let_1) (tptp.hAPP_P1975530577nt_int (tptp.produc1518849193nt_int (tptp.hAPP_f465821005nt_int (tptp.hAPP_f1081447804nt_int tptp.cOMBS_1470252563nt_int (tptp.hAPP_f617310012nt_int (tptp.hAPP_f197974549nt_int tptp.cOMBB_638531587nt_int tptp.cOMBS_1891347093nt_int) (tptp.hAPP_f1148171384nt_int (tptp.hAPP_f334321603nt_int tptp.cOMBB_1484610687nt_int (tptp.hAPP_f1582586579nt_int tptp.cOMBC_707974837nt_int (tptp.hAPP_f251264923nt_int (tptp.hAPP_f279307923nt_int tptp.cOMBB_662120866nt_int tptp.if_Pro1731782967nt_int) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) tptp.zero_zero_int)))) (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f465821005nt_int tptp.cOMBC_1964283556nt_int (tptp.hAPP_f1574055885nt_int _let_2 tptp.uminus_uminus_int)) tptp.zero_zero_int)))) (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f960630521nt_int tptp.cOMBC_1805044090nt_int (tptp.hAPP_f142232355nt_int (tptp.hAPP_f1377453843nt_int tptp.cOMBB_320287386nt_int tptp.cOMBB_1846624359nt_int) (tptp.hAPP_f1574055885nt_int _let_2 (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int tptp.minus_minus_int) tptp.uminus_uminus_int)) tptp.one_one_int)))) (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int tptp.abs_abs_int L))))) _let_1)))))))))))))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_nat_real F N_2))) (tptp.hAPP_nat_real G N_2)))) (=> (tptp.hBOOL (tptp.summable_real G)) (and (tptp.hBOOL (tptp.summable_real F)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f352196356l_real tptp.suminf_real F)) (tptp.hAPP_f352196356l_real tptp.suminf_real G))))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real F N_2)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real F N_2)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real F N_2)))) (=> (tptp.hBOOL (tptp.summable_real F)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than D) (tptp.collec1347809874nt_int (tptp.produc93441119t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f1878066172t_bool tptp.cOMBS_1720984575t_bool (tptp.hAPP_f1315737299t_bool (tptp.hAPP_f538565589t_bool tptp.cOMBB_1211207212ol_int tptp.cOMBB_bool_bool_int) (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int D)))) tptp.ord_less_int))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than2 D) (tptp.collec1347809874nt_int (tptp.produc93441119t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int D)))) tptp.ord_less_int))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.fact_fact_nat) _let_1))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))) (tptp.hAPP_real_real tptp.sin X_1))))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.sin_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (tptp.hAPP_real_real tptp.sin X_1)))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) tptp.cos_coeff)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (tptp.hAPP_real_real tptp.cos X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real _let_28)) tptp.suc)) tptp.one_one_real)) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_1)))) (let ((_let_3 (tptp.hAPP_int_real tptp.number267125858f_real _let_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real _let_2) _let_3))) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) _let_3)))) _let_2)))))) (forall ((G tptp.fun_nat_real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real G) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_r195310020l_real (tptp.hAPP_f2126667875l_real tptp.cOMBC_746811033l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) tptp.zero_zero_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat G) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.div_div_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.minus_minus_nat) tptp.one_one_nat))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) X_1)))) (forall ((F tptp.fun_nat_real) (Y_2 tptp.real) (G tptp.fun_nat_real) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real G) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real F) Y_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat F) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.div_div_nat) _let_1)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat G) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.div_div_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.minus_minus_nat) tptp.one_one_nat))) _let_1)))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real X_1) Y_2))))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.fact_fact_nat) _let_1))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1))) (tptp.hAPP_real_real tptp.cos X_1))))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.sums_complex X_3) A)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.sums_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat tptp.cnj) X_3)) (tptp.hAPP_complex_complex tptp.cnj A))))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.sums_complex X_3) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.re) X_3)) (tptp.hAPP_complex_real tptp.re A))))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.sums_complex X_3) A)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.sums_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.im) X_3)) (tptp.hAPP_complex_real tptp.im A))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.diffs_real tptp.sin_coeff) N_1) (tptp.hAPP_nat_real tptp.cos_coeff N_1))) (= (tptp.diffs_real tptp.sin_coeff) tptp.cos_coeff) (forall ((X_2 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.diffs_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))) X_2) (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat X_2))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat tptp.suc Ma)) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.nat_case_bool tptp.fFalse (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma)) N_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.diffs_real tptp.cos_coeff) N_1) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_nat_real tptp.sin_coeff N_1)))) (forall ((X_2 tptp.nat)) (= (tptp.hAPP_nat_real (tptp.diffs_real tptp.cos_coeff) X_2) (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.hAPP_nat_real tptp.sin_coeff X_2)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat Ma))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_nat_nat (tptp.nat_case_nat tptp.zero_zero_nat tptp.cOMBI_nat) (tptp.hAPP_nat_nat _let_1 N_1))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F N_2)) (tptp.hAPP_nat_real G N_2)))) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (tptp.hBOOL (tptp.summable_real G)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f352196356l_real tptp.suminf_real F)) (tptp.hAPP_f352196356l_real tptp.suminf_real G))))))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj))) (= (tptp.hAPP_real_real tptp.arctan Y_2) (tptp.the_real (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)))) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_2 (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool tptp.ord_less_real) _let_1))) (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) tptp.tan)) Y_2)))))))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.pi) (tptp.hAPP_int_real tptp.number267125858f_real (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj))) (= (tptp.hAPP_real_real tptp.arcsin Y_2) (tptp.the_real (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_2 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.uminus_uminus_real _let_1)))) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_2 (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool tptp.ord_less_eq_real) _let_1))) (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) tptp.sin)) Y_2)))))))) (forall ((X_1 tptp.real)) (= (tptp.hAPP_real_real tptp.ln X_1) (tptp.the_real (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) tptp.exp_real)) X_1)))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real tptp.root N_1) X_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)))) (let ((_let_3 (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real tptp.power_power_real) N_1))))) (let ((_let_4 (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_5 (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj) _let_4)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_real_bool _let_4 X_1)))) (and (=> _let_6 (= _let_1 (tptp.the_real (tptp.hAPP_f1861673493l_bool _let_5 (tptp.hAPP_r1134773055l_bool _let_3 X_1))))) (=> (not _let_6) (and (=> _let_2 (= _let_1 (tptp.hAPP_real_real tptp.uminus_uminus_real (tptp.the_real (tptp.hAPP_f1861673493l_bool _let_5 (tptp.hAPP_r1134773055l_bool _let_3 (tptp.hAPP_real_real tptp.uminus_uminus_real X_1))))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))))))) (forall ((Y_2 tptp.real)) (let ((_let_1 (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real tptp.fconj))) (= (tptp.hAPP_real_real tptp.arccos Y_2) (tptp.the_real (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_1 (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool (tptp.hAPP_f60716669l_bool _let_1 (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool tptp.ord_less_eq_real) tptp.pi))) (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real tptp.fequal_real) tptp.cos)) Y_2))))))) (= tptp.pi (tptp.hAPP_real_real _let_26 _let_25)) (= _let_14 _let_25) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.divmod_nat Ma N_1) (tptp.the_Pr588456374at_nat (tptp.divmod_nat_rel Ma N_1)))) (forall ((X_1 tptp.real)) (= (tptp.archim1246769320r_real X_1) (tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_r481142414t_bool (tptp.hAPP_f1845081853t_bool tptp.cOMBC_int_real_bool (tptp.hAPP_f801032407l_bool (tptp.hAPP_f499530369l_bool tptp.cOMBB_1317819104ol_int tptp.ord_less_eq_real) tptp.ring_1_of_int_real)) X_1))) (tptp.hAPP_f429384717t_bool (tptp.hAPP_f1173902867t_bool tptp.cOMBB_real_bool_int (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1)) (tptp.hAPP_f563293398t_real (tptp.hAPP_f134192053t_real tptp.cOMBB_int_real_int tptp.ring_1_of_int_real) (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.plus_plus_int) tptp.one_one_int))))))) (forall ((X_1 tptp.rat)) (= (tptp.archim791455193or_rat X_1) (tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_r1900510169t_bool (tptp.hAPP_f1480506641t_bool tptp.cOMBC_int_rat_bool (tptp.hAPP_f601898971t_bool (tptp.hAPP_f857296063t_bool tptp.cOMBB_214503962ol_int tptp.ord_less_eq_rat) tptp.ring_1_of_int_rat)) X_1))) (tptp.hAPP_f1241350704t_bool (tptp.hAPP_f1131424617t_bool tptp.cOMBB_rat_bool_int (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat X_1)) (tptp.hAPP_f1900950721nt_rat (tptp.hAPP_f1270196437nt_rat tptp.cOMBB_int_rat_int tptp.ring_1_of_int_rat) (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.plus_plus_int) tptp.one_one_int))))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.rRset2norRR A_1 Ma) A))) (let ((_let_2 (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1))))) (and (=> _let_2 (= _let_1 (tptp.hilbert_Eps_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool (tptp.zcong A)) Ma))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma)))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((A tptp.int) (A_1 tptp.fun_int_bool) (Ma tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.norRRset Ma))) (let ((_let_2 (tptp.zcong A))) (let ((_let_3 (tptp.hilbert_Eps_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool _let_2) Ma))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) _let_1))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.one_one_int) Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.is_RRset A_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A) A_1)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool _let_2 _let_3) Ma)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int _let_3) _let_1)))))))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real tptp.sin X_1)) (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_r195310020l_real (tptp.hAPP_f2126667875l_real tptp.cOMBC_746811033l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) tptp.zero_zero_real)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.div_div_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.minus_minus_nat) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))))) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) N_1))))) (forall ((U tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_2) (tptp.hAPP_nat_nat F N_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat) F)) U)))))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat L) U)))) (forall ((F tptp.fun_nat_real) (N_1 tptp.nat) (R_2 tptp.real)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) _let_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) R_2)) (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.minus_minus_real) F)) R_2)) _let_1)))) (forall ((K_1 tptp.nat) (N_1 tptp.nat) (F_2 tptp.fun_nat_real)) (let ((_let_1 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F_2))) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat F_2) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K_1))) (tptp.hAPP_n1699378549t_bool _let_1 N_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_f1406902706l_real _let_2 (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) K_1)))) (tptp.hAPP_f1406902706l_real _let_2 (tptp.hAPP_n1699378549t_bool _let_1 K_1))))))) (forall ((K_1 tptp.nat) (N_2 tptp.nat) (F_2 tptp.fun_nat_real)) (let ((_let_1 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F_2))) (= (tptp.hAPP_f1406902706l_real _let_2 (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_2) K_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat F_2) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K_1))) (tptp.hAPP_n1699378549t_bool _let_1 N_2))) (tptp.hAPP_f1406902706l_real _let_2 (tptp.hAPP_n1699378549t_bool _let_1 K_1))))))) (forall ((F tptp.fun_nat_real) (N_1 tptp.nat)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) F)) (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) N_1)) tptp.zero_zero_real)) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat)) (= (exists ((M_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 M_1)))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat)) (= (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 M_1)))) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X_2)))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat L) U)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (=> (not (= X_1 tptp.one_one_real)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_nat_real _let_1 N_1)) tptp.one_one_real)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real X_1) tptp.one_one_real)))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat tptp.suc L)) U) (tptp.hAPP_n1699378549t_bool (tptp.ord_gr660468384an_nat L) U))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat I_1) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K_1)))) (forall ((I_1 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat I_1) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat (tptp.hAPP_nat_nat tptp.suc I_1)) (tptp.hAPP_nat_nat tptp.suc J)))) (forall ((Diff tptp.fun_na182379510l_real) (N_1 tptp.nat) (X_1 tptp.real)) (=> (= X_1 tptp.zero_zero_real) (=> (not (= N_1 tptp.zero_zero_nat)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1)) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((A_1 tptp.fun_nat_bool) (K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A_1))))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_1) _let_1)) (= A_1 _let_1)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (N_1 tptp.nat)) (let ((_let_1 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool _let_1 N_1))) (let ((_let_3 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) F)) G)) (tptp.hAPP_n1699378549t_bool _let_1 (tptp.hAPP_nat_nat _let_3 N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat F) _let_3)) _let_2)) (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat G) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) _let_3)) tptp.one_one_nat))) _let_2))))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) tptp.suc)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_1))) tptp.zero_zero_real)) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.div_div_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real)))) tptp.zero_zero_real)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.one_one_nat) N_1)) tptp.zero_zero_real)) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.div_div_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls))))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) tptp.zero_zero_real))) (tptp.hAPP_r474017924t_real tptp.power_power_real tptp.zero_zero_real))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc N_1))) tptp.one_one_real)) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real tptp.sin X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_r195310020l_real (tptp.hAPP_f2126667875l_real tptp.cOMBC_746811033l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) tptp.zero_zero_real)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.div_div_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.minus_minus_nat) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real T) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real _let_2))) (tptp.hAPP_nat_real tptp.real_nat N_1))) tptp.pi)))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real tptp.cos X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.div_div_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) tptp.zero_zero_real))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.cos (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real T) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real _let_2))) (tptp.hAPP_nat_real tptp.real_nat N_1))) tptp.pi)))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((L tptp.int) (U tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int L) U)))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_2) X_1)) (= (tptp.comple124823625p_real (tptp.hAPP_r1134773055l_bool (tptp.ord_at1496968948n_real Y_2) X_1)) X_1))) (forall ((U tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int tptp.zero_zero_int) U)))) (forall ((U tptp.int)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int tptp.zero_zero_int) U)) (tptp.hAPP_int_nat tptp.nat_1 U))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int L) U)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int U) L)))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int L) tptp.one_one_int)) U) (tptp.hAPP_i1948725293t_bool (tptp.ord_gr1297742076an_int L) U))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.image_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int tptp.plus_plus_int) L) (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int U) L))) (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int L) U))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (= (tptp.hAPP_real_real tptp.sin X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_r195310020l_real (tptp.hAPP_f2126667875l_real tptp.cOMBC_746811033l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat tptp.if_real) tptp.even_odd_even_nat)) tptp.zero_zero_real)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min))) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.div_div_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.minus_minus_nat) (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.hAPP_int_nat tptp.number_number_of_nat _let_2))))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.sin (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real T) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real) (tptp.hAPP_int_real tptp.number267125858f_real _let_2))) (tptp.hAPP_nat_real tptp.real_nat N_1))) tptp.pi)))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))) (forall ((B_1 tptp.real) (K_1 tptp.nat) (Diff tptp.fun_na182379510l_real) (H tptp.real) (N_1 tptp.nat)) (=> (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T))))) (=> (= N_1 (tptp.hAPP_nat_nat tptp.suc K_1)) (forall ((M_1 tptp.nat) (T tptp.real)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc M_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1))) (let ((_let_3 (tptp.hAPP_nat_nat _let_2 _let_1))) (let ((_let_4 (tptp.hAPP_r474017924t_real tptp.power_power_real T))) (let ((_let_5 (tptp.hAPP_r1250527377l_real tptp.times_times_real B_1))) (let ((_let_6 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_7 (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))) (let ((_let_8 (tptp.hAPP_f224989205l_real tptp.cOMBB_1419615765al_nat Diff))) (let ((_let_9 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real))) (let ((_let_10 (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real))) (let ((_let_11 (tptp.hAPP_nat_nat _let_2 M_1))) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.minus_minus_real) (tptp.hAPP_n546711566l_real Diff M_1))) (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.plus_plus_real) (tptp.hAPP_f2119584768l_real (tptp.hAPP_f59594445l_real tptp.cOMBC_2010481033l_real (tptp.hAPP_f1523861863l_real (tptp.hAPP_f1067681227l_real tptp.cOMBB_1934313333l_real tptp.big_co604158596t_real) (tptp.hAPP_f1993765077t_real (tptp.hAPP_f895854793t_real tptp.cOMBB_1948233853l_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_10 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_9 (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f1904307534l_real _let_8 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_1))) tptp.zero_zero_real))) _let_7)))) tptp.power_power_real))) (tptp.hAPP_n1699378549t_bool _let_6 _let_11)))) (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real _let_5) (tptp.hAPP_r1250527377l_real (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.inverse_divide_real) (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real tptp.power_power_real) _let_11))) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_11)))))) T) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff _let_1) T)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_10 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real _let_9 (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f1904307534l_real _let_8 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1))) tptp.zero_zero_real))) _let_7))) _let_4)) (tptp.hAPP_n1699378549t_bool _let_6 _let_3))) (tptp.hAPP_real_real _let_5 (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real _let_4 _let_3)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat _let_3)))))))))))))))))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (=> (not (= X_1 tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_real_real tptp.abs_abs_real T))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real tptp.exp_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) _let_1)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.exp_real T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real)) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real tptp.exp_real X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) _let_1)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat))) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real tptp.exp_real T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))) (forall ((K_1 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((D_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) D_2))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real F (tptp.hAPP_nat_nat _let_2 _let_1))) (tptp.hAPP_nat_real F (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) K_1))) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((F tptp.fun_real_real) (J tptp.fun_nat_real) (N_1 tptp.nat) (H tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (exists ((B_6 tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) J)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real B_6) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_nat_real _let_1 N_1)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))))))))) (forall ((N_1 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real F M_1))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((N_1 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) M_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real F M_1))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_f352196356l_real tptp.suminf_real F)))))) (forall ((X_1 tptp.real) (N_1 tptp.nat) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (not (= X_1 tptp.zero_zero_real)) (=> (forall ((M_1 tptp.nat) (X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) X_2) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) X_2)))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_real_real tptp.abs_abs_real T))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real)) (=> (and (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (forall ((M_1 tptp.nat) (X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) X_2) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) X_2)))) (not (= X_1 tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (let ((_let_2 (tptp.hAPP_real_real tptp.abs_abs_real T))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_2) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))))) (forall ((X_1 tptp.real) (N_1 tptp.nat) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))))) (forall ((Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (N_1 tptp.nat) (H tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T)))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real T) H)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((N_1 tptp.nat) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (H tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T)))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (N_1 tptp.nat) (H tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H) tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real H) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) tptp.zero_zero_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real T) tptp.zero_zero_real)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))))))) (forall ((N_1 tptp.nat) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (H tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))))) (forall ((Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (N_1 tptp.nat) (H tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real H) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) tptp.zero_zero_real))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T)))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real H) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real T) tptp.zero_zero_real)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real) (N_1 tptp.nat) (H tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (forall ((M_1 tptp.nat) (T tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real T) H))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) T) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) T))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real H))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) T)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real T) H)) (= (tptp.hAPP_real_real F H) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real)) (=> (and (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (forall ((M_1 tptp.nat) (X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) X_2) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) X_2))))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1))))))))) (forall ((N_1 tptp.nat) (X_1 tptp.real) (Diff tptp.fun_na182379510l_real) (F tptp.fun_real_real)) (=> (= (tptp.hAPP_n546711566l_real Diff tptp.zero_zero_nat) F) (=> (forall ((M_1 tptp.nat) (X_2 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real Diff M_1) X_2) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff (tptp.hAPP_nat_nat tptp.suc M_1)) X_2)))) (exists ((T tptp.real)) (let ((_let_1 (tptp.hAPP_r474017924t_real tptp.power_power_real X_1))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real T)) (tptp.hAPP_real_real tptp.abs_abs_real X_1))) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.inverse_divide_real) (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real Diff) tptp.zero_zero_real))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.fact_fact_nat)))) _let_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real Diff N_1) T)) (tptp.hAPP_nat_real tptp.real_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)))) (tptp.hAPP_nat_real _let_1 N_1)))))))))) (forall ((F tptp.fun_nat_real) (K_3 tptp.real) (N_1 tptp.nat)) (=> (forall ((P_4 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat P_4) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F P_4)) K_3)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1))) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real (tptp.hAPP_nat_real tptp.real_nat N_1)) K_3))))) (forall ((F tptp.fun_na182379510l_real) (X_1 tptp.real) (F_1 tptp.fun_na182379510l_real) (N_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat Ma) N_1))) (=> (forall ((R_1 tptp.nat)) (=> (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Ma) R_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat R_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ma) N_1)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_n546711566l_real F R_1) X_1) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real F_1 R_1) X_1))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real (tptp.hAPP_f2119584768l_real (tptp.hAPP_f59594445l_real tptp.cOMBC_2010481033l_real (tptp.hAPP_f1523861863l_real (tptp.hAPP_f1067681227l_real tptp.cOMBB_1934313333l_real tptp.big_co604158596t_real) (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real F))) _let_1) X_1) (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real F_1) X_1)) _let_1)))))) (forall ((X_1 tptp.real) (F tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.summable_real F)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_2))) X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f352196356l_real tptp.suminf_real F)) X_1))))) (forall ((F tptp.fun_int_int) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int F X_2)))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_f1594865479ol_int (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F) A_1)))))) (forall ((X_1 tptp.real) (F tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real F N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real F) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_2))) X_1))) (tptp.hBOOL (tptp.summable_real F))))) (forall ((A tptp.int) (D tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) (tptp.hAPP_f659380387ol_int (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int (tptp.hAPP_f1139079189at_int (tptp.hAPP_f1431025877at_int tptp.cOMBB_int_int_nat _let_1) (tptp.hAPP_int_fun_nat_int (tptp.hAPP_f1673103573at_int tptp.cOMBC_nat_int_int (tptp.hAPP_f1935805932nt_int (tptp.hAPP_f125788821nt_int tptp.cOMBB_859312247nt_nat tptp.times_times_int) tptp.semiri1621563631at_int)) D))) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) tptp.one_one_nat))) D))))))) (forall ((K_3 tptp.real) (K_1 tptp.real) (F tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_real F N_2))) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real K_1) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real _let_1) K_3))))) (tptp.hBOOL (tptp.bseq_real F)))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K_1)))) (forall ((U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat U)) U)) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) N_1) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (forall ((S tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S)) (exists ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool S) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K)))))) (forall ((A tptp.nat) (D tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat))) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat _let_1) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) D))) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N_1) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) tptp.one_one_nat)) D))))))) (forall ((U tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) U)) (= (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int tptp.zero_zero_int) U) (tptp.image_nat_int tptp.semiri1621563631at_int (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat (tptp.hAPP_int_nat tptp.nat_1 U)))))) (forall ((S tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S)) (exists ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool S) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K)))))) (forall ((N_1 tptp.nat) (Q_3 tptp.fun_nat_nat) (P_1 tptp.fun_nat_nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat Q_3 X_2)) (tptp.hAPP_nat_nat P_1 X_2)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat P_1) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat Q_3) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.minus_minus_nat) P_1)) Q_3)) _let_1))))) (forall ((X_1 tptp.real)) (= (tptp.comple124823625p_real (tptp.hAPP_r1134773055l_bool tptp.ord_lessThan_real X_1)) X_1)) (forall ((P_2 tptp.fun_int_bool) (P_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))))) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2))))) (= (tptp.collect_int (tptp.hAPP_f1805168059t_bool _let_1 P_1)) (tptp.collect_int (tptp.hAPP_f1805168059t_bool _let_1 P_2)))))) (forall ((P_3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int P_3))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int P_3))) (let ((_let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (tptp.hAPP_int_int tptp.uminus_uminus_int _let_3))) (let ((_let_5 (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_1))) (let ((_let_6 (tptp.hAPP_int_fun_int_int tptp.div_div_int _let_2))) (let ((_let_7 (tptp.normalize P_3))) (let ((_let_8 (= _let_1 tptp.zero_zero_int))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)))) (and (=> _let_9 (= _let_7 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int _let_6 _let_3)) (tptp.hAPP_int_int _let_5 _let_3)))) (=> (not _let_9) (and (=> _let_8 (= _let_7 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_8) (= _let_7 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int (tptp.hAPP_int_int _let_6 _let_4)) (tptp.hAPP_int_int _let_5 _let_4))))))))))))))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y)) X))) (forall ((X tptp.int) (Y tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y)) Y))) (forall ((N tptp.nat) (M tptp.nat) (A_3 tptp.int) (B_2 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) M)) tptp.one_one_int))) (forall ((X tptp.int) (Y tptp.int) (M tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)) M) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) M) tptp.one_one_int))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Y)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.hAPP_int_int (tptp.div_mod_int X) Y))))) (forall ((B_5 tptp.int) (A_5 tptp.int) (A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2))) (=> (not (= _let_1 tptp.zero_zero_int)) (=> (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_5) _let_1)) (=> (= B_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_5) _let_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_5) B_5) tptp.one_one_int)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat X) Y)))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) M)) N)) (tptp.hAPP_int_int _let_1 N)))) (forall ((M tptp.int) (N tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) N)) N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int M) N)) (tptp.hAPP_int_int _let_1 N)))) (forall ((N tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int N) tptp.one_one_int)) N) tptp.one_one_int)) (forall ((N tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int N) tptp.one_one_int)) N) tptp.one_one_int)) (forall ((E_1 tptp.int) (B_2 tptp.int) (D_3 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_3) A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int E_1) B_2)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D_3) E_1) tptp.one_one_int))))) (forall ((N tptp.nat) (D_3 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D_3))) (=> (= (tptp.hAPP_int_int _let_1 A_3) tptp.one_one_int) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) tptp.one_one_int)))) (forall ((M tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)) (forall ((Ma tptp.int) (N_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int Ma) N_1) tptp.zero_zero_int) (and (= Ma tptp.zero_zero_int) (= N_1 tptp.zero_zero_int)))) (forall ((A_3 tptp.int) (N tptp.nat) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int A_3) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int B_2) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2)) N))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int B_2) A_3))) (forall ((B_2 tptp.int) (A_3 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int B_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 C_1)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 C_1)))))) (forall ((A_3 tptp.int) (B_2 tptp.int) (C_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int _let_1 B_2)) C_1) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int B_2) C_1))))) (forall ((I tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int I))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N))))) (forall ((I tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int I))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M))))) (forall ((N tptp.int) (K_2 tptp.int) (M tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N))))))) (forall ((K_1 tptp.int) (Ma tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 N_1)))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.hAPP_int_int (tptp.div_mod_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y))) (= (tptp.hAPP_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((X tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) X) (tptp.hAPP_int_int tptp.abs_abs_int X))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int tptp.abs_abs_int X)) (tptp.hAPP_int_int tptp.abs_abs_int Y)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.abs_abs_int Y)) (tptp.hAPP_int_int _let_1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int tptp.abs_abs_int X)) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int tptp.uminus_uminus_int X)) Y) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int tptp.uminus_uminus_int Y)) (tptp.hAPP_int_int _let_1 Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X) Y)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_int_int tptp.abs_abs_int X)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int Y) X)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_int_int tptp.abs_abs_int Y)))) (forall ((K_2 tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.abs_abs_int K_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int _let_1 M)) (tptp.hAPP_int_int _let_1 N))))) (forall ((Ma tptp.int) (N_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int Ma) N_1))) (or (not (= Ma tptp.zero_zero_int)) (not (= N_1 tptp.zero_zero_int))))) (forall ((D_3 tptp.int) (A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D_3))) (=> (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) tptp.one_one_int) (= (tptp.hAPP_int_int _let_1 B_2) tptp.one_one_int)))) (forall ((D_3 tptp.int) (A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D_3))) (=> (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) tptp.one_one_int) (= (tptp.hAPP_int_int _let_1 A_3) tptp.one_one_int)))) (forall ((B_2 tptp.int) (D_3 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D_3))) (=> (= (tptp.hAPP_int_int _let_1 A_3) tptp.one_one_int) (=> (= (tptp.hAPP_int_int _let_1 B_2) tptp.one_one_int) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_3) B_2)) tptp.one_one_int))))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int K_2) N) tptp.one_one_int) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K_2) M)) N) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N)))) (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int D))) (= (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A) B)) tptp.one_one_int) (and (= (tptp.hAPP_int_int _let_1 A) tptp.one_one_int) (= (tptp.hAPP_int_int _let_1 B) tptp.one_one_int))))) (forall ((X tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int tptp.zero_zero_int) X) (tptp.hAPP_int_int tptp.abs_abs_int X))) (forall ((X tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) tptp.zero_zero_int) (tptp.hAPP_int_int tptp.abs_abs_int X))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2))) (= (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) _let_1)) (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_3) B_2)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2))) (=> (or (not (= A_3 tptp.zero_zero_int)) (not (= B_2 tptp.zero_zero_int))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int A_3) _let_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int B_2) _let_1)) tptp.one_one_int)))) (forall ((M tptp.int) (K_2 tptp.int) (N tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_2))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int K_2) N) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 M)))))) (forall ((Ma tptp.int) (K_1 tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int K_1))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int K_1) N_1) tptp.one_one_int) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ma) N_1))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Ma)))))) (forall ((N tptp.int) (M tptp.int) (R_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int M) R_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int N) R_3)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int M) N) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int M) N)) R_3)))))) (forall ((P_1 tptp.fun_int_bool) (Y_2 tptp.int) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int _let_1 Y_2))))) (let ((_let_3 (tptp.hAPP_int_int tptp.uminus_uminus_int Y_2))) (let ((_let_4 (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int (tptp.hAPP_int_int tptp.uminus_uminus_int X_1)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_2) tptp.zero_zero_int)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) tptp.zero_zero_int)))) (let ((_let_7 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP_int_bool _let_7 Y_2)))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP_int_bool _let_7 X_1)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int _let_4 Y_2))))) (=> (=> _let_6 (=> _let_5 (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((B tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (= (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) D)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B)) (forall ((E tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int E))) (=> (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 D)))))) (= D (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A) B))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y))))))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_2)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2)) B_2)))) (forall ((B_2 tptp.int) (A_3 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) A_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2)) A_3)))) (forall ((B tptp.int) (C tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.abs_abs_int D))) (let ((_let_2 (tptp.hAPP_int_int tptp.abs_abs_int C))) (let ((_let_3 (tptp.hAPP_int_int tptp.abs_abs_int B))) (let ((_let_4 (tptp.hAPP_int_int tptp.abs_abs_int A))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A) D) tptp.one_one_int) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int B) C) tptp.one_one_int) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_4) _let_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int K_1) L) (tptp.hAPP_int_int tptp.abs_abs_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_b1463609396nt_int tptp.if_int (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int L) tptp.zero_zero_int)) K_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int L) (tptp.hAPP_int_int (tptp.div_mod_int (tptp.hAPP_int_int tptp.abs_abs_int K_1)) (tptp.hAPP_int_int tptp.abs_abs_int L))))))) (forall ((X tptp.int) (A_3 tptp.int) (B_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int X))) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2) tptp.one_one_int) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_3)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_2)) (= (tptp.hAPP_int_int tptp.abs_abs_int X) tptp.one_one_int)))))) (forall ((R_3 tptp.rat) (P_3 tptp.int) (Q_2 tptp.int)) (=> (= (tptp.quotient_of R_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int P_3) Q_2) tptp.one_one_int))) (forall ((R_3 tptp.product_prod_int_int) (P_3 tptp.int) (Q_2 tptp.int)) (=> (= (tptp.normalize R_3) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int P_3) Q_2) tptp.one_one_int))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A) B) tptp.one_one_int) (forall ((D_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D_2))) (= (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) D_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B))) (= D_2 tptp.one_one_int)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_int_nat tptp.nat_1 X)) (tptp.hAPP_int_nat tptp.nat_1 Y)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y))))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int X))) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int tptp.abs_abs_int Y)))))) (forall ((P_3 tptp.int) (Q_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int tptp.product_Pair_int_int P_3) Q_2))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) Q_2)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int P_3) Q_2) tptp.one_one_int) (= (tptp.normalize _let_1) _let_1))))) (forall ((X_1 tptp.rat)) (let ((_let_1 (tptp.hAPP_f1961001761l_bool tptp.cOMBB_1550063917nt_int tptp.fconj))) (= (tptp.quotient_of X_1) (tptp.the_Pr2103884470nt_int (tptp.hAPP_f237669397t_bool (tptp.hAPP_f461489489t_bool tptp.cOMBS_400904860l_bool (tptp.hAPP_f365317245l_bool _let_1 (tptp.hAPP_f1084724746t_bool (tptp.hAPP_f374502857t_bool tptp.cOMBB_569260360nt_int (tptp.hAPP_r2115560837t_bool tptp.fequal_rat X_1)) (tptp.hAPP_f1065357839nt_rat (tptp.hAPP_f1120137083nt_rat tptp.cOMBS_549334880nt_rat (tptp.hAPP_f1547007718nt_rat (tptp.hAPP_f382317021nt_rat tptp.cOMBB_170828966nt_int tptp.fract) tptp.product_fst_int_int)) tptp.product_snd_int_int)))) (tptp.hAPP_f237669397t_bool (tptp.hAPP_f461489489t_bool tptp.cOMBS_400904860l_bool (tptp.hAPP_f365317245l_bool _let_1 (tptp.hAPP_f892584630t_bool (tptp.hAPP_f492612297t_bool tptp.cOMBB_798864284nt_int (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int)) tptp.product_snd_int_int))) (tptp.hAPP_i119638232t_bool (tptp.hAPP_f2018027565t_bool tptp.cOMBC_33652895t_bool (tptp.hAPP_f291087797t_bool (tptp.hAPP_f214467655t_bool tptp.cOMBB_182850971nt_int tptp.fequal_int) (tptp.hAPP_f521271395nt_int (tptp.hAPP_f1914742907nt_int tptp.cOMBS_2019229620nt_int (tptp.hAPP_f1855025978nt_int (tptp.hAPP_f1038672605nt_int tptp.cOMBB_1506897658nt_int tptp.gcd_gcd_int) tptp.product_fst_int_int)) tptp.product_snd_int_int))) tptp.one_one_int))))))) (forall ((R_3 tptp.rat)) (exists ((X_2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int X_2))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int X_2))) (and (= R_3 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1) tptp.one_one_int) (forall ((Y_1 tptp.product_prod_int_int)) (let ((_let_1 (tptp.hAPP_P1175774780nt_int tptp.product_snd_int_int Y_1))) (let ((_let_2 (tptp.hAPP_P1175774780nt_int tptp.product_fst_int_int Y_1))) (=> (and (= R_3 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1) tptp.one_one_int)) (= Y_1 X_2)))))))))) (forall ((Q_2 tptp.rat)) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (=> (= Q_2 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_2) B_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_4)) (=> (not (= A_2 tptp.zero_zero_int)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_2) B_4) tptp.one_one_int)))))) (= Q_2 tptp.zero_zero_rat))) (forall ((Q_2 tptp.rat)) (not (forall ((A_2 tptp.int) (B_4 tptp.int)) (=> (= Q_2 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_2) B_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_4)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_2) B_4) tptp.one_one_int))))))) (forall ((Q_1 tptp.rat) (P_1 tptp.fun_rat_bool)) (=> (forall ((A_2 tptp.int) (B_4 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) B_4)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_2) B_4) tptp.one_one_int) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 (tptp.hAPP_int_rat (tptp.hAPP_int_fun_int_rat tptp.fract A_2) B_4)))))) (tptp.hBOOL (tptp.hAPP_rat_bool P_1 Q_1)))) (forall ((N_1 tptp.nat) (S tptp.fun_fu819804446l_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool S)) (=> (forall ((X_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_2) S)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int X_2)))) (=> (forall ((X_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f215623910l_bool (tptp.hAPP_f628503027l_bool tptp.member_fun_int_bool X_2) S)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int X_2) N_1))) (= (tptp.hAPP_f521865025ol_nat (tptp.hAPP_f93439879ol_nat tptp.big_co1758102091ol_nat tptp.finite_card_int) S) (tptp.hAPP_f521865025ol_nat (tptp.hAPP_f93439879ol_nat tptp.big_co1758102091ol_nat (tptp.cOMBK_1643584600t_bool N_1)) S)))))) (= tptp.zOdd (tptp.collect_int (tptp.hAPP_f2119767738t_bool _let_20 (tptp.hAPP_f1791153283t_bool _let_19 (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int (tptp.hAPP_f1760145644nt_int _let_22 _let_18)) tptp.one_one_int))))) (= tptp.field_1210416355s_real (tptp.collect_real (tptp.hAPP_f101635158l_bool _let_16 (tptp.hAPP_f1625314454t_bool (tptp.hAPP_f340152631t_bool tptp.cOMBB_1453147152l_real _let_20) (tptp.hAPP_f1832844496t_bool (tptp.hAPP_f1990636069t_bool tptp.cOMBC_412863505t_bool (tptp.hAPP_f704188951t_bool (tptp.hAPP_f1456711209t_bool tptp.cOMBB_690122963l_real tptp.cOMBC_1683390479t_bool) (tptp.hAPP_f1063001928t_bool (tptp.hAPP_f2050994651t_bool tptp.cOMBB_2138578194l_real (tptp.hAPP_f85237525t_bool tptp.cOMBB_389152643ol_int tptp.cOMBS_int_bool_bool)) (tptp.hAPP_f381769257l_bool (tptp.hAPP_f512004221l_bool tptp.cOMBB_188663909l_real (tptp.hAPP_f1830214065l_bool tptp.cOMBB_793166024ol_int _let_21)) (tptp.hAPP_f956464319t_bool (tptp.hAPP_f422375781t_bool tptp.cOMBC_243356514t_bool (tptp.hAPP_f332806115t_bool (tptp.hAPP_f1177545951t_bool tptp.cOMBB_1459832681l_real tptp.cOMBB_95956018ol_int) (tptp.hAPP_f1920544743t_bool (tptp.hAPP_f866672739t_bool tptp.cOMBB_1247074793l_real tptp.cOMBB_real_bool_int) tptp.fequal_real))) (tptp.hAPP_f1323932638t_real (tptp.hAPP_f352226557t_real tptp.cOMBC_824100275t_real (tptp.hAPP_f74147283t_real (tptp.hAPP_f1169087445t_real tptp.cOMBB_2129825580al_int tptp.cOMBB_real_real_int) _let_15)) tptp.real_int)))))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int tptp.fNot) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) tptp.zero_zero_int))))))) (= tptp.zEven (tptp.collect_int (tptp.hAPP_f2119767738t_bool _let_20 (tptp.hAPP_f1791153283t_bool _let_19 _let_18)))) (forall ((A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f292751352t_real (tptp.hAPP_f1607377819t_real tptp.cOMBB_1533963633al_nat (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1)) (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat (tptp.ord_at4362885an_nat tptp.zero_zero_nat)) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1) tptp.sequentially)))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real X_1) tptp.zero_zero_real tptp.sequentially))))) (forall ((Y_3 tptp.fun_nat_real) (Y_2 tptp.real) (X_3 tptp.fun_nat_real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real X_3 X_1 tptp.sequentially)) (=> (tptp.hBOOL (tptp.tendsto_nat_real Y_3 Y_2 tptp.sequentially)) (=> (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real X_3 N_2)) (tptp.hAPP_nat_real Y_3 N_2)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) Y_2)))))) (forall ((A tptp.real) (X_3 tptp.fun_nat_real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real X_3 X_1 tptp.sequentially)) (=> (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real X_3 N_2)) A))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) A))))) (forall ((A tptp.real) (X_3 tptp.fun_nat_real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real X_3 X_1 tptp.sequentially)) (=> (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) (tptp.hAPP_nat_real X_3 N_2)))))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_1))))) (forall ((X_1 tptp.real) (A tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (=> (tptp.hBOOL (tptp.tendsto_nat_real A X_1 tptp.sequentially)) (or (and (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A N_2)) X_1))) (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A M_1)) (tptp.hAPP_nat_real A N_2)))))) (and (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) (tptp.hAPP_nat_real A N_2)))) (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A N_2)) (tptp.hAPP_nat_real A M_1)))))))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X_1)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) tptp.zero_zero_real tptp.sequentially)))) (forall ((R_2 tptp.real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.plus_plus_real R_2)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.suc))) R_2 tptp.sequentially))) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real F L tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.abs_abs_real) F) (tptp.hAPP_real_real tptp.abs_abs_real L) tptp.sequentially)))) (forall ((F tptp.fun_nat_real)) (= (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.abs_abs_real) F) tptp.zero_zero_real tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_real F tptp.zero_zero_real tptp.sequentially)))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real _let_17 tptp.suc)) tptp.zero_zero_real tptp.sequentially)) (forall ((A tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.one_one_real) X_1)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real A)) (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) tptp.zero_zero_real tptp.sequentially)))) (forall ((C tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.abs_abs_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) tptp.one_one_real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real _let_1) tptp.zero_zero_real tptp.sequentially))))) (forall ((C tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real C)) tptp.one_one_real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_r474017924t_real tptp.power_power_real C) tptp.zero_zero_real tptp.sequentially)))) (forall ((R_2 tptp.real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.plus_plus_real R_2)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.uminus_uminus_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.suc)))) R_2 tptp.sequentially))) (forall ((Sa tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) Sa)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.powr) tptp.real_nat)) (tptp.hAPP_real_real tptp.uminus_uminus_real Sa)) tptp.zero_zero_real tptp.sequentially)))) (forall ((R_2 tptp.real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.times_times_real R_2)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.plus_plus_real tptp.one_one_real)) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.uminus_uminus_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) tptp.suc))))) R_2 tptp.sequentially))) (forall ((A tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A)))))) (forall ((X_1 tptp.real)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.times_times_nat) (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real X_1)) tptp.one_one_real)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat (tptp.hAPP_r1250527377l_real tptp.inverse_divide_real tptp.one_one_real)) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat tptp.real_nat) _let_1)))) (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat (tptp.hAPP_r474017924t_real tptp.power_power_real X_1)) _let_1)) tptp.zero_zero_real tptp.sequentially))))) (= tptp.field_1210416355s_real (tptp.collect_real (tptp.hAPP_f101635158l_bool _let_16 (tptp.hAPP_f1341793266t_bool (tptp.hAPP_f571820015t_bool tptp.cOMBB_1159313332l_real (tptp.hAPP_f389116883t_bool tptp.cOMBB_1593174431ol_int tptp.fEx_nat)) (tptp.hAPP_f1115375056t_bool (tptp.hAPP_f271976045t_bool tptp.cOMBC_1801450329t_bool (tptp.hAPP_f1927674023t_bool (tptp.hAPP_f1261108921t_bool tptp.cOMBB_172850899l_real tptp.cOMBC_678732631t_bool) (tptp.hAPP_f2084827628t_bool (tptp.hAPP_f1121609875t_bool tptp.cOMBB_2125215742l_real (tptp.hAPP_f1182713365t_bool tptp.cOMBB_2087181719ol_int tptp.cOMBS_nat_bool_bool)) (tptp.hAPP_f834119977l_bool (tptp.hAPP_f848516149l_bool tptp.cOMBB_270132509l_real (tptp.hAPP_f643658017l_bool tptp.cOMBB_2046938128ol_int (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj))) (tptp.hAPP_f1459420095t_bool (tptp.hAPP_f693283245t_bool tptp.cOMBC_1113900202t_bool (tptp.hAPP_f77155443t_bool (tptp.hAPP_f403082607t_bool tptp.cOMBB_984071017l_real tptp.cOMBB_1647910634ol_int) (tptp.hAPP_f1840085295t_bool (tptp.hAPP_f1083049571t_bool tptp.cOMBB_2050079537l_real tptp.cOMBB_real_bool_nat) tptp.fequal_real))) (tptp.hAPP_f1613846310t_real (tptp.hAPP_f1720068861t_real tptp.cOMBC_295337211t_real (tptp.hAPP_f1295083291t_real (tptp.hAPP_f212164053t_real tptp.cOMBB_929094628al_int tptp.cOMBB_real_real_nat) _let_15)) tptp.real_nat)))))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat tptp.fNot) (tptp.hAPP_n1699378549t_bool _let_11 tptp.zero_zero_nat))))))) (forall ((A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f292751352t_real (tptp.hAPP_f1607377819t_real tptp.cOMBB_1533963633al_nat (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1)) (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat (tptp.ord_at4362885an_nat tptp.zero_zero_nat)) (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1) tptp.sequentially)))))) (forall ((A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real A N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hAPP_nat_real A N_2)))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f292751352t_real (tptp.hAPP_f1607377819t_real tptp.cOMBB_1533963633al_nat (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1)) (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat (tptp.ord_at4362885an_nat tptp.zero_zero_nat)) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) tptp.one_one_nat))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1) tptp.sequentially))))))) (forall ((N_1 tptp.nat) (A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real A N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hAPP_nat_real A N_2)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1)) (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_1)) tptp.one_one_nat)))))))))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.tendsto_nat_complex X_3 A tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat tptp.cnj) X_3) (tptp.hAPP_complex_complex tptp.cnj A) tptp.sequentially)))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.tendsto_nat_complex X_3 A tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.re) X_3) (tptp.hAPP_complex_real tptp.re A) tptp.sequentially)))) (forall ((X_3 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.hBOOL (tptp.tendsto_nat_complex X_3 A tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat tptp.im) X_3) (tptp.hAPP_complex_real tptp.im A) tptp.sequentially)))) (forall ((Y_3 tptp.fun_nat_real) (B tptp.real) (X_3 tptp.fun_nat_real) (A tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real X_3 A tptp.sequentially)) (=> (tptp.hBOOL (tptp.tendsto_nat_real Y_3 B tptp.sequentially)) (tptp.hBOOL (tptp.tendsto_nat_complex (tptp.hAPP_f219720582omplex (tptp.hAPP_f1052840010omplex tptp.cOMBS_696648398omplex (tptp.hAPP_f23851874omplex (tptp.hAPP_f406530075omplex tptp.cOMBB_1714920583ex_nat tptp.complex_1) X_3)) Y_3) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A) B) tptp.sequentially))))) (forall ((P_1 tptp.fun_Pr1127657839l_bool) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.bolzano_bisect P_1 A B))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) B)))) (=> _let_2 (=> _let_2 (=> _let_2 (=> (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.minus_minus_real) (tptp.hAPP_f73570213t_real (tptp.hAPP_f918606171t_real tptp.cOMBB_64450052al_nat tptp.produc1935615926l_real) _let_1))) (tptp.hAPP_f73570213t_real (tptp.hAPP_f918606171t_real tptp.cOMBB_64450052al_nat tptp.produc556554744l_real) _let_1)) tptp.zero_zero_real tptp.sequentially)) (exists ((L_1 tptp.real)) (let ((_let_1 (tptp.bolzano_bisect P_1 A B))) (and (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_P731461727l_real tptp.produc1935615926l_real (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_2))) L_1))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f73570213t_real (tptp.hAPP_f918606171t_real tptp.cOMBB_64450052al_nat tptp.produc1935615926l_real) _let_1) L_1 tptp.sequentially)) (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real L_1) (tptp.hAPP_P731461727l_real tptp.produc556554744l_real (tptp.hAPP_n332733730l_real (tptp.bolzano_bisect P_1 A B) N_2))))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f73570213t_real (tptp.hAPP_f918606171t_real tptp.cOMBB_64450052al_nat tptp.produc556554744l_real) _let_1) L_1 tptp.sequentially)))))))))))) (forall ((A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real A N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hAPP_nat_real A N_2)))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f292751352t_real (tptp.hAPP_f1607377819t_real tptp.cOMBB_1533963633al_nat (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1)) (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat (tptp.ord_at4362885an_nat tptp.zero_zero_nat)) (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1) tptp.sequentially))))))) (forall ((N_1 tptp.nat) (A tptp.fun_nat_real)) (let ((_let_1 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real A N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hAPP_nat_real A N_2)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_f1406902706l_real (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat tptp.zero_zero_nat) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_1)))) (tptp.hAPP_f352196356l_real tptp.suminf_real _let_1)))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_nat_real A tptp.zero_zero_nat)) tptp.zero_zero_real)) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_2))) (let ((_let_2 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (let ((_let_4 (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_3))) (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real (tptp.hAPP_f352196356l_real tptp.suminf_real _let_3)) (tptp.hAPP_r1134773055l_bool (tptp.ord_at1589558736t_real (tptp.hAPP_f1406902706l_real _let_4 (tptp.hAPP_n1699378549t_bool _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (tptp.hAPP_f1406902706l_real _let_4 (tptp.hAPP_n1699378549t_bool _let_2 _let_1)))))))))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (tptp.hBOOL (tptp.monoseq_real A)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_nat_real A tptp.zero_zero_nat))) (forall ((N_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat tptp.number_number_of_nat (tptp.hAPP_int_int tptp.bit0 (tptp.hAPP_int_int tptp.bit1 tptp.pls)))) N_2))) (let ((_let_2 (tptp.ord_at4362885an_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))) (let ((_let_4 (tptp.hAPP_f1509287679l_real tptp.big_co604158596t_real _let_3))) (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real (tptp.hAPP_f352196356l_real tptp.suminf_real _let_3)) (tptp.hAPP_r1134773055l_bool (tptp.ord_at1589558736t_real (tptp.hAPP_f1406902706l_real _let_4 (tptp.hAPP_n1699378549t_bool _let_2 _let_1))) (tptp.hAPP_f1406902706l_real _let_4 (tptp.hAPP_n1699378549t_bool _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))))) (forall ((Y_2 tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real Y_2) X_1)) (= (tptp.comple124823625p_real (tptp.hAPP_r1134773055l_bool (tptp.ord_at1589558736t_real Y_2) X_1)) X_1))) (forall ((A tptp.fun_nat_real)) (=> (tptp.hBOOL (tptp.tendsto_nat_real A tptp.zero_zero_real tptp.sequentially)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_nat_real A N_2)))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real A (tptp.hAPP_nat_nat tptp.suc N_2))) (tptp.hAPP_nat_real A N_2)))) (tptp.hBOOL (tptp.summable_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat tptp.times_times_real) (tptp.hAPP_r474017924t_real tptp.power_power_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)))) A))))))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U)))) (forall ((L tptp.int) (U tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int L) U)))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int X_1) Y_2))))) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat)) (= (forall ((M_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 M_1)))) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X_2)))))) (forall ((P_1 tptp.fun_nat_bool) (N_1 tptp.nat)) (= (exists ((M_1 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_1) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 M_1)))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool P_1 X_2)))))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat Ma) N_1) (tptp.image_int_nat tptp.nat_1 (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int Ma)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))))) (forall ((I_1 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat I_1) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat tptp.suc I_1)) (tptp.hAPP_nat_nat tptp.suc J)))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat I_1) J)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1) (tptp.big_co1705425894at_nat tptp.cOMBI_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.one_one_nat) N_1)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at4362885an_nat L) (tptp.hAPP_nat_nat tptp.suc U)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.tendsto_complex_real tptp.re (tptp.hAPP_complex_real tptp.re A) (tptp.at_complex A)))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.tendsto_complex_real tptp.im (tptp.hAPP_complex_real tptp.im A) (tptp.at_complex A)))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.tendst1507391555omplex tptp.cnj (tptp.hAPP_complex_complex tptp.cnj A) (tptp.at_complex A)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat tptp.suc U)) L))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.ord_at641636577an_int L) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int U) tptp.one_one_int)) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int L) U))) (forall ((K_1 tptp.nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (= (tptp.hAPP_nat_nat F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat tptp.suc tptp.zero_zero_nat)) K_1)) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) K_1)))))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int L) U)) (tptp.hAPP_int_nat tptp.nat_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int U) L)) tptp.one_one_int)))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_1) Ma)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.div_div_nat (tptp.hAPP_nat_nat tptp.fact_fact_nat Ma)) (tptp.hAPP_nat_nat tptp.fact_fact_nat N_1)) (tptp.big_co1705425894at_nat tptp.cOMBI_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) tptp.one_one_nat)) Ma))))) (forall ((N_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) N_1)) (= (tptp.hAPP_int_int tptp.fact_fact_int N_1) (tptp.big_co1548731110nt_int tptp.cOMBI_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) N_1))))) (tptp.hBOOL (tptp.tendsto_real_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real tptp.inverse_divide_real) tptp.cos)) tptp.sin) tptp.zero_zero_real (tptp.at_real _let_14))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_real_real F L (tptp.at_real C))) (=> (not (= L tptp.zero_zero_real)) (exists ((R_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_1)) (forall ((X_2 tptp.real)) (=> (and (not (= X_2 C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) X_2))) R_1))) (not (= (tptp.hAPP_real_real F X_2) tptp.zero_zero_real))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_real_real F L (tptp.at_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((R_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_1)) (forall ((X_2 tptp.real)) (=> (and (not (= X_2 C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) X_2))) R_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.hAPP_real_real F X_2)))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.hBOOL (tptp.tendsto_real_real F L (tptp.at_real C))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((R_1 tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) R_1)) (forall ((X_2 tptp.real)) (=> (and (not (= X_2 C)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real C) X_2))) R_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F X_2)) tptp.zero_zero_real))))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ta) tptp.one_one_int)) A_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1)) Ta)))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ta))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1))))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_2) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)) Ta))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ta) tptp.one_one_int)) B_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ta))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)))))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Ta))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1))))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)) Ta))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ta) tptp.one_one_int)) B_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (= X_2 Ta) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1) Ta))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ta) tptp.one_one_int)) A_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (= X_2 Ta) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1) Ta))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ta) A_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (not (= X_2 Ta)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1) Ta)))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ta) B_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (not (= X_2 Ta)) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1) Ta)))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ta) A_1)) (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Ta)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1)) Ta)))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ta) B_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Ta))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)))))))))) (forall ((P_1 tptp.fun_int_bool) (D tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X_2 tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D)))))) (= (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D))) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int _let_1 Ta)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 D_1)) Ta))))))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)) Ta)))))))))) (forall ((Ta tptp.int) (B_1 tptp.fun_int_bool) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)) Ta))))))))) (forall ((Ta tptp.int) (A_1 tptp.fun_int_bool) (D tptp.int) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D) D_1)) (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2))) (let ((_let_2 (tptp.hAPP_i1948725293t_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int _let_1 Ta))) (tptp.hBOOL (tptp.hAPP_int_bool _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 D_1)) Ta)))))))))) (forall ((X_3 tptp.fun_nat_real)) (=> (forall ((R_1 tptp.real)) (exists ((N_3 tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_3) N_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real R_1) (tptp.hAPP_nat_real X_3 N_2))))))) (tptp.hBOOL (tptp.tendsto_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat tptp.inverse_inverse_real) X_3) tptp.zero_zero_real tptp.sequentially)))) (forall ((A_3 tptp.real) (X tptp.real)) (= (tptp.hAPP_real_real (tptp.scaleR_scaleR_real A_3) X) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real A_3) X))) (forall ((R_3 tptp.real) (X tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3) (tptp.hAPP_complex_real tptp.im X)))) (forall ((R_3 tptp.real) (X tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) X)) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3) (tptp.hAPP_complex_real tptp.re X)))) (forall ((R_3 tptp.real) (A_3 tptp.real) (B_2 tptp.real)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3))) (= (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 A_3) B_2)) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real _let_1 A_3)) (tptp.hAPP_real_real _let_1 B_2))))) (forall ((R_3 tptp.real) (X tptp.complex)) (= (tptp.hAPP_complex_real tptp.re (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) X)) (tptp.hAPP_real_real (tptp.scaleR_scaleR_real R_3) (tptp.hAPP_complex_real tptp.re X)))) (forall ((R_3 tptp.real) (X tptp.complex)) (= (tptp.hAPP_complex_real tptp.im (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) X)) (tptp.hAPP_real_real (tptp.scaleR_scaleR_real R_3) (tptp.hAPP_complex_real tptp.im X)))) (forall ((R_3 tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.scaleR1652505878omplex R_3))) (= (tptp.hAPP_complex_complex tptp.cnj (tptp.hAPP_complex_complex _let_1 X)) (tptp.hAPP_complex_complex _let_1 (tptp.hAPP_complex_complex tptp.cnj X))))) (forall ((X tptp.complex)) (= (tptp.hAPP_complex_complex tptp.sgn_sgn_complex X) (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex (tptp.hAPP_real_real tptp.inverse_inverse_real (tptp.hAPP_complex_real tptp.norm_norm_complex X))) X))) (forall ((R_3 tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.hAPP_r1250527377l_real tptp.times_times_real R_3))) (= (tptp.hAPP_complex_complex (tptp.scaleR1652505878omplex R_3) X) (tptp.hAPP_real_complex (tptp.hAPP_r265291036omplex tptp.complex_1 (tptp.hAPP_real_real _let_1 (tptp.hAPP_complex_real tptp.re X))) (tptp.hAPP_real_real _let_1 (tptp.hAPP_complex_real tptp.im X)))))) (not (tptp.hBOOL (tptp.trivial_limit_nat tptp.sequentially))) (= tptp.pred_nat (tptp.collec1979865426at_nat (tptp.produc1922581855t_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat _let_11) tptp.suc)))) (forall ((A_3 tptp.int) (B_2 tptp.int)) (=> (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2) tptp.zero_zero_int)) (exists ((A_4 tptp.int) (B_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_3) B_2))) (and (= A_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_4) _let_1)) (= B_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_3) _let_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int A_4) B_3) tptp.one_one_int)))))) (forall ((N_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat (tptp.hAPP_int_bool tptp.nat_neg _let_1)) tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat N_1) (tptp.hAPP_int_nat tptp.nat_1 _let_1))))))) (forall ((V tptp.int) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat (tptp.hAPP_int_bool tptp.nat_neg _let_1)) tptp.zero_zero_nat) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_int_nat tptp.nat_1 _let_1)) N_1)))))) (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat M) N)) I))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat M) N)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Ma) (tptp.hAPP_nat_nat tptp.suc N_1)) (tptp.hAPP_nat_nat (tptp.nat_case_nat tptp.zero_zero_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.suc) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.ord_min_nat) N_1))) Ma))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat tptp.suc N_1)) Ma) (tptp.hAPP_nat_nat (tptp.nat_case_nat tptp.zero_zero_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.suc) (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat N_1))) Ma))) (forall ((Y_3 tptp.fun_nat_rat) (X_3 tptp.fun_nat_rat)) (=> (exists ((A_2 tptp.rat)) (and (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) A_2)) (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat tptp.abs_abs_rat (tptp.hAPP_nat_rat X_3 N_2))) A_2))))) (=> (tptp.hBOOL (tptp.vanishes Y_3)) (tptp.hBOOL (tptp.vanishes (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1131305186at_rat tptp.cOMBS_nat_rat_rat (tptp.hAPP_f1830834240at_rat (tptp.hAPP_f1073644437at_rat tptp.cOMBB_1926947at_nat tptp.times_times_rat) X_3)) Y_3)))))) (forall ((N_1 tptp.int) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Ma)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat N_1)) (= (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int Ma) N_1) (tptp.image_nat_int tptp.semiri1621563631at_int (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_int_nat tptp.nat_1 Ma)) (tptp.hAPP_int_nat tptp.nat_1 N_1))))))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_1)))) (forall ((Y_3 tptp.fun_nat_rat) (X_3 tptp.fun_nat_rat)) (=> (tptp.hBOOL (tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.vanishes Y_3)) (tptp.hBOOL (tptp.vanishes (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1131305186at_rat tptp.cOMBS_nat_rat_rat (tptp.hAPP_f1830834240at_rat (tptp.hAPP_f1073644437at_rat tptp.cOMBB_1926947at_nat tptp.minus_minus_rat) X_3)) Y_3)))))) (forall ((Y_3 tptp.fun_nat_rat) (X_3 tptp.fun_nat_rat)) (=> (tptp.hBOOL (tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.vanishes Y_3)) (tptp.hBOOL (tptp.vanishes (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1131305186at_rat tptp.cOMBS_nat_rat_rat (tptp.hAPP_f1830834240at_rat (tptp.hAPP_f1073644437at_rat tptp.cOMBB_1926947at_nat tptp.plus_plus_rat) X_3)) Y_3)))))) (forall ((C tptp.rat)) (= (tptp.hBOOL (tptp.vanishes (tptp.cOMBK_rat_nat C))) (= C tptp.zero_zero_rat))) (forall ((X_3 tptp.fun_nat_rat)) (=> (tptp.hBOOL (tptp.vanishes X_3)) (tptp.hBOOL (tptp.vanishes (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1082758869at_rat tptp.cOMBB_rat_rat_nat tptp.uminus_uminus_rat) X_3))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y)))))) (forall ((N tptp.nat) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_int_int (tptp.div_mod_int X) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.div_div_int X) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_int_int (tptp.nat_tsub X) Y)))))) (forall ((X_1 tptp.int) (A_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X_1))))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat tptp.zero_zero_int)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat tptp.one_one_int)) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y)))))) (forall ((Z_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat (tptp.hAPP_nat_int tptp.semiri1621563631at_int Z_1)))) (forall ((Y_2 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int X_1) Y_2))))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat _let_10)) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.gcd_gcd_int X) Y)))))) (forall ((X tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_int_int tptp.fact_fact_int X))))) (forall ((A_1 tptp.fun_int_bool) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.nat_nat_set A_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_int_nat tptp.nat_1 X_1)) (tptp.image_int_nat tptp.nat_1 A_1))))))) (tptp.hBOOL (tptp.hAPP_int_bool tptp.nat_is_nat _let_8)) (forall ((X_3 tptp.fun_nat_rat)) (= (tptp.hBOOL (tptp.vanishes X_3)) (forall ((R_1 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) R_1)) (exists ((K tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_2)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat tptp.abs_abs_rat (tptp.hAPP_nat_rat X_3 N_2))) R_1))))))))) (forall ((R_2 tptp.rat) (X_3 tptp.fun_nat_rat)) (=> (tptp.hBOOL (tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) R_2)) (exists ((K tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_2)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat tptp.abs_abs_rat (tptp.hAPP_nat_rat X_3 N_2))) R_2)))))))) (forall ((X_3 tptp.fun_nat_rat)) (=> (forall ((R_1 tptp.rat)) (=> (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat tptp.zero_zero_rat) R_1)) (exists ((K tptp.nat)) (forall ((N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N_2)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.ord_less_rat (tptp.hAPP_rat_rat tptp.abs_abs_rat (tptp.hAPP_nat_rat X_3 N_2))) R_1))))))) (tptp.hBOOL (tptp.vanishes X_3)))) (forall ((Ma tptp.int) (X_2 tptp.int) (Xa tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcongm Ma) X_2) Xa)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong X_2) Xa) Ma)))) (forall ((B_1 tptp.fun_int_bool) (P_2 tptp.fun_int_bool) (P_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X_2) Z)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))))) (=> (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) B_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) D_1)))))) (=> (forall ((X_2 tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1)))))) (= (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1))) (or (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (exists ((Xa tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) B_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Xa) X_2)))))))))))))) (forall ((A_1 tptp.fun_int_bool) (B_1 tptp.fun_int_bool) (Ma tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f1469637905l_bool (tptp.hAPP_P1681069257l_bool tptp.member308914164t_bool (tptp.hAPP_f538843494t_bool (tptp.hAPP_f1418982953t_bool tptp.produc713279741t_bool A_1) B_1)) (tptp.bijR_int_int (tptp.zcongm Ma)))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.zcong (tptp.big_co1548731110nt_int tptp.cOMBI_int A_1)) (tptp.big_co1548731110nt_int tptp.cOMBI_int B_1)) Ma)))) (forall ((A_1 tptp.fun_int_bool) (P_2 tptp.fun_int_bool) (P_1 tptp.fun_int_bool) (D_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) D_1)) (=> (exists ((Z tptp.int)) (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z) X_2)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))))) (=> (forall ((X_2 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (forall ((Xb tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xb) A_1)) (not (= X_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xb) Xa))))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_2) D_1)))))) (=> (forall ((X_2 tptp.int) (K tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP_int_bool P_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_2) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int K) D_1)))))) (= (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 X1))) (or (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (tptp.hBOOL (tptp.hAPP_int_bool P_2 X_2)))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.one_one_int) D_1))) (exists ((Xa tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Xa) A_1)) (tptp.hBOOL (tptp.hAPP_int_bool P_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Xa) X_2)))))))))))))) (forall ((L tptp.real) (F tptp.fun_nat_real)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F N_2)) (tptp.hAPP_nat_real F (tptp.hAPP_nat_nat tptp.suc N_2))))) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_nat_real F N_2)) L))) (=> (forall ((E tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real L) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.plus_plus_real (tptp.hAPP_nat_real F N_2)) E)))))) (tptp.hBOOL (tptp.tendsto_nat_real F L tptp.sequentially)))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.ln) X_1)))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real (tptp.hAPP_n546711566l_real tptp.root N_1)) X_1)))) (forall ((X_1 tptp.real)) (=> (not (= (tptp.hAPP_real_real tptp.cos X_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.tan) X_1)))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.cos) X_1))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.arctan) X_1))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.sqrt) X_1))) (forall ((X_1 tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.sin) X_1))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.isCont156215680omplex tptp.cnj) A))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.isCont_complex_real tptp.im) A))) (forall ((A tptp.complex)) (tptp.hBOOL (tptp.hAPP_complex_bool (tptp.isCont_complex_real tptp.re) A))) (forall ((A tptp.real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.abs_abs_real) A))) (forall ((N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real (tptp.hAPP_n546711566l_real tptp.root N_1)) tptp.zero_zero_real)))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.zero_zero_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real (tptp.hAPP_n546711566l_real tptp.root N_1)) X_1))))) (forall ((X_1 tptp.real) (N_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real (tptp.hAPP_n546711566l_real tptp.root N_1)) X_1))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.arccos) X_1))))) (forall ((X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_int_real tptp.number267125858f_real tptp.min)) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) tptp.one_one_real)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real tptp.arcsin) X_1))))) (forall ((F tptp.fun_real_real) (B tptp.real) (X_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real B) X_1)) (=> (forall ((X_2 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_f1501066425l_bool (tptp.hAPP_r1130899993l_bool tptp.member_real X_2) (tptp.hAPP_r1134773055l_bool (tptp.ord_gr788844697n_real B) X_1))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real F X_2))))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.hAPP_real_real F X_1))))))) (forall ((B tptp.real) (A tptp.real) (F tptp.fun_real_real) (G tptp.fun_real_real) (X_1 tptp.real) (D_1 tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F (tptp.hAPP_real_real G X_1)) D_1)) (=> (not (= D_1 tptp.zero_zero_real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_1) B)) (=> (forall ((Y_1 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) Y_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real Y_1) B))) (= (tptp.hAPP_real_real F (tptp.hAPP_real_real G Y_1)) Y_1))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real G) X_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real G X_1) (tptp.hAPP_real_real tptp.inverse_inverse_real D_1)))))))))) (forall ((G tptp.fun_real_real) (F tptp.fun_real_real) (X_1 tptp.real) (D tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (= (tptp.hAPP_real_real G (tptp.hAPP_real_real F Z)) Z))) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) Z)))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real G) (tptp.hAPP_real_real F X_1))))))) (forall ((X_1 tptp.real) (F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) X_2)))) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) tptp.zero_zero_real)))) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_1) B)) (= (tptp.hAPP_real_real F X_1) (tptp.hAPP_real_real F A)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) X_2)))) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) tptp.zero_zero_real)))) (= (tptp.hAPP_real_real F B) (tptp.hAPP_real_real F A)))))) (forall ((F tptp.fun_real_real) (A tptp.real) (B tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) B)) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) X_2)))) (=> (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real X_2) B))) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.deriv_real F X_2) tptp.zero_zero_real)))) (forall ((X_2 tptp.real)) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real A) X_2)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real X_2) B))) (= (tptp.hAPP_real_real F X_2) (tptp.hAPP_real_real F A)))))))) (forall ((G tptp.fun_real_real) (F tptp.fun_real_real) (X_1 tptp.real) (D tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (= (tptp.hAPP_real_real G (tptp.hAPP_real_real F Z)) Z))) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) Z)))) (exists ((E tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (forall ((Y_1 tptp.real)) (let ((_let_1 (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Y_1) (tptp.hAPP_real_real F X_1))))) (=> (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real _let_1) E))) (= (tptp.hAPP_real_real F (tptp.hAPP_real_real G Y_1)) Y_1)))))))))) (forall ((G tptp.fun_real_real) (F tptp.fun_real_real) (X_1 tptp.real) (D tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (= (tptp.hAPP_real_real G (tptp.hAPP_real_real F Z)) Z))) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) Z)))) (exists ((Z tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F Z)) (tptp.hAPP_real_real F X_1))))))))) (forall ((G tptp.fun_real_real) (F tptp.fun_real_real) (X_1 tptp.real) (D tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (= (tptp.hAPP_real_real G (tptp.hAPP_real_real F Z)) Z))) (=> (forall ((Z tptp.real)) (=> (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.isCont_real_real F) Z)))) (exists ((Z tptp.real)) (and (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_eq_real (tptp.hAPP_real_real tptp.abs_abs_real (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real tptp.minus_minus_real Z) X_1))) D)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.ord_less_real (tptp.hAPP_real_real F X_1)) (tptp.hAPP_real_real F Z))))))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat N_1) (tptp.image_int_nat tptp.nat_1 (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))))) (forall ((N_1 tptp.nat) (V tptp.int)) (let ((_let_1 (tptp.hAPP_int_int tptp.number_number_of_int (tptp.hAPP_int_int tptp.pred V)))) (let ((_let_2 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat _let_2) (tptp.hAPP_int_nat tptp.number_number_of_nat V)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat (tptp.hAPP_int_bool tptp.nat_neg _let_1)) _let_2) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N_1) (tptp.hAPP_int_nat tptp.nat_1 _let_1)))))))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat K_1)))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat tptp.zero_zero_nat) N_1) (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat N_1))) (forall ((K_1 tptp.nat)) (= (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat (tptp.hAPP_nat_nat tptp.suc K_1)) (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat K_1))) (forall ((N_1 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat _let_1) Ma) (tptp.hAPP_nat_nat (tptp.nat_case_nat _let_1 (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.suc) (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N_1))) Ma)))) (forall ((Ma tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat tptp.suc N_1))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat Ma) _let_1) (tptp.hAPP_nat_nat (tptp.nat_case_nat _let_1 (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat tptp.suc) (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.ord_max_nat) N_1))) Ma)))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M)) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N) M))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N) tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat (tptp.hAPP_nat_nat tptp.suc M)) (tptp.hAPP_nat_nat tptp.suc N)) (tptp.hAPP_nat_nat tptp.suc (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat M) N)))) (forall ((U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat U)) (tptp.hAPP_nat_nat tptp.suc U))) (forall ((S tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S)) (exists ((K tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool S) (tptp.hAPP_n1699378549t_bool tptp.ord_atMost_nat K)))))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (tptp.hBOOL tptp.fTrue) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.fdisj P Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.fdisj P Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.fdisj P Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_b1463609396nt_int tptp.if_int tptp.fTrue) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_b1463609396nt_int tptp.if_int tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_b992065680at_nat tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.fun_int_bool) (X tptp.int)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool P X))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.fEx_int P)))) (forall ((P tptp.fun_nat_bool) (X tptp.nat)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool P X))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.fEx_nat P)))) (forall ((P tptp.int)) (= (tptp.hAPP_int_int tptp.cOMBI_int P) P)) (forall ((P tptp.nat)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.fequal_rat X) Y))) (= X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_rat_bool (tptp.hAPP_r2115560837t_bool tptp.fequal_rat X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real (tptp.hAPP_b646336293l_real tptp.if_real tptp.fTrue) X) Y) X)) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real (tptp.hAPP_b646336293l_real tptp.if_real tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.real)) (= (tptp.hAPP_real_real tptp.cOMBI_real P) P)) (forall ((X tptp.real) (Y tptp.real)) (or (not (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.fequal_real X) Y))) (= X Y))) (forall ((X tptp.real) (Y tptp.real)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool tptp.fequal_real X) Y)))) (forall ((P tptp.rat) (Q tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.cOMBK_rat_nat P) Q) P)) (forall ((P tptp.bool) (Q tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.cOMBK_bool_nat P) Q) P)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.hAPP_P1975530577nt_int (tptp.hAPP_P1145851913nt_int (tptp.hAPP_b40753821nt_int tptp.if_Pro1731782967nt_int tptp.fTrue) X) Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.hAPP_P1975530577nt_int (tptp.hAPP_P1145851913nt_int (tptp.hAPP_b40753821nt_int tptp.if_Pro1731782967nt_int tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.fun_int_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_f1356864277nt_int (tptp.hAPP_f747162069nt_int tptp.cOMBB_int_int_int P) Q) R) (tptp.hAPP_int_int P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_int_int) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_f1139079189at_int (tptp.hAPP_f1431025877at_int tptp.cOMBB_int_int_nat P) Q) R) (tptp.hAPP_int_int P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_int_rat) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_rat (tptp.hAPP_f1900950721nt_rat (tptp.hAPP_f1270196437nt_rat tptp.cOMBB_int_rat_int P) Q) R) (tptp.hAPP_int_rat P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_rat_rat) (Q tptp.fun_nat_rat) (R tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1082758869at_rat tptp.cOMBB_rat_rat_nat P) Q) R) (tptp.hAPP_rat_rat P (tptp.hAPP_nat_rat Q R)))) (forall ((P tptp.fun_int_fun_int_int) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int (tptp.hAPP_f2135977429nt_int tptp.cOMBC_int_int_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int P R) Q))) (forall ((P tptp.fun_int_fun_nat_int) (Q tptp.nat) (R tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_nat_fun_int_int (tptp.hAPP_f2105620693nt_int tptp.cOMBC_int_nat_int P) Q) R) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int P R) Q))) (forall ((P tptp.fun_nat_fun_int_int) (Q tptp.int) (R tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int (tptp.hAPP_f1673103573at_int tptp.cOMBC_nat_int_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_nat_fun_int_int P R) Q))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat P R) Q))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat P R) (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_nat_fun_rat_rat) (Q tptp.fun_nat_rat) (R tptp.nat)) (= (tptp.hAPP_nat_rat (tptp.hAPP_f2062659861at_rat (tptp.hAPP_f1131305186at_rat tptp.cOMBS_nat_rat_rat P) Q) R) (tptp.hAPP_rat_rat (tptp.hAPP_nat_fun_rat_rat P R) (tptp.hAPP_nat_rat Q R)))) (forall ((X tptp.produc914805421l_real) (Y tptp.produc914805421l_real)) (= (tptp.hAPP_P1860904029l_real (tptp.hAPP_P1982799375l_real (tptp.hAPP_b1482221219l_real tptp.if_Pro313124157l_real tptp.fTrue) X) Y) X)) (forall ((X tptp.produc914805421l_real) (Y tptp.produc914805421l_real)) (= (tptp.hAPP_P1860904029l_real (tptp.hAPP_P1982799375l_real (tptp.hAPP_b1482221219l_real tptp.if_Pro313124157l_real tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f429935748t_bool (tptp.hAPP_f1512942609t_bool tptp.cOMBB_int_bool_int P) Q) R) (tptp.hAPP_int_bool P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f1154658180t_bool (tptp.hAPP_f1361476881t_bool tptp.cOMBB_int_bool_nat P) Q) R) (tptp.hAPP_int_bool P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1448486952t_bool (tptp.hAPP_f696844121t_bool tptp.cOMBB_nat_bool_int P) Q) R) (tptp.hAPP_nat_bool P (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_rat_bool) (Q tptp.fun_int_rat) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1241350704t_bool (tptp.hAPP_f1131424617t_bool tptp.cOMBB_rat_bool_int P) Q) R) (tptp.hAPP_rat_bool P (tptp.hAPP_int_rat Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P tptp.fun_int_fun_rat_bool) (Q tptp.rat) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_r1900510169t_bool (tptp.hAPP_f1480506641t_bool tptp.cOMBC_int_rat_bool P) Q) R) (tptp.hAPP_rat_bool (tptp.hAPP_i16292313t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_in531499254l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_na1469252690l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_n1006566506l_bool P R) (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_int_real) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_real (tptp.hAPP_f563293398t_real (tptp.hAPP_f134192053t_real tptp.cOMBB_int_real_int P) Q) R) (tptp.hAPP_int_real P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_nat_real) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f1676298106t_real (tptp.hAPP_f1566856189t_real tptp.cOMBB_nat_real_nat P) Q) R) (tptp.hAPP_nat_real P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_int_real) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f429384717t_bool (tptp.hAPP_f1173902867t_bool tptp.cOMBB_real_bool_int P) Q) R) (tptp.hAPP_real_bool P (tptp.hAPP_int_real Q R)))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f737665877t_bool (tptp.hAPP_f605995867t_bool tptp.cOMBB_real_bool_nat P) Q) R) (tptp.hAPP_real_bool P (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_in1251377736l_bool) (Q tptp.real) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_r481142414t_bool (tptp.hAPP_f1845081853t_bool tptp.cOMBC_int_real_bool P) Q) R) (tptp.hAPP_real_bool (tptp.hAPP_i688218208l_bool P R) Q))) (forall ((P tptp.fun_re1114994977l_bool) (Q tptp.fun_real_bool) (R tptp.real)) (= (tptp.hAPP_real_bool (tptp.hAPP_f1861673493l_bool (tptp.hAPP_f1010710745l_bool tptp.cOMBS_real_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_r1938957037l_bool P R) (tptp.hAPP_real_bool Q R)))) (forall ((P tptp.fun_real_real) (Q tptp.fun_int_real) (R tptp.int)) (= (tptp.hAPP_int_real (tptp.hAPP_f269654879t_real (tptp.hAPP_f766218899t_real tptp.cOMBB_real_real_int P) Q) R) (tptp.hAPP_real_real P (tptp.hAPP_int_real Q R)))) (forall ((P tptp.fun_real_real) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f1690286043t_real tptp.cOMBB_real_real_nat P) Q) R) (tptp.hAPP_real_real P (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_na182379510l_real) (Q tptp.real) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real (tptp.hAPP_f42270917t_real tptp.cOMBC_nat_real_real P) Q) R) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real P R) Q))) (forall ((P tptp.fun_re1927296998t_real) (Q tptp.nat) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real (tptp.hAPP_f248847589l_real tptp.cOMBC_real_nat_real P) Q) R) (tptp.hAPP_nat_real (tptp.hAPP_r474017924t_real P R) Q))) (forall ((P tptp.nat) (Q tptp.fun_int_bool)) (= (tptp.hAPP_f957591787ol_nat (tptp.cOMBK_1643584600t_bool P) Q) P)) (forall ((P tptp.fun_na182379510l_real) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f1888375463t_real (tptp.hAPP_f197615720t_real tptp.cOMBS_nat_real_real P) Q) R) (tptp.hAPP_real_real (tptp.hAPP_n546711566l_real P R) (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_real_bool) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_real_bool (tptp.hAPP_f1402056515l_bool (tptp.hAPP_f824790735l_bool tptp.cOMBB_real_bool_real P) Q) R) (tptp.hAPP_real_bool P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_re413263731l_bool) (Q tptp.real) (R tptp.real)) (= (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f695504873l_bool tptp.cOMBC_real_real_bool P) Q) R) (tptp.hAPP_real_bool (tptp.hAPP_r1134773055l_bool P R) Q))) (forall ((P tptp.fun_complex_real) (Q tptp.fun_nat_complex) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f1290670424t_real (tptp.hAPP_f327026105t_real tptp.cOMBB_722610049al_nat P) Q) R) (tptp.hAPP_complex_real P (tptp.hAPP_nat_complex Q R)))) (forall ((P tptp.fun_na1566252557omplex) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_f219720582omplex (tptp.hAPP_f1052840010omplex tptp.cOMBS_696648398omplex P) Q) R) (tptp.hAPP_real_complex (tptp.hAPP_n1983812447omplex P R) (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_real_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f1992866895l_real tptp.cOMBB_real_real_real P) Q) R) (tptp.hAPP_real_real P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_re229243589l_real) (Q tptp.real) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real (tptp.hAPP_f203520653l_real tptp.cOMBC_real_real_real P) Q) R) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real P R) Q))) (forall ((P tptp.fun_re229243589l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_f1950183573l_real (tptp.hAPP_f2069516469l_real tptp.cOMBS_real_real_real P) Q) R) (tptp.hAPP_real_real (tptp.hAPP_r1250527377l_real P R) (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_complex_complex) (Q tptp.fun_nat_complex) (R tptp.nat)) (= (tptp.hAPP_nat_complex (tptp.hAPP_f1646117269omplex (tptp.hAPP_f1457396693omplex tptp.cOMBB_117013006ex_nat P) Q) R) (tptp.hAPP_complex_complex P (tptp.hAPP_nat_complex Q R)))) (forall ((P tptp.fun_int_fun_int_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_fun_int_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f1629352853nt_int tptp.cOMBB_1496585939nt_int P) Q) R) (tptp.hAPP_int_fun_int_int P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_int_fun_int_int) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_nat_fun_int_int (tptp.hAPP_f1935805932nt_int (tptp.hAPP_f125788821nt_int tptp.cOMBB_859312247nt_nat P) Q) R) (tptp.hAPP_int_fun_int_int P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_rat_fun_rat_rat) (Q tptp.fun_nat_rat) (R tptp.nat)) (= (tptp.hAPP_nat_fun_rat_rat (tptp.hAPP_f1830834240at_rat (tptp.hAPP_f1073644437at_rat tptp.cOMBB_1926947at_nat P) Q) R) (tptp.hAPP_rat_fun_rat_rat P (tptp.hAPP_nat_rat Q R)))) (forall ((P tptp.fun_int_int) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1175774780nt_int (tptp.hAPP_f521271395nt_int (tptp.hAPP_f11151005nt_int tptp.cOMBB_47643171nt_int P) Q) R) (tptp.hAPP_int_int P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_in2003698982nt_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1524277240nt_int (tptp.hAPP_f883232462nt_int (tptp.hAPP_f2002277285nt_int tptp.cOMBB_1846624359nt_int P) Q) R) (tptp.hAPP_i1524277240nt_int P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_rat_fun_rat_bool) (Q tptp.fun_int_rat) (R tptp.int)) (= (tptp.hAPP_i16292313t_bool (tptp.hAPP_f601898971t_bool (tptp.hAPP_f857296063t_bool tptp.cOMBB_214503962ol_int P) Q) R) (tptp.hAPP_r2115560837t_bool P (tptp.hAPP_int_rat Q R)))) (forall ((P tptp.fun_in351380826t_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_i345030060t_bool (tptp.hAPP_f791698359t_bool tptp.cOMBC_241247961t_bool P) Q) R) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_i345030060t_bool P R) Q))) (forall ((P tptp.fun_in1111845413nt_int) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f465821005nt_int tptp.cOMBC_1964283556nt_int P) Q) R) (tptp.hAPP_i1524277240nt_int (tptp.hAPP_i1584592887nt_int P R) Q))) (forall ((P tptp.fun_Pr2134412615nt_int) (Q tptp.int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1175774780nt_int (tptp.hAPP_i61245889nt_int (tptp.hAPP_f578362681nt_int tptp.cOMBC_1417754532nt_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_P2110489235nt_int P R) Q))) (forall ((P tptp.fun_Pr2134412615nt_int) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1175774780nt_int (tptp.hAPP_f521271395nt_int (tptp.hAPP_f1914742907nt_int tptp.cOMBS_2019229620nt_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_P2110489235nt_int P R) (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_Pr1826394355nt_rat) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1853363688nt_rat (tptp.hAPP_f1065357839nt_rat (tptp.hAPP_f1120137083nt_rat tptp.cOMBS_549334880nt_rat P) Q) R) (tptp.hAPP_int_rat (tptp.hAPP_P507092031nt_rat P R) (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_f892584630t_bool (tptp.hAPP_f492612297t_bool tptp.cOMBB_798864284nt_int P) Q) R) (tptp.hAPP_int_bool P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_rat_bool) (Q tptp.fun_Pr1024438428nt_rat) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_f1084724746t_bool (tptp.hAPP_f374502857t_bool tptp.cOMBB_569260360nt_int P) Q) R) (tptp.hAPP_rat_bool P (tptp.hAPP_P1853363688nt_rat Q R)))) (forall ((P tptp.fun_fu819804446l_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f2119767738t_bool (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int P) Q) R) (tptp.hAPP_f448129468l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu425979586l_bool) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f41603166t_bool (tptp.hAPP_f389116883t_bool tptp.cOMBB_1593174431ol_int P) Q) R) (tptp.hAPP_f54304608l_bool P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_in938817141l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool P R) Q))) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P tptp.fun_Pr1149636328t_bool) (Q tptp.int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_i119638232t_bool (tptp.hAPP_f2018027565t_bool tptp.cOMBC_33652895t_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_P252494982t_bool P R) Q))) (forall ((P tptp.fun_Pr1149636328t_bool) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_f892584630t_bool (tptp.hAPP_f1325804733t_bool tptp.cOMBS_480885903t_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_P252494982t_bool P R) (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Pr974702441t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_f237669397t_bool (tptp.hAPP_f513299955t_bool tptp.cOMBB_1344650379nt_int P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_P603027463t_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i68813070l_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1006566506l_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_Pr189909033l_bool) (Q tptp.fun_Pr974702441t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P603027463t_bool (tptp.hAPP_f237669397t_bool (tptp.hAPP_f461489489t_bool tptp.cOMBS_400904860l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_P921862901l_bool P R) (tptp.hAPP_P603027463t_bool Q R)))) (forall ((P tptp.fun_fu95670548l_real) (Q tptp.fun_nat_fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f292751352t_real (tptp.hAPP_f1607377819t_real tptp.cOMBB_1533963633al_nat P) Q) R) (tptp.hAPP_f1406902706l_real P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P tptp.fun_fu819804446l_bool) (Q tptp.fun_re546217968t_bool) (R tptp.real)) (= (tptp.hAPP_real_bool (tptp.hAPP_f101635158l_bool (tptp.hAPP_f1925507189l_bool tptp.cOMBB_1121934354l_real P) Q) R) (tptp.hAPP_f448129468l_bool P (tptp.hAPP_r481142414t_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_real_bool) (R tptp.real)) (= (tptp.hAPP_r1938957037l_bool (tptp.hAPP_f60716669l_bool (tptp.hAPP_f1485493409l_bool tptp.cOMBB_624415285l_real P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_real_bool Q R)))) (forall ((P tptp.fun_na182379510l_real) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n546711566l_real (tptp.hAPP_f1904307534l_real (tptp.hAPP_f224989205l_real tptp.cOMBB_1419615765al_nat P) Q) R) (tptp.hAPP_n546711566l_real P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_re413263731l_bool) (Q tptp.fun_int_real) (R tptp.int)) (= (tptp.hAPP_i688218208l_bool (tptp.hAPP_f801032407l_bool (tptp.hAPP_f499530369l_bool tptp.cOMBB_1317819104ol_int P) Q) R) (tptp.hAPP_r1134773055l_bool P (tptp.hAPP_int_real Q R)))) (forall ((P tptp.fun_re1879328022l_real) (Q tptp.fun_nat_bool) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_f2119584768l_real (tptp.hAPP_f59594445l_real tptp.cOMBC_2010481033l_real P) Q) R) (tptp.hAPP_f1406902706l_real (tptp.hAPP_r1409264866l_real P R) Q))) (forall ((P tptp.fun_re1927296998t_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r474017924t_real (tptp.hAPP_f1407095736t_real (tptp.hAPP_f1796904975t_real tptp.cOMBB_599996122l_real P) Q) R) (tptp.hAPP_r474017924t_real P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_re229243589l_real) (Q tptp.fun_int_real) (R tptp.int)) (= (tptp.hAPP_i371647666l_real (tptp.hAPP_f1352333353l_real (tptp.hAPP_f318350629l_real tptp.cOMBB_1946221070al_int P) Q) R) (tptp.hAPP_r1250527377l_real P (tptp.hAPP_int_real Q R)))) (forall ((P tptp.fun_re229243589l_real) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_n546711566l_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f1092742621l_real tptp.cOMBB_1308947378al_nat P) Q) R) (tptp.hAPP_r1250527377l_real P (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_fu1122561126l_real) (Q tptp.fun_re1927296998t_real) (R tptp.real)) (= (tptp.hAPP_real_real (tptp.hAPP_f1122023986l_real (tptp.hAPP_f1786887945l_real tptp.cOMBB_1896127834l_real P) Q) R) (tptp.hAPP_f352196356l_real P (tptp.hAPP_r474017924t_real Q R)))) (forall ((P tptp.fun_na768876520l_real) (Q tptp.real) (R tptp.nat)) (= (tptp.hAPP_n546711566l_real (tptp.hAPP_r195310020l_real (tptp.hAPP_f2126667875l_real tptp.cOMBC_746811033l_real P) Q) R) (tptp.hAPP_r1250527377l_real (tptp.hAPP_n682674106l_real P R) Q))) (forall ((P tptp.fun_na768876520l_real) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_n546711566l_real (tptp.hAPP_f451358433l_real (tptp.hAPP_f335634176l_real tptp.cOMBS_337378985l_real P) Q) R) (tptp.hAPP_r1250527377l_real (tptp.hAPP_n682674106l_real P R) (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_re413263731l_bool) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f1393328161l_bool (tptp.hAPP_f1900646853l_bool tptp.cOMBB_430461877l_real P) Q) R) (tptp.hAPP_r1134773055l_bool P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_Pr608224961l_real) (Q tptp.fun_na1745536976l_real) (R tptp.nat)) (= (tptp.hAPP_nat_real (tptp.hAPP_f73570213t_real (tptp.hAPP_f918606171t_real tptp.cOMBB_64450052al_nat P) Q) R) (tptp.hAPP_P731461727l_real P (tptp.hAPP_n332733730l_real Q R)))) (forall ((P tptp.fun_Pr1127657839l_bool) (Q tptp.fun_re785671361l_real) (R tptp.real)) (= (tptp.hAPP_real_bool (tptp.hAPP_f330985925l_bool (tptp.hAPP_f940061907l_bool tptp.cOMBB_1795223523l_real P) Q) R) (tptp.hAPP_P1333854989l_bool P (tptp.hAPP_r1195171167l_real Q R)))) (forall ((P tptp.fun_re398676606omplex) (Q tptp.fun_nat_real) (R tptp.nat)) (= (tptp.hAPP_n1983812447omplex (tptp.hAPP_f23851874omplex (tptp.hAPP_f406530075omplex tptp.cOMBB_1714920583ex_nat P) Q) R) (tptp.hAPP_r265291036omplex P (tptp.hAPP_nat_real Q R)))) (forall ((P tptp.fun_re229243589l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r1250527377l_real (tptp.hAPP_f556082547l_real (tptp.hAPP_f1960414057l_real tptp.cOMBB_882763271l_real P) Q) R) (tptp.hAPP_r1250527377l_real P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_re1227808089l_real) (Q tptp.real) (R tptp.real)) (= (tptp.hAPP_r1250527377l_real (tptp.hAPP_r337325687l_real (tptp.hAPP_f1644353557l_real tptp.cOMBC_1508019322l_real P) Q) R) (tptp.hAPP_r1250527377l_real (tptp.hAPP_r337325687l_real P R) Q))) (forall ((P tptp.fun_re785671361l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r1195171167l_real (tptp.hAPP_f617735571l_real (tptp.hAPP_f800361423l_real tptp.cOMBB_2107848501l_real P) Q) R) (tptp.hAPP_r1195171167l_real P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_re1550493891l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r1195171167l_real (tptp.hAPP_f617735571l_real (tptp.hAPP_f1730463541l_real tptp.cOMBS_511527878l_real P) Q) R) (tptp.hAPP_r1195171167l_real (tptp.hAPP_r2019696015l_real P R) (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_in1797533524nt_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_int_fun_int_int (tptp.hAPP_f1760145644nt_int (tptp.hAPP_f808647893nt_int tptp.cOMBC_736024425nt_int P) Q) R) (tptp.hAPP_f1356864277nt_int (tptp.hAPP_i744251628nt_int P R) Q))) (forall ((P tptp.fun_int_fun_int_int) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P2110489235nt_int (tptp.hAPP_f1855025978nt_int (tptp.hAPP_f1038672605nt_int tptp.cOMBB_1506897658nt_int P) Q) R) (tptp.hAPP_int_fun_int_int P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_int_fun_int_rat) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P507092031nt_rat (tptp.hAPP_f1547007718nt_rat (tptp.hAPP_f382317021nt_rat tptp.cOMBB_170828966nt_int P) Q) R) (tptp.hAPP_int_fun_int_rat P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_in1111845413nt_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f2054677283nt_int tptp.cOMBB_782625832nt_int P) Q) R) (tptp.hAPP_i1584592887nt_int P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_na257798253at_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n1865633855at_nat (tptp.hAPP_f837737749at_nat (tptp.hAPP_f999082675at_nat tptp.cOMBB_348438404at_nat P) Q) R) (tptp.hAPP_n1865633855at_nat P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_fu205926450t_bool) (Q tptp.fun_int_fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f720654810t_bool (tptp.hAPP_f908327869t_bool tptp.cOMBB_1290694363ol_int P) Q) R) (tptp.hAPP_f429935748t_bool P (tptp.hAPP_int_fun_int_int Q R)))) (forall ((P tptp.fun_in67169585t_bool) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f735247205t_bool tptp.cOMBC_983868720t_bool P) Q) R) (tptp.hAPP_f429935748t_bool (tptp.hAPP_i872162435t_bool P R) Q))) (forall ((P tptp.fun_in865885604nt_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f434654626nt_int tptp.cOMBS_2011279539nt_int P) Q) R) (tptp.hAPP_i1584592887nt_int (tptp.hAPP_i1778081398nt_int P R) (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P252494982t_bool (tptp.hAPP_f291087797t_bool (tptp.hAPP_f214467655t_bool tptp.cOMBB_182850971nt_int P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n215258509l_bool (tptp.hAPP_f66927821l_bool (tptp.hAPP_f2037783381l_bool tptp.cOMBB_1146692694ol_nat P) Q) R) (tptp.hAPP_n215258509l_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_fu554825757t_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_Pr241715507nt_int) (Q tptp.fun_in2003698982nt_int) (R tptp.int)) (= (tptp.hAPP_i1524277240nt_int (tptp.hAPP_f1735705551nt_int (tptp.hAPP_f151095827nt_int tptp.cOMBB_1389251822nt_int P) Q) R) (tptp.hAPP_P1975530577nt_int P (tptp.hAPP_i1524277240nt_int Q R)))) (forall ((P tptp.fun_in719570932t_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool P R) Q))) (forall ((P tptp.fun_in319042876t_bool) (Q tptp.fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_i418383825t_bool (tptp.hAPP_f289318786t_bool (tptp.hAPP_f729588221t_bool tptp.cOMBC_678732631t_bool P) Q) R) (tptp.hAPP_f800510211t_bool (tptp.hAPP_i1796122964t_bool P R) Q))) (forall ((P tptp.fun_in719570932t_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f1878066172t_bool tptp.cOMBS_1720984575t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool P R) (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_in989261322nt_int) (Q tptp.fun_in2003698982nt_int) (R tptp.int)) (= (tptp.hAPP_i1524277240nt_int (tptp.hAPP_f1735705551nt_int (tptp.hAPP_f713949180nt_int tptp.cOMBS_1891347093nt_int P) Q) R) (tptp.hAPP_P1975530577nt_int (tptp.hAPP_i1216375074nt_int P R) (tptp.hAPP_i1524277240nt_int Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_Pr974702441t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P921862901l_bool (tptp.hAPP_f365317245l_bool (tptp.hAPP_f1961001761l_bool tptp.cOMBB_1550063917nt_int P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_P603027463t_bool Q R)))) (forall ((P tptp.fun_fu2100483183t_bool) (Q tptp.fun_int_fun_int_real) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f351634443t_bool (tptp.hAPP_f1576199059t_bool tptp.cOMBB_95956018ol_int P) Q) R) (tptp.hAPP_f429384717t_bool P (tptp.hAPP_i627165055t_real Q R)))) (forall ((P tptp.fun_fu1532576183t_bool) (Q tptp.fun_int_fun_nat_real) (R tptp.int)) (= (tptp.hAPP_i418383825t_bool (tptp.hAPP_f1222178131t_bool (tptp.hAPP_f743790483t_bool tptp.cOMBB_1647910634ol_int P) Q) R) (tptp.hAPP_f737665877t_bool P (tptp.hAPP_i157317923t_real Q R)))) (forall ((P tptp.fun_in1390825880t_real) (Q tptp.fun_int_real) (R tptp.int)) (= (tptp.hAPP_i627165055t_real (tptp.hAPP_f1323932638t_real (tptp.hAPP_f352226557t_real tptp.cOMBC_824100275t_real P) Q) R) (tptp.hAPP_f269654879t_real (tptp.hAPP_i1671359920t_real P R) Q))) (forall ((P tptp.fun_in464278240t_real) (Q tptp.fun_nat_real) (R tptp.int)) (= (tptp.hAPP_i157317923t_real (tptp.hAPP_f1613846310t_real (tptp.hAPP_f1720068861t_real tptp.cOMBC_295337211t_real P) Q) R) (tptp.hAPP_f1888375463t_real (tptp.hAPP_i447943416t_real P R) Q))) (forall ((P tptp.fun_re573205052t_real) (Q tptp.fun_nat_nat) (R tptp.real)) (= (tptp.hAPP_r474017924t_real (tptp.hAPP_f1501741374t_real (tptp.hAPP_f1135648319t_real tptp.cOMBC_1329014627t_real P) Q) R) (tptp.hAPP_f1676298106t_real (tptp.hAPP_r50993370t_real P R) Q))) (forall ((P tptp.fun_fu1569755401t_real) (Q tptp.fun_re1927296998t_real) (R tptp.real)) (= (tptp.hAPP_r474017924t_real (tptp.hAPP_f1993765077t_real (tptp.hAPP_f895854793t_real tptp.cOMBB_1948233853l_real P) Q) R) (tptp.hAPP_f1888375463t_real P (tptp.hAPP_r474017924t_real Q R)))) (forall ((P tptp.fun_bo1998411783l_real) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n682674106l_real (tptp.hAPP_f1129044203l_real (tptp.hAPP_f264196187l_real tptp.cOMBB_1480366270al_nat P) Q) R) (tptp.hAPP_b646336293l_real P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_re1550493891l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r2019696015l_real (tptp.hAPP_f1591894897l_real (tptp.hAPP_f2114902373l_real tptp.cOMBB_237479429l_real P) Q) R) (tptp.hAPP_r2019696015l_real P (tptp.hAPP_real_real Q R)))) (forall ((P tptp.fun_fu215647537t_bool) (Q tptp.fun_int_fun_int_int) (R tptp.int)) (= (tptp.hAPP_i345030060t_bool (tptp.hAPP_f725770969t_bool (tptp.hAPP_f983569339t_bool tptp.cOMBB_550562460ol_int P) Q) R) (tptp.hAPP_f1791153283t_bool P (tptp.hAPP_int_fun_int_int Q R)))) (forall ((P tptp.fun_in2078400507nt_int) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f1574055885nt_int (tptp.hAPP_f960630521nt_int tptp.cOMBC_1805044090nt_int P) Q) R) (tptp.hAPP_f883232462nt_int (tptp.hAPP_i998473677nt_int P R) Q))) (forall ((P tptp.fun_re923322561l_real) (Q tptp.fun_re785671361l_real) (R tptp.real)) (= (tptp.hAPP_r1195171167l_real (tptp.hAPP_f1736103445l_real (tptp.hAPP_f1908301369l_real tptp.cOMBS_902912708l_real P) Q) R) (tptp.hAPP_P1860904029l_real (tptp.hAPP_r938550413l_real P R) (tptp.hAPP_r1195171167l_real Q R)))) (forall ((P tptp.fun_in1211676399nt_int) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1668131738nt_int (tptp.hAPP_f167782601nt_int (tptp.hAPP_f400538607nt_int tptp.cOMBB_866192175nt_int P) Q) R) (tptp.hAPP_i61245889nt_int P (tptp.hAPP_P1175774780nt_int Q R)))) (forall ((P tptp.fun_fu610077323l_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1823918693l_bool (tptp.hAPP_f1344929775l_bool (tptp.hAPP_f1830214065l_bool tptp.cOMBB_793166024ol_int P) Q) R) (tptp.hAPP_f2144054103l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu2104074051l_bool) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_i614188481l_bool (tptp.hAPP_f252743847l_bool (tptp.hAPP_f643658017l_bool tptp.cOMBB_2046938128ol_int P) Q) R) (tptp.hAPP_f1146629647l_bool P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_fu1221449756t_bool) (Q tptp.fun_re386138607t_bool) (R tptp.real)) (= (tptp.hAPP_r481142414t_bool (tptp.hAPP_f1625314454t_bool (tptp.hAPP_f340152631t_bool tptp.cOMBB_1453147152l_real P) Q) R) (tptp.hAPP_f2119767738t_bool P (tptp.hAPP_r632163725t_bool Q R)))) (forall ((P tptp.fun_fu1290768832t_bool) (Q tptp.fun_re2063775123t_bool) (R tptp.real)) (= (tptp.hAPP_r481142414t_bool (tptp.hAPP_f1341793266t_bool (tptp.hAPP_f571820015t_bool tptp.cOMBB_1159313332l_real P) Q) R) (tptp.hAPP_f41603166t_bool P (tptp.hAPP_r373117745t_bool Q R)))) (forall ((P tptp.fun_re1058169246t_bool) (Q tptp.fun_int_bool) (R tptp.real)) (= (tptp.hAPP_r632163725t_bool (tptp.hAPP_f1832844496t_bool (tptp.hAPP_f1990636069t_bool tptp.cOMBC_412863505t_bool P) Q) R) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_r1623423338t_bool P R) Q))) (forall ((P tptp.fun_re507499238t_bool) (Q tptp.fun_nat_bool) (R tptp.real)) (= (tptp.hAPP_r373117745t_bool (tptp.hAPP_f1115375056t_bool (tptp.hAPP_f271976045t_bool tptp.cOMBC_1801450329t_bool P) Q) R) (tptp.hAPP_f289318786t_bool (tptp.hAPP_r653725362t_bool P R) Q))) (forall ((P tptp.fun_fu705349683l_real) (Q tptp.fun_re1927296998t_real) (R tptp.real)) (= (tptp.hAPP_r1409264866l_real (tptp.hAPP_f1523861863l_real (tptp.hAPP_f1067681227l_real tptp.cOMBB_1934313333l_real P) Q) R) (tptp.hAPP_f1509287679l_real P (tptp.hAPP_r474017924t_real Q R)))) (forall ((P tptp.fun_fu1480724285nt_int) (Q tptp.fun_int_fun_int_int) (R tptp.int)) (= (tptp.hAPP_i744251628nt_int (tptp.hAPP_f836602773nt_int (tptp.hAPP_f888249301nt_int tptp.cOMBB_1875755114nt_int P) Q) R) (tptp.hAPP_f747162069nt_int P (tptp.hAPP_int_fun_int_int Q R)))) (forall ((P tptp.fun_fu1843361787nt_int) (Q tptp.fun_int_fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1778081398nt_int (tptp.hAPP_f2004554147nt_int (tptp.hAPP_f1228585167nt_int tptp.cOMBB_1102189010nt_int P) Q) R) (tptp.hAPP_f1574055885nt_int P (tptp.hAPP_int_fun_int_int Q R)))) (forall ((P tptp.fun_fu1280874925l_bool) (Q tptp.fun_re1550493891l_real) (R tptp.real)) (= (tptp.hAPP_r1134773055l_bool (tptp.hAPP_f1884005689l_bool (tptp.hAPP_f172451459l_bool tptp.cOMBB_421479067l_real P) Q) R) (tptp.hAPP_f330985925l_bool P (tptp.hAPP_r2019696015l_real Q R)))) (forall ((P tptp.fun_fu2112913523t_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i872162435t_bool (tptp.hAPP_f1251097615t_bool (tptp.hAPP_f1475822739t_bool tptp.cOMBB_2027861294ol_int P) Q) R) (tptp.hAPP_f1512942609t_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu257678363t_bool) (Q tptp.fun_in351380826t_bool) (R tptp.int)) (= (tptp.hAPP_i345030060t_bool (tptp.hAPP_f791698359t_bool (tptp.hAPP_f847817363t_bool tptp.cOMBB_562416518ol_int P) Q) R) (tptp.hAPP_f428220345t_bool P (tptp.hAPP_i345030060t_bool Q R)))) (forall ((P tptp.fun_in792564872nt_int) (Q tptp.fun_in1111845413nt_int) (R tptp.int)) (= (tptp.hAPP_i1584592887nt_int (tptp.hAPP_f465821005nt_int (tptp.hAPP_f1081447804nt_int tptp.cOMBS_1470252563nt_int P) Q) R) (tptp.hAPP_f1735705551nt_int (tptp.hAPP_i1836591008nt_int P R) (tptp.hAPP_i1584592887nt_int Q R)))) (forall ((P tptp.fun_in941977532nt_int) (Q tptp.product_prod_int_int) (R tptp.int)) (= (tptp.hAPP_i1216375074nt_int (tptp.hAPP_P621635040nt_int (tptp.hAPP_f1582586579nt_int tptp.cOMBC_707974837nt_int P) Q) R) (tptp.hAPP_P1145851913nt_int (tptp.hAPP_i2104874254nt_int P R) Q))) (forall ((P tptp.fun_in941977532nt_int) (Q tptp.fun_in2003698982nt_int) (R tptp.int)) (= (tptp.hAPP_i1216375074nt_int (tptp.hAPP_f1375227553nt_int (tptp.hAPP_f1311564564nt_int tptp.cOMBS_1640193733nt_int P) Q) R) (tptp.hAPP_P1145851913nt_int (tptp.hAPP_i2104874254nt_int P R) (tptp.hAPP_i1524277240nt_int Q R)))) (forall ((P tptp.fun_fu1909738875t_bool) (Q tptp.fun_in531499254l_bool) (R tptp.int)) (= (tptp.hAPP_i1529485324t_bool (tptp.hAPP_f1315737299t_bool (tptp.hAPP_f538565589t_bool tptp.cOMBB_1211207212ol_int P) Q) R) (tptp.hAPP_f627970963t_bool P (tptp.hAPP_i68813070l_bool Q R)))) (forall ((P tptp.fun_fu2120820641l_real) (Q tptp.fun_re229243589l_real) (R tptp.real)) (= (tptp.hAPP_r337325687l_real (tptp.hAPP_f1732848529l_real (tptp.hAPP_f1310479593l_real tptp.cOMBB_2092576745l_real P) Q) R) (tptp.hAPP_f556082547l_real P (tptp.hAPP_r1250527377l_real Q R)))) (forall ((P tptp.fun_re955532029l_real) (Q tptp.fun_real_real) (R tptp.real)) (= (tptp.hAPP_r2019696015l_real (tptp.hAPP_f1591894897l_real (tptp.hAPP_f644105375l_real tptp.cOMBC_467724138l_real P) Q) R) (tptp.hAPP_f617735571l_real (tptp.hAPP_r712953929l_real P R) Q))) (forall ((P tptp.fun_re955532029l_real) (Q tptp.fun_re229243589l_real) (R tptp.real)) (= (tptp.hAPP_r2019696015l_real (tptp.hAPP_f320596107l_real (tptp.hAPP_f850851693l_real tptp.cOMBS_193881978l_real P) Q) R) (tptp.hAPP_f617735571l_real (tptp.hAPP_r712953929l_real P R) (tptp.hAPP_r1250527377l_real Q R)))) (forall ((P tptp.fun_re521366895t_bool) (Q tptp.fun_int_fun_int_real) (R tptp.real)) (= (tptp.hAPP_r632163725t_bool (tptp.hAPP_f956464319t_bool (tptp.hAPP_f422375781t_bool tptp.cOMBC_243356514t_bool P) Q) R) (tptp.hAPP_f351634443t_bool (tptp.hAPP_r1392521531t_bool P R) Q))) (forall ((P tptp.fun_re811280567t_bool) (Q tptp.fun_int_fun_nat_real) (R tptp.real)) (= (tptp.hAPP_r373117745t_bool (tptp.hAPP_f1459420095t_bool (tptp.hAPP_f693283245t_bool tptp.cOMBC_1113900202t_bool P) Q) R) (tptp.hAPP_f1222178131t_bool (tptp.hAPP_r2052264067t_bool P R) Q))) (forall ((P tptp.fun_fu1719442527t_real) (Q tptp.fun_re1927296998t_real) (R tptp.real)) (= (tptp.hAPP_r50993370t_real (tptp.hAPP_f1163894827t_real (tptp.hAPP_f1998755145t_real tptp.cOMBB_421464275l_real P) Q) R) (tptp.hAPP_f1566856189t_real P (tptp.hAPP_r474017924t_real Q R)))) (forall ((P tptp.fun_fu1716408315t_bool) (Q tptp.fun_re413263731l_bool) (R tptp.real)) (= (tptp.hAPP_r847664445t_bool (tptp.hAPP_f1920544743t_bool (tptp.hAPP_f866672739t_bool tptp.cOMBB_1247074793l_real P) Q) R) (tptp.hAPP_f1173902867t_bool P (tptp.hAPP_r1134773055l_bool Q R)))) (forall ((P tptp.fun_fu1635948867t_bool) (Q tptp.fun_re413263731l_bool) (R tptp.real)) (= (tptp.hAPP_r279757445t_bool (tptp.hAPP_f1840085295t_bool (tptp.hAPP_f1083049571t_bool tptp.cOMBB_2050079537l_real P) Q) R) (tptp.hAPP_f605995867t_bool P (tptp.hAPP_r1134773055l_bool Q R)))) (forall ((P tptp.fun_fu2064567419t_real) (Q tptp.fun_in7315610l_real) (R tptp.int)) (= (tptp.hAPP_i1671359920t_real (tptp.hAPP_f74147283t_real (tptp.hAPP_f1169087445t_real tptp.cOMBB_2129825580al_int P) Q) R) (tptp.hAPP_f766218899t_real P (tptp.hAPP_i371647666l_real Q R)))) (forall ((P tptp.fun_fu1138019779t_real) (Q tptp.fun_in7315610l_real) (R tptp.int)) (= (tptp.hAPP_i447943416t_real (tptp.hAPP_f1295083291t_real (tptp.hAPP_f212164053t_real tptp.cOMBB_929094628al_int P) Q) R) (tptp.hAPP_f1690286043t_real P (tptp.hAPP_i371647666l_real Q R)))) (forall ((P tptp.fun_Pr1238001172nt_int) (Q tptp.fun_in2003698982nt_int) (R tptp.int)) (= (tptp.hAPP_i1153444985nt_int (tptp.hAPP_f1148171384nt_int (tptp.hAPP_f334321603nt_int tptp.cOMBB_1484610687nt_int P) Q) R) (tptp.hAPP_P621635040nt_int P (tptp.hAPP_i1524277240nt_int Q R)))) (forall ((P tptp.fun_Pr642042703nt_int) (Q tptp.fun_Pr480351984nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1668131738nt_int (tptp.hAPP_f167782601nt_int (tptp.hAPP_f1769710159nt_int tptp.cOMBC_2037038898nt_int P) Q) R) (tptp.hAPP_f521271395nt_int (tptp.hAPP_P752050971nt_int P R) Q))) (forall ((P tptp.fun_bo1552468991nt_int) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i2104874254nt_int (tptp.hAPP_f251264923nt_int (tptp.hAPP_f279307923nt_int tptp.cOMBB_662120866nt_int P) Q) R) (tptp.hAPP_b40753821nt_int P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_fu587508068t_bool) (Q tptp.fun_in397122125l_bool) (R tptp.int)) (= (tptp.hAPP_i1529485324t_bool (tptp.hAPP_f1545556668t_bool (tptp.hAPP_f85237525t_bool tptp.cOMBB_389152643ol_int P) Q) R) (tptp.hAPP_f727283836t_bool P (tptp.hAPP_i1823918693l_bool Q R)))) (forall ((P tptp.fun_fu1901564496t_bool) (Q tptp.fun_in1678813097l_bool) (R tptp.int)) (= (tptp.hAPP_i1796122964t_bool (tptp.hAPP_f1902329768t_bool (tptp.hAPP_f1182713365t_bool tptp.cOMBB_2087181719ol_int P) Q) R) (tptp.hAPP_f561022312t_bool P (tptp.hAPP_i614188481l_bool Q R)))) (forall ((P tptp.fun_Pr755126262t_bool) (Q tptp.fun_Pr2144253564nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P989584703t_bool (tptp.hAPP_f1187443546t_bool (tptp.hAPP_f11709033t_bool tptp.cOMBS_1676841879t_bool P) Q) R) (tptp.hAPP_f892584630t_bool (tptp.hAPP_P1400155668t_bool P R) (tptp.hAPP_P1668131738nt_int Q R)))) (forall ((P tptp.fun_fu2112443261t_bool) (Q tptp.fun_Pr313471731t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P989584703t_bool (tptp.hAPP_f1781059817t_bool (tptp.hAPP_f326728547t_bool tptp.cOMBB_2086486755nt_int P) Q) R) (tptp.hAPP_f237669397t_bool P (tptp.hAPP_P989584703t_bool Q R)))) (forall ((P tptp.fun_Pr1254492423t_bool) (Q tptp.fun_Pr313471731t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P989584703t_bool (tptp.hAPP_f1781059817t_bool (tptp.hAPP_f125837377t_bool tptp.cOMBS_1610675060t_bool P) Q) R) (tptp.hAPP_f237669397t_bool (tptp.hAPP_P877703507t_bool P R) (tptp.hAPP_P989584703t_bool Q R)))) (forall ((P tptp.fun_fu1230750243l_bool) (Q tptp.fun_re386138607t_bool) (R tptp.real)) (= (tptp.hAPP_r1150855451l_bool (tptp.hAPP_f381769257l_bool (tptp.hAPP_f512004221l_bool tptp.cOMBB_188663909l_real P) Q) R) (tptp.hAPP_f1344929775l_bool P (tptp.hAPP_r632163725t_bool Q R)))) (forall ((P tptp.fun_fu970548443l_bool) (Q tptp.fun_re2063775123t_bool) (R tptp.real)) (= (tptp.hAPP_r285062775l_bool (tptp.hAPP_f834119977l_bool (tptp.hAPP_f848516149l_bool tptp.cOMBB_270132509l_real P) Q) R) (tptp.hAPP_f252743847l_bool P (tptp.hAPP_r373117745t_bool Q R)))) (forall ((P tptp.fun_fu888010351l_real) (Q tptp.fun_re1227808089l_real) (R tptp.real)) (= (tptp.hAPP_r337325687l_real (tptp.hAPP_f1644353557l_real (tptp.hAPP_f1874145443l_real tptp.cOMBB_1768400739l_real P) Q) R) (tptp.hAPP_f203520653l_real P (tptp.hAPP_r337325687l_real Q R)))) (forall ((P tptp.fun_fu1950887583l_real) (Q tptp.fun_re229243589l_real) (R tptp.real)) (= (tptp.hAPP_r579619957l_real (tptp.hAPP_f823702159l_real (tptp.hAPP_f1040184293l_real tptp.cOMBB_557258983l_real P) Q) R) (tptp.hAPP_f1591894897l_real P (tptp.hAPP_r1250527377l_real Q R)))) (forall ((P tptp.fun_re1233422975l_real) (Q tptp.fun_re1550493891l_real) (R tptp.real)) (= (tptp.hAPP_r2019696015l_real (tptp.hAPP_f2072293513l_real (tptp.hAPP_f1763467369l_real tptp.cOMBS_163651580l_real P) Q) R) (tptp.hAPP_f1736103445l_real (tptp.hAPP_r224952523l_real P R) (tptp.hAPP_r2019696015l_real Q R)))) (forall ((P tptp.fun_re1761459671l_real) (Q tptp.fun_re785671361l_real) (R tptp.real)) (= (tptp.hAPP_r938550413l_real (tptp.hAPP_f1293550189l_real (tptp.hAPP_f183342685l_real tptp.cOMBS_794971624l_real P) Q) R) (tptp.hAPP_P1982799375l_real (tptp.hAPP_r931665397l_real P R) (tptp.hAPP_r1195171167l_real Q R)))) (forall ((P tptp.fun_fu2104383023nt_int) (Q tptp.fun_in865885604nt_int) (R tptp.int)) (= (tptp.hAPP_i1778081398nt_int (tptp.hAPP_f2094497995nt_int (tptp.hAPP_f534361363nt_int tptp.cOMBB_1657320178nt_int P) Q) R) (tptp.hAPP_f465821005nt_int P (tptp.hAPP_i1778081398nt_int Q R)))) (forall ((P tptp.fun_fu156492935nt_int) (Q tptp.fun_in1111845413nt_int) (R tptp.int)) (= (tptp.hAPP_i998473677nt_int (tptp.hAPP_f142232355nt_int (tptp.hAPP_f1377453843nt_int tptp.cOMBB_320287386nt_int P) Q) R) (tptp.hAPP_f2002277285nt_int P (tptp.hAPP_i1584592887nt_int Q R)))) (forall ((P tptp.fun_fu1379407829nt_int) (Q tptp.fun_in1111845413nt_int) (R tptp.int)) (= (tptp.hAPP_i1153444985nt_int (tptp.hAPP_f55007289nt_int (tptp.hAPP_f747475781nt_int tptp.cOMBB_222539774nt_int P) Q) R) (tptp.hAPP_f1375227553nt_int P (tptp.hAPP_i1584592887nt_int Q R)))) (forall ((P tptp.fun_fu686082665t_bool) (Q tptp.fun_Pr2144253564nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P2053772734t_bool (tptp.hAPP_f1198736473t_bool (tptp.hAPP_f2042071795t_bool tptp.cOMBB_773384995nt_int P) Q) R) (tptp.hAPP_f291087797t_bool P (tptp.hAPP_P1668131738nt_int Q R)))) (forall ((P tptp.fun_bo1189210245l_real) (Q tptp.fun_real_bool) (R tptp.real)) (= (tptp.hAPP_r931665397l_real (tptp.hAPP_f1607917947l_real (tptp.hAPP_f1076489843l_real tptp.cOMBB_415306361l_real P) Q) R) (tptp.hAPP_b1482221219l_real P (tptp.hAPP_real_bool Q R)))) (forall ((P tptp.fun_fu2013528197nt_int) (Q tptp.fun_Pr2134412615nt_int) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P752050971nt_int (tptp.hAPP_f301246617nt_int (tptp.hAPP_f1151807883nt_int tptp.cOMBB_563965291nt_int P) Q) R) (tptp.hAPP_f11151005nt_int P (tptp.hAPP_P2110489235nt_int Q R)))) (forall ((P tptp.fun_fu201758811t_bool) (Q tptp.fun_Pr189909033l_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P877703507t_bool (tptp.hAPP_f1965248563t_bool (tptp.hAPP_f1273270095t_bool tptp.cOMBB_595786433nt_int P) Q) R) (tptp.hAPP_f513299955t_bool P (tptp.hAPP_P921862901l_bool Q R)))) (forall ((P tptp.fun_fu1269744292t_bool) (Q tptp.fun_re1598305103l_bool) (R tptp.real)) (= (tptp.hAPP_r1962736578t_bool (tptp.hAPP_f1063001928t_bool (tptp.hAPP_f2050994651t_bool tptp.cOMBB_2138578194l_real P) Q) R) (tptp.hAPP_f1545556668t_bool P (tptp.hAPP_r1150855451l_bool Q R)))) (forall ((P tptp.fun_fu553683856t_bool) (Q tptp.fun_re1564496555l_bool) (R tptp.real)) (= (tptp.hAPP_r1562208522t_bool (tptp.hAPP_f2084827628t_bool (tptp.hAPP_f1121609875t_bool tptp.cOMBB_2125215742l_real P) Q) R) (tptp.hAPP_f1902329768t_bool P (tptp.hAPP_r285062775l_bool Q R)))) (forall ((P tptp.fun_fu383125559l_real) (Q tptp.fun_re1550493891l_real) (R tptp.real)) (= (tptp.hAPP_r712953929l_real (tptp.hAPP_f1119546819l_real (tptp.hAPP_f555557763l_real tptp.cOMBB_422423973l_real P) Q) R) (tptp.hAPP_f800361423l_real P (tptp.hAPP_r2019696015l_real Q R)))) (forall ((P tptp.fun_re1414183599l_real) (Q tptp.fun_re1550493891l_real) (R tptp.real)) (= (tptp.hAPP_r1230691443l_real (tptp.hAPP_f324002831l_real (tptp.hAPP_f677014621l_real tptp.cOMBS_107495110l_real P) Q) R) (tptp.hAPP_f1293550189l_real (tptp.hAPP_r1043989325l_real P R) (tptp.hAPP_r2019696015l_real Q R)))) (forall ((P tptp.fun_fu2102390523nt_int) (Q tptp.fun_in989261322nt_int) (R tptp.int)) (= (tptp.hAPP_i1836591008nt_int (tptp.hAPP_f400200275nt_int (tptp.hAPP_f1731308757nt_int tptp.cOMBB_735549356nt_int P) Q) R) (tptp.hAPP_f151095827nt_int P (tptp.hAPP_i1216375074nt_int Q R)))) (forall ((P tptp.fun_fu407119589t_bool) (Q tptp.fun_re1979725814t_bool) (R tptp.real)) (= (tptp.hAPP_r1623423338t_bool (tptp.hAPP_f704188951t_bool (tptp.hAPP_f1456711209t_bool tptp.cOMBB_690122963l_real P) Q) R) (tptp.hAPP_f472159229t_bool P (tptp.hAPP_r1962736578t_bool Q R)))) (forall ((P tptp.fun_fu1083576549t_bool) (Q tptp.fun_re506364222t_bool) (R tptp.real)) (= (tptp.hAPP_r653725362t_bool (tptp.hAPP_f1927674023t_bool (tptp.hAPP_f1261108921t_bool tptp.cOMBB_172850899l_real P) Q) R) (tptp.hAPP_f729588221t_bool P (tptp.hAPP_r1562208522t_bool Q R)))) (forall ((P tptp.fun_fu916648827t_bool) (Q tptp.fun_re1171866993t_bool) (R tptp.real)) (= (tptp.hAPP_r1392521531t_bool (tptp.hAPP_f332806115t_bool (tptp.hAPP_f1177545951t_bool tptp.cOMBB_1459832681l_real P) Q) R) (tptp.hAPP_f1576199059t_bool P (tptp.hAPP_r847664445t_bool Q R)))) (forall ((P tptp.fun_fu1861895035t_bool) (Q tptp.fun_re1091407545t_bool) (R tptp.real)) (= (tptp.hAPP_r2052264067t_bool (tptp.hAPP_f77155443t_bool (tptp.hAPP_f403082607t_bool tptp.cOMBB_984071017l_real P) Q) R) (tptp.hAPP_f743790483t_bool P (tptp.hAPP_r279757445t_bool Q R)))) (forall ((P tptp.fun_fu380422627l_real) (Q tptp.fun_re413263731l_bool) (R tptp.real)) (= (tptp.hAPP_r794344869l_real (tptp.hAPP_f517738447l_real (tptp.hAPP_f1879982819l_real tptp.cOMBB_731595089l_real P) Q) R) (tptp.hAPP_f1607917947l_real P (tptp.hAPP_r1134773055l_bool Q R)))) (forall ((P tptp.fun_fu1698495721l_real) (Q tptp.fun_re665330775l_real) (R tptp.real)) (= (tptp.hAPP_r712953929l_real (tptp.hAPP_f1108539711l_real (tptp.hAPP_f1109256153l_real tptp.cOMBB_44084907l_real P) Q) R) (tptp.hAPP_f1730463541l_real P (tptp.hAPP_r579619957l_real Q R)))) (forall ((P tptp.fun_fu1280007140nt_int) (Q tptp.fun_in2124216673nt_int) (R tptp.int)) (= (tptp.hAPP_i1836591008nt_int (tptp.hAPP_f617310012nt_int (tptp.hAPP_f197974549nt_int tptp.cOMBB_638531587nt_int P) Q) R) (tptp.hAPP_f713949180nt_int P (tptp.hAPP_i1153444985nt_int Q R)))) (forall ((P tptp.fun_fu581830891t_bool) (Q tptp.fun_Pr820506994t_bool) (R tptp.product_prod_int_int)) (= (tptp.hAPP_P1400155668t_bool (tptp.hAPP_f223623489t_bool (tptp.hAPP_f1815301987t_bool tptp.cOMBB_650041899nt_int P) Q) R) (tptp.hAPP_f1325804733t_bool P (tptp.hAPP_P2053772734t_bool Q R)))) (forall ((P tptp.fun_fu2079587053l_real) (Q tptp.fun_re10870101l_real) (R tptp.real)) (= (tptp.hAPP_r224952523l_real (tptp.hAPP_f1663701695l_real (tptp.hAPP_f774948957l_real tptp.cOMBB_3698607l_real P) Q) R) (tptp.hAPP_f1908301369l_real P (tptp.hAPP_r1230691443l_real Q R)))) (forall ((P tptp.fun_fu209750539l_real) (Q tptp.fun_re69907033l_real) (R tptp.real)) (= (tptp.hAPP_r1043989325l_real (tptp.hAPP_f1161935955l_real (tptp.hAPP_f328572565l_real tptp.cOMBB_520243667l_real P) Q) R) (tptp.hAPP_f183342685l_real P (tptp.hAPP_r794344869l_real Q R)))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.35/8.59 )
% 8.35/8.59 % SZS output end Proof for NUM924_4
% 8.35/8.59 % cvc5---1.0.5 exiting
% 8.35/8.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------